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701 | paragraph-let-u-1-and-u-2-be-two-urns-such-that-u-1-contains-3-white-and-2-red-balls-and-u-2-contains-only-1-white-ball-a-fair-coin-is-tossed-if-head--1 | paragraph-let-u-1-and-u-2-be-two-urns-such-that-u-1-contains-3-white-and-2-red-balls-and-u-2-contains-only-1-white-ball-a-fair-coin-is-tossed-if-head-1-84793 | <div class="question"><strong>Paragraph:</strong><br/>Let $U_1$ and $U_2$ be two urns such that $U_1$ contains 3 white and 2 red balls and $U_2$ contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from $U_1$ and put into $U_2$. However, if tail appears then 2 balls are drawn at random from $U_1$ and put into $U_2$. Now, 1 ball is drawn at random from $U_2$.<strong>Question:</strong><br/>Given that the drawn ball from $U_2$ is white, the probability that head appeared on the coin is</div> | ['Mathematics', 'Probability', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{17}{23}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{11}{23}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{15}{23}$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{12}{23}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{12}{23}$</span> </div> | <div class="solution">$P$ (head appeared/white from $V_2$ )<br/>$$<br/>\begin{aligned}<br/>& =P(H) \cdot \frac{\left\{\frac{{ }^3 C_1}{{ }^5 C_1} \times \frac{{ }^2 C_1}{{ }^2 C_1}+\frac{{ }^2 C_1}{{ }^5 C_1} \times \frac{{ }^1 C_1}{{ }^2 C_1}\right\}}{\frac{23}{30}} \\<br/>& =\frac{1}{2} \frac{\left\{\frac{3}{5} \times 1+\frac{2}{5} \times \frac{1}{2}\right\}}{\frac{23}{30}}=\frac{12}{23} \\<br/>&<br/>\end{aligned}<br/>$$</div> | MarksBatch2_P2.db |
702 | paragraph-let-u-1-and-u-2-be-two-urns-such-that-u-1-contains-3-white-and-2-red-balls-and-u-2-contains-only-1-white-ball-a-fair-coin-is-tossed-if-head- | paragraph-let-u-1-and-u-2-be-two-urns-such-that-u-1-contains-3-white-and-2-red-balls-and-u-2-contains-only-1-white-ball-a-fair-coin-is-tossed-if-head-30433 | <div class="question"><strong>Paragraph:</strong><br/>Let $U_1$ and $U_2$ be two urns such that $U_1$ contains 3 white and 2 red balls and $U_2$ contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from $U_1$ and put into $U_2$. However, if tail appears then 2 balls are drawn at random from $U_1$ and put into $U_2$. Now, 1 ball is drawn at random from $U_2$.<strong>Question:</strong><br/>The probability of the drawn ball from $U_2$ being white is</div> | ['Mathematics', 'Probability', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{13}{30}$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{23}{30}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{19}{30}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{11}{30}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{23}{30}$<br/></span> </div> | <div class="solution">Now, probability of the drawn ball from $\mathrm{V}_2$ being white is<br/>$$<br/>\Rightarrow P \text { (white/ } V_2 \text { ) }<br/>$$<br/><br/>$$<br/>\begin{aligned}<br/>& \left.\Rightarrow P \text { (white/ } V_2\right) \\<br/>& =P(H) \cdot\left\{\frac{{ }^3 C_1}{{ }^5 C_1} \times \frac{{ }^2 C_1}{{ }^2 C_1}+\frac{{ }^2 C_1}{{ }^5 C_1} \times \frac{{ }^1 C_1}{{ }^2 C_1}\right\} \\<br/>& +P(T)\left\{\frac{{ }^3 C_2}{{ }^5 C_2} \times \frac{{ }^3 C_2}{{ }^3 C_2}+\frac{{ }^2 C_2}{{ }^5 C_2} \times \frac{{ }^1 C_1}{{ }^3 C_2}\right. \\<br/>& \left.+\frac{{ }^3 C_1 \cdot{ }^2 C_1}{{ }^5 C_2} \times \frac{{ }^2 C_1}{{ }^3 C_2}\right\} \\<br/>& \text { Now, } P\left(\text { white } / V_2\right)=\frac{1}{2}\left\{\frac{3}{5} \times 1+\frac{2}{5} \times \frac{1}{2}\right\} \\<br/>& +\frac{1}{2}\left\{\frac{3}{10} \times 1+\frac{1}{10} \times \frac{1}{3}+\frac{6}{10} \times \frac{2}{3}\right\}=\frac{23}{30} \\<br/>&<br/>\end{aligned}<br/>$$</div> | MarksBatch2_P2.db |
703 | paragraph-let-v-r-denotes-the-sum-of-the-first-r-terms-of-an-arithmetic-progression-a-p-whose-first-term-is-r-and-the-common-difference-is-2-r-1-let-t-1 | paragraph-let-v-r-denotes-the-sum-of-the-first-r-terms-of-an-arithmetic-progression-a-p-whose-first-term-is-r-and-the-common-difference-is-2-r-1-let-t-1-53467 | <div class="question"><strong>Paragraph:</strong><br/>Let $V_r$ denotes the sum of the first $r$ terms of an arithmetic progression $(A P)$ whose first term is $r$ and the common difference is $(2 r-1)$. Let $T_r=V_{r+1}-V_r-2$ and $Q_r=T_{r+1}-T_r$ for $r=1,2, \ldots$<strong>Question:</strong><br/>$T_r$ is always</div> | ['Mathematics', 'Sequences and Series', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>an odd number<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>an even number<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>a prime number<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>a composite number</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>a composite number</span> </div> | <div class="solution">$V_{r+1}-V_r=(r+1)^3-r^3-\frac{1}{2}\left[(r+1)^2-r^2\right]+\frac{1}{2}(1)$<br/>$$<br/>\begin{aligned}<br/>& =3 r^2+2 r+1 \\<br/>\therefore \quad T_r & =3 r^2+2 r-1=(r+1)(3 r-1)<br/>\end{aligned}<br/>$$<br/>which is a composite number.</div> | MarksBatch2_P2.db |
704 | paragraph-let-v-r-denotes-the-sum-of-the-first-r-terms-of-an-arithmetic-progression-a-p-whose-first-term-is-r-and-the-common-difference-is-2-r-1-let-t-2 | paragraph-let-v-r-denotes-the-sum-of-the-first-r-terms-of-an-arithmetic-progression-a-p-whose-first-term-is-r-and-the-common-difference-is-2-r-1-let-t-2-11660 | <div class="question"><strong>Paragraph:</strong><br/>Let $V_r$ denotes the sum of the first $r$ terms of an arithmetic progression $(A P)$ whose first term is $r$ and the common difference is $(2 r-1)$. Let $T_r=V_{r+1}-V_r-2$ and $Q_r=T_{r+1}-T_r$ for $r=1,2, \ldots$<strong>Question:</strong><br/>Which one of the following is a correct statement?</div> | ['Mathematics', 'Sequences and Series', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$Q_1, Q_2, Q_3, \ldots$ are in AP with common difference 5<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$Q_1, Q_2, Q_3, \ldots$ are in AP with common difference 6<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$Q_1, Q_2, Q_3, \ldots$ are in AP with common difference 11<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$Q_1=Q_2=Q_3=\ldots$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$Q_1, Q_2, Q_3, \ldots$ are in AP with common difference 6<br/></span> </div> | <div class="solution">Since, $T_r=3 r^2+2 r-1$<br/>$$<br/>\begin{array}{rlrl} <br/>& \therefore & T_{r+1} & =3(r+1)^2+2(r+1)-1 \\<br/>& \therefore & Q_r & =T_{r+1}-T_r=3[2 r+1]+2[1] \\<br/>\Rightarrow & Q_r & =6 r+5 \\<br/>\Rightarrow & Q_{r+1} & =6(r+1)+5<br/>\end{array}<br/>$$<br/>Common difference $=Q_{r+1}-Q_r=6$</div> | MarksBatch2_P2.db |
705 | paragraph-let-v-r-denotes-the-sum-of-the-first-r-terms-of-an-arithmetic-progression-a-p-whose-first-term-is-r-and-the-common-difference-is-2-r-1-let-t | paragraph-let-v-r-denotes-the-sum-of-the-first-r-terms-of-an-arithmetic-progression-a-p-whose-first-term-is-r-and-the-common-difference-is-2-r-1-let-t-91576 | <div class="question"><strong>Paragraph:</strong><br/>Let $V_r$ denotes the sum of the first $r$ terms of an arithmetic progression $(A P)$ whose first term is $r$ and the common difference is $(2 r-1)$. Let $T_r=V_{r+1}-V_r-2$ and $Q_r=T_{r+1}-T_r$ for $r=1,2, \ldots$<strong>Question:</strong><br/>The sum $V_1+V_2+\ldots+V_n$ is</div> | ['Mathematics', 'Sequences and Series', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{1}{12} n(n+1)\left(3 n^2-n+1\right)$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{1}{12} n(n+1)\left(3 n^2+n+2\right)$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{1}{2} n\left(2 n^2-n+1\right)$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{1}{3}\left(2 n^3-2 n+3\right)$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{1}{12} n(n+1)\left(3 n^2+n+2\right)$<br/></span> </div> | <div class="solution">$$<br/>\begin{aligned}<br/>& V_r=\frac{r}{2}[2 r+(r-1)(2 r-1)]=\frac{1}{2}\left(2 r^3-r^2+r\right) \\<br/>& \therefore \quad \Sigma V_r=\frac{1}{2}\left[2 \Sigma r^3-\Sigma r^2+\Sigma r\right] \\<br/>& =\frac{1}{2}\left[2\left(\frac{n(n+1)}{2}\right)^2-\frac{n(n+1)(2 n+1)}{6}+\frac{n(n+1)}{2}\right] \\<br/>& =\frac{1}{12} n(n+1)\left(3 n^2+n+2\right) \text {. } \\<br/>&<br/>\end{aligned}<br/>$$</div> | MarksBatch2_P2.db |
706 | paragraph-modern-trains-are-based-on-maglev-technology-in-which-trains-are-magnetically-leviated-which-runs-its-eds-maglev-system-there-are-coils-on-b-1 | paragraph-modern-trains-are-based-on-maglev-technology-in-which-trains-are-magnetically-leviated-which-runs-its-eds-maglev-system-there-are-coils-on-b-1-79693 | <div class="question"><strong>Paragraph:</strong><br/>Modern trains are based on Maglev technology in which trains are magnetically leviated, which runs its EDS Maglev system.<br/>There are coils on both sides of wheels. Due to motion of train, current induces in the coil of track which levitate it. This is in accordance with Lenz's law. If trains lower down then due to Lenz's law a repulsive force increases due to which train gets uplifted and if it goes much high then there is a net downward force disc to gravity. The advantage of Maglev train is that there is no friction between the train and the track, thereby reducing power consumption and enabling the train to attain very high speeds.<br/>Disadvantage of Maglev train is that as it slows down the electromagnetic forces decreases and it becomes difficult to keep it leviated and as it moves forward according to Lenz law, there is an electromagnetic drag force.<strong>Question:</strong><br/>What is the disadvantage of this system?</div> | ['Physics', 'Electromagnetic Induction', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Train experiences upward force according to Lenz's law<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Friction force create a drag on the train<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Retardation<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>By Lenz's law train experience a drag</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>By Lenz's law train experience a drag</span> </div> | <div class="solution">No solution is required.</div> | MarksBatch2_P2.db |
707 | paragraph-modern-trains-are-based-on-maglev-technology-in-which-trains-are-magnetically-leviated-which-runs-its-eds-maglev-system-there-are-coils-on-b-2 | paragraph-modern-trains-are-based-on-maglev-technology-in-which-trains-are-magnetically-leviated-which-runs-its-eds-maglev-system-there-are-coils-on-b-2-92409 | <div class="question"><strong>Paragraph:</strong><br/>Modern trains are based on Maglev technology in which trains are magnetically leviated, which runs its EDS Maglev system.<br/>There are coils on both sides of wheels. Due to motion of train, current induces in the coil of track which levitate it. This is in accordance with Lenz's law. If trains lower down then due to Lenz's law a repulsive force increases due to which train gets uplifted and if it goes much high then there is a net downward force disc to gravity. The advantage of Maglev train is that there is no friction between the train and the track, thereby reducing power consumption and enabling the train to attain very high speeds.<br/>Disadvantage of Maglev train is that as it slows down the electromagnetic forces decreases and it becomes difficult to keep it leviated and as it moves forward according to Lenz law, there is an electromagnetic drag force.<strong>Question:</strong><br/>What is the advantage of this system?</div> | ['Physics', 'Electromagnetic Induction', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>No friction hence no power consumption<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>No electric power is used<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Gravitation force is zero<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Electrostatic force draws the train</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>No friction hence no power consumption<br/></span> </div> | <div class="solution">No solution is required.</div> | MarksBatch2_P2.db |
708 | paragraph-modern-trains-are-based-on-maglev-technology-in-which-trains-are-magnetically-leviated-which-runs-its-eds-maglev-system-there-are-coils-on-b | paragraph-modern-trains-are-based-on-maglev-technology-in-which-trains-are-magnetically-leviated-which-runs-its-eds-maglev-system-there-are-coils-on-b-44957 | <div class="question"><strong>Paragraph:</strong><br/>Modern trains are based on Maglev technology in which trains are magnetically leviated, which runs its EDS Maglev system.<br/>There are coils on both sides of wheels. Due to motion of train, current induces in the coil of track which levitate it. This is in accordance with Lenz's law. If trains lower down then due to Lenz's law a repulsive force increases due to which train gets uplifted and if it goes much high then there is a net downward force disc to gravity. The advantage of Maglev train is that there is no friction between the train and the track, thereby reducing power consumption and enabling the train to attain very high speeds.<br/>Disadvantage of Maglev train is that as it slows down the electromagnetic forces decreases and it becomes difficult to keep it leviated and as it moves forward according to Lenz law, there is an electromagnetic drag force.<strong>Question:</strong><br/>Which force causes the train to elevate up?</div> | ['Physics', 'Electromagnetic Induction', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Electrostatic force<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Time varying electric field<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>Magnetic force<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Induced electric field</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Magnetic force<br/></span> </div> | <div class="solution">No solution is required.</div> | MarksBatch2_P2.db |
709 | paragraph-p-14-16-paragraph-for-questions-nos-14-to-16-a-fixed-thermally-conducting-cylinder-has-a-radius-r-and-height-l-0-the-cylinder-is-open-at-its-1 | paragraph-p-14-16-paragraph-for-questions-nos-14-to-16-a-fixed-thermally-conducting-cylinder-has-a-radius-r-and-height-l-0-the-cylinder-is-open-at-its-1-66827 | <div class="question"><strong>Paragraph:</strong><br/>$P_{14-16}$ : Paragraph for Questions Nos. 14 to 16 A fixed thermally conducting cylinder has a radius $R$ and height $L_0$. The cylinder is open at its bottom and has a small hole at its top. A piston of mass $M$ is held at a distance $L$ from the top surface as shown in the figure. The atmospheric pressure is $p_0$.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/4uUwDqNsXDagR3met7Ief3ZxT31gi025zIfyrEsgmZk.original.fullsize.png"/><br/><strong>Question:</strong><br/>While the piston is at a distance $2 L$ from the top, the hole at the top is sealed. The piston is then released, to a position where it can stay in equilibrium. In this condition, the distance of the piston from the top is</div> | ['Physics', 'Thermodynamics', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\left(\frac{2 p_0 \pi R^2}{\pi R^2 p_0+M g}\right)(2 L)$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\left(\frac{p_0 \pi R^2-M g}{\pi R^2 p_0}\right)(2 L)$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\left(\frac{p_0 \pi R^2+M g}{\pi R^2 p_0}\right)(2 L)$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$\left(\frac{p_0 \pi R^2}{\pi R^2 p_0-M g}\right)(2 L)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\left(\frac{p_0 \pi R^2}{\pi R^2 p_0-M g}\right)(2 L)$</span> </div> | <div class="solution">Let $p$ be the pressure in equilibrium<br/>Then,<br/>$$<br/>\begin{aligned}<br/>& \therefore \quad p=p_0-\frac{M g}{A}=p_0-\frac{M g}{\pi R^2} \\<br/>& \text { Applying } \quad p_1 V_1=p_2 V_2 \\<br/>& p_0(2 A L)=(p)\left(A L^{\prime}\right) \\<br/>& L^{\prime}=\frac{2 p_0 L}{p}=\left(\frac{p_0}{p_0-\frac{M g}{\pi R^2}}\right) \text { (2L) } \\<br/>& =\left(\frac{p_0 \pi R^2}{\pi R^2 p_0-M g}\right)(2 L) \\<br/>&<br/>\end{aligned}<br/>$$<br/>$\therefore$ Option (d) is correct.</div> | MarksBatch2_P2.db |
710 | paragraph-p-14-16-paragraph-for-questions-nos-14-to-16-a-fixed-thermally-conducting-cylinder-has-a-radius-r-and-height-l-0-the-cylinder-is-open-at-its-2 | paragraph-p-14-16-paragraph-for-questions-nos-14-to-16-a-fixed-thermally-conducting-cylinder-has-a-radius-r-and-height-l-0-the-cylinder-is-open-at-its-2-65104 | <div class="question"><strong>Paragraph:</strong><br/>$P_{14-16}$ : Paragraph for Questions Nos. 14 to 16 A fixed thermally conducting cylinder has a radius $R$ and height $L_0$. The cylinder is open at its bottom and has a small hole at its top. A piston of mass $M$ is held at a distance $L$ from the top surface as shown in the figure. The atmospheric pressure is $p_0$.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/4uUwDqNsXDagR3met7Ief3ZxT31gi025zIfyrEsgmZk.original.fullsize.png"/><br/><strong>Question:</strong><br/>The piston is now pulled out slowly and held at a distance $2 L$ from the top. The pressure in the cylinder between its top and the piston will then be</div> | ['Physics', 'Thermodynamics', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$p_0$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{p_0}{2}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{p_0}{2}+\frac{M g}{\pi R^2}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{p_0}{2}-\frac{M g}{\pi R^2}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$p_0$<br/></span> </div> | <div class="solution">Since it is open from top, pressure will be $p_0$. $\therefore$ Option (a) is correct.</div> | MarksBatch2_P2.db |
711 | paragraph-p-14-16-paragraph-for-questions-nos-14-to-16-a-fixed-thermally-conducting-cylinder-has-a-radius-r-and-height-l-0-the-cylinder-is-open-at-its-3 | paragraph-p-14-16-paragraph-for-questions-nos-14-to-16-a-fixed-thermally-conducting-cylinder-has-a-radius-r-and-height-l-0-the-cylinder-is-open-at-its-3-93752 | <div class="question"><strong>Paragraph:</strong><br/>$P_{14-16}$ : Paragraph for Questions Nos. 14 to 16 A fixed thermally conducting cylinder has a radius $R$ and height $L_0$. The cylinder is open at its bottom and has a small hole at its top. A piston of mass $M$ is held at a distance $L$ from the top surface as shown in the figure. The atmospheric pressure is $p_0$.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/4uUwDqNsXDagR3met7Ief3ZxT31gi025zIfyrEsgmZk.original.fullsize.png"/><br/><strong>Question:</strong><br/>The piston is taken completely out of the cylinder. The hole at the top is sealed. A water tank is brought below the cylinder and put in a position so that the water surface in the tank is at the same level as the top of the cylinder as shown in the figure. The density of the water is $\rho$. In equilibrium, the height $H$ of the water column in the cylinder satisfies<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/u6L69mqUQ4YOY0tduE71-0P8gZFsbvh9f1xHSgJEuBU.original.fullsize.png"/><br/></div> | ['Physics', 'Thermodynamics', 'JEE Main'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\rho g\left(L_0-H\right)^2+p_0\left(L_0-H\right)+L_0 p_0=0$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\rho g\left(L_0-H\right)^2-p_0\left(L_0-H\right)-L_0 p_0=0$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\rho g\left(L_0-H\right)^2+p_0\left(L_0-H\right)-L_0 p_0=0$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\rho g\left(L_0-H\right)^2-p_0\left(L_0-H\right)+L_0 p_0=0$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\rho g\left(L_0-H\right)^2+p_0\left(L_0-H\right)-L_0 p_0=0$<br/></span> </div> | <div class="solution">$$<br/>\begin{gathered}<br/>p_1=p_2 \\<br/>p_0+\rho g\left(L_0-H\right)=p<br/>\end{gathered}<br/>$$<br/>Now, applying $p_1 V_1=p_2 V_2$<br/>for the air inside the cylinder, we have<br/>$$<br/>p_0\left(L_0\right)=p\left(L_0-H\right)<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/7oQA8KNhtTUSHFHvt9EQSIUJcVfMbFX9a2U9386X-5c.original.fullsize.png"/><br/><br/>$\therefore \quad p=\frac{p_0 L_0}{L_0-H}$<br/>Substituting in Eq. (i), we have<br/>$$<br/>p_0+\rho g\left(L_0-H\right)=\frac{p_0 L_0}{L_0-H}<br/>$$<br/>or $\rho g\left(L_0-H\right)^2+p_0\left(L_0-H\right)-p_0 L_0=0$<br/>$\therefore$ Option (c) is correct.</div> | MarksBatch2_P2.db |
712 | paragraph-p-14-16-paragraph-for-questions-nos-14-to-16-a-fixed-thermally-conducting-cylinder-has-a-radius-r-and-height-l-0-the-cylinder-is-open-at-its-4 | paragraph-p-14-16-paragraph-for-questions-nos-14-to-16-a-fixed-thermally-conducting-cylinder-has-a-radius-r-and-height-l-0-the-cylinder-is-open-at-its-4-18500 | <div class="question"><strong>Paragraph:</strong><br/>$P_{14-16}$ : Paragraph for Questions Nos. 14 to 16 A fixed thermally conducting cylinder has a radius $R$ and height $L_0$. The cylinder is open at its bottom and has a small hole at its top. A piston of mass $M$ is held at a distance $L$ from the top surface as shown in the figure. The atmospheric pressure is $p_0$.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/4uUwDqNsXDagR3met7Ief3ZxT31gi025zIfyrEsgmZk.original.fullsize.png"/><br/><strong>Question:</strong><br/>While the piston is at a distance $2 L$ from the top, the hole at the top is sealed. The piston is then released, to a position where it can stay in equilibrium. In this condition, the distance of the piston from the top is</div> | ['Physics', 'Thermodynamics', 'JEE Main'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\left(\frac{2 p_0 \pi R^2}{\pi R^2 p_0+M g}\right)(2 L)$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\left(\frac{p_0 \pi R^2-M g}{\pi R^2 p_0}\right)(2 L)$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\left(\frac{p_0 \pi R^2+M g}{\pi R^2 p_0}\right)(2 L)$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$\left(\frac{p_0 \pi R^2}{\pi R^2 p_0-M g}\right)(2 L)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\left(\frac{p_0 \pi R^2}{\pi R^2 p_0-M g}\right)(2 L)$</span> </div> | <div class="solution">Let $p$ be the pressure in equilibrium<br/>Then,<br/>$$<br/>\begin{aligned}<br/>& \therefore \quad p=p_0-\frac{M g}{A}=p_0-\frac{M g}{\pi R^2} \\<br/>& \text { Applying } \quad p_1 V_1=p_2 V_2 \\<br/>& p_0(2 A L)=(p)\left(A L^{\prime}\right) \\<br/>& L^{\prime}=\frac{2 p_0 L}{p}=\left(\frac{p_0}{p_0-\frac{M g}{\pi R^2}}\right) \text { (2L) } \\<br/>& =\left(\frac{p_0 \pi R^2}{\pi R^2 p_0-M g}\right)(2 L) \\<br/>&<br/>\end{aligned}<br/>$$<br/>$\therefore$ Option (d) is correct.</div> | MarksBatch2_P2.db |
713 | paragraph-p-14-16-paragraph-for-questions-nos-14-to-16-a-fixed-thermally-conducting-cylinder-has-a-radius-r-and-height-l-0-the-cylinder-is-open-at-its | paragraph-p-14-16-paragraph-for-questions-nos-14-to-16-a-fixed-thermally-conducting-cylinder-has-a-radius-r-and-height-l-0-the-cylinder-is-open-at-its-80281 | <div class="question"><strong>Paragraph:</strong><br/>$P_{14-16}$ : Paragraph for Questions Nos. 14 to 16 A fixed thermally conducting cylinder has a radius $R$ and height $L_0$. The cylinder is open at its bottom and has a small hole at its top. A piston of mass $M$ is held at a distance $L$ from the top surface as shown in the figure. The atmospheric pressure is $p_0$.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/4uUwDqNsXDagR3met7Ief3ZxT31gi025zIfyrEsgmZk.original.fullsize.png"/><br/><strong>Question:</strong><br/>The piston is taken completely out of the cylinder. The hole at the top is sealed. A water tank is brought below the cylinder and put in a position so that the water surface in the tank is at the same level as the top of the cylinder as shown in the figure. The density of the water is $\rho$. In equilibrium, the height $H$ of the water column in the cylinder satisfies<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/u6L69mqUQ4YOY0tduE71-0P8gZFsbvh9f1xHSgJEuBU.original.fullsize.png"/><br/></div> | ['Physics', 'Thermodynamics', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\rho g\left(L_0-H\right)^2+p_0\left(L_0-H\right)+L_0 p_0=0$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\rho g\left(L_0-H\right)^2-p_0\left(L_0-H\right)-L_0 p_0=0$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\rho g\left(L_0-H\right)^2+p_0\left(L_0-H\right)-L_0 p_0=0$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\rho g\left(L_0-H\right)^2-p_0\left(L_0-H\right)+L_0 p_0=0$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\rho g\left(L_0-H\right)^2+p_0\left(L_0-H\right)-L_0 p_0=0$<br/></span> </div> | <div class="solution">$$<br/>\begin{gathered}<br/>p_1=p_2 \\<br/>p_0+\rho g\left(L_0-H\right)=p<br/>\end{gathered}<br/>$$<br/>Now, applying $p_1 V_1=p_2 V_2$<br/>for the air inside the cylinder, we have<br/>$$<br/>p_0\left(L_0\right)=p\left(L_0-H\right)<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/7oQA8KNhtTUSHFHvt9EQSIUJcVfMbFX9a2U9386X-5c.original.fullsize.png"/><br/><br/>$\therefore \quad p=\frac{p_0 L_0}{L_0-H}$<br/>Substituting in Eq. (i), we have<br/>$$<br/>p_0+\rho g\left(L_0-H\right)=\frac{p_0 L_0}{L_0-H}<br/>$$<br/>or $\rho g\left(L_0-H\right)^2+p_0\left(L_0-H\right)-p_0 L_0=0$<br/>$\therefore$ Option (c) is correct.</div> | MarksBatch2_P2.db |
714 | paragraph-p-17-19-paragraph-for-questions-nos-17-to-19-two-discs-a-and-b-are-mounted-coaxially-on-a-vertical-axle-the-discs-have-moments-of-inertia-i--1 | paragraph-p-17-19-paragraph-for-questions-nos-17-to-19-two-discs-a-and-b-are-mounted-coaxially-on-a-vertical-axle-the-discs-have-moments-of-inertia-i-1-42236 | <div class="question"><strong>Paragraph:</strong><br/>$\mathbf{P}_{17 \text { - } 19}$ : Paragraph for Questions Nos. 17 to 19 Two discs $A$ and $B$ are mounted coaxially on a vertical axle. The discs have moments of inertia I and 2I, respectively about the common axis. Disc $A$ is imparted an initial angular velocity $2 \omega$ using the entire potential energy of a spring compressed by a distance $x_1$. Disc $B$ is imparted an angular velocity $\omega$ by a spring having the same spring constant and compressed by a distance $x_2$. Both the discs rotate in the clockwise direction.<strong>Question:</strong><br/>The loss of kinetic energy during the above process is</div> | ['Physics', 'Rotational Motion', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{I \omega^2}{2}$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{i \omega^2}{3}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{I \omega^2}{4}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{I \omega^2}{6}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{i \omega^2}{3}$<br/></span> </div> | <div class="solution">Loss of kinetic energy $=K_i-K_f$<br/>$$<br/>\begin{aligned}<br/>& =\left\{\frac{1}{2} I(2 \omega)^2+\frac{1}{2}(2 I)(\omega)^2\right\}-\frac{1}{2}(3 I)\left(\frac{4}{3} \omega\right)^2 \\<br/>& =\frac{1}{3} I \omega^2<br/>\end{aligned}<br/>$$<br/>$\therefore$ Option (b) is correct.</div> | MarksBatch2_P2.db |
715 | paragraph-p-17-19-paragraph-for-questions-nos-17-to-19-two-discs-a-and-b-are-mounted-coaxially-on-a-vertical-axle-the-discs-have-moments-of-inertia-i--2 | paragraph-p-17-19-paragraph-for-questions-nos-17-to-19-two-discs-a-and-b-are-mounted-coaxially-on-a-vertical-axle-the-discs-have-moments-of-inertia-i-2-66363 | <div class="question"><strong>Paragraph:</strong><br/>$\mathbf{P}_{17 \text { - } 19}$ : Paragraph for Questions Nos. 17 to 19 Two discs $A$ and $B$ are mounted coaxially on a vertical axle. The discs have moments of inertia I and 2I, respectively about the common axis. Disc $A$ is imparted an initial angular velocity $2 \omega$ using the entire potential energy of a spring compressed by a distance $x_1$. Disc $B$ is imparted an angular velocity $\omega$ by a spring having the same spring constant and compressed by a distance $x_2$. Both the discs rotate in the clockwise direction.<strong>Question:</strong><br/>The ratio $\frac{x_1}{x_2}$ is</div> | ['Physics', 'Rotational Motion', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>2<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{1}{2}$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\sqrt{2}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{1}{\sqrt{2}}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\sqrt{2}$<br/></span> </div> | <div class="solution">$$<br/>\begin{aligned}<br/>\frac{1}{2} I(2 \omega)^2 & =\frac{1}{2} k x_1^2 \\<br/>\frac{1}{2}(2 I)(\omega)^2 & =\frac{1}{2} k x_2^2<br/>\end{aligned}<br/>$$<br/>From Eqs. (i) and (ii), we have<br/>$$<br/>\frac{x_1}{x_2}=\sqrt{2}<br/>$$<br/>$\therefore$ Option (c) is correct.</div> | MarksBatch2_P2.db |
716 | paragraph-p-17-19-paragraph-for-questions-nos-17-to-19-two-discs-a-and-b-are-mounted-coaxially-on-a-vertical-axle-the-discs-have-moments-of-inertia-i- | paragraph-p-17-19-paragraph-for-questions-nos-17-to-19-two-discs-a-and-b-are-mounted-coaxially-on-a-vertical-axle-the-discs-have-moments-of-inertia-i-74108 | <div class="question"><strong>Paragraph:</strong><br/>$\mathbf{P}_{17 \text { - } 19}$ : Paragraph for Questions Nos. 17 to 19 Two discs $A$ and $B$ are mounted coaxially on a vertical axle. The discs have moments of inertia I and 2I, respectively about the common axis. Disc $A$ is imparted an initial angular velocity $2 \omega$ using the entire potential energy of a spring compressed by a distance $x_1$. Disc $B$ is imparted an angular velocity $\omega$ by a spring having the same spring constant and compressed by a distance $x_2$. Both the discs rotate in the clockwise direction.<strong>Question:</strong><br/>When disc $B$ is brought in contact with disc $A$, they acquire a common angular velocity in time $t$. The average frictional torque on one disc by the other during this period is</div> | ['Physics', 'Rotational Motion', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{2 I \omega}{3 t}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{9 I \omega}{2 t}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{91 \omega}{4 t}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{3 I \omega}{2 t}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{2 I \omega}{3 t}$<br/></span> </div> | <div class="solution">Let $\omega^{\prime}$ be the common velocity. Then from conservation of angular momentum, we have<br/>$$<br/>\begin{aligned}<br/>(i+2 I) \omega^{\prime} & =I(2 \omega)+2 I(\omega) \\<br/>\omega^{\prime} & =\frac{4}{3} \omega<br/>\end{aligned}<br/>$$<br/>From the equation,<br/>Angular impulse = change in angular momentum for any of the disc, we have<br/>$$<br/>\begin{aligned}<br/>\tau t & =I(2 \omega)-I\left(\frac{4}{3} \omega\right)=\frac{2 I \omega}{3} \\<br/>\tau & =\frac{2 I \omega}{3 t}<br/>\end{aligned}<br/>$$<br/>$\therefore$ Option (a) is correct.</div> | MarksBatch2_P2.db |
717 | paragraph-paminon-ndimethylaniline-is-added-to-a-strongly-acidic-solution-of-x-the-resulting-solution-is-treated-with-a-few-drops-of-aqueous-solution--1 | paragraph-paminon-ndimethylaniline-is-added-to-a-strongly-acidic-solution-of-x-the-resulting-solution-is-treated-with-a-few-drops-of-aqueous-solution-1-48501 | <div class="question"><strong>Paragraph:</strong><br/>p-amino-N, N-dimethylaniline is added to a strongly acidic solution of $X$. The resulting solution is treated with a few drops of aqueous solution of $Y$ to yield blue colouration due to the formation of methylene blue. Treatment of the aqueous solution of $Y$ with the reagent potassium hexacyanoferrate(II) leads to the formation of an intense blue precipitate. The precipitate dissolves an excess addition of the reagent. Similarly, treatment of the solution of $Y$ with the solution of potassium hexacyanoferrate(III) leads to a brown colouration due to the formation of $Z$.<strong>Question:</strong><br/>The compound $Y$, is</div> | ['Chemistry', 'Amines', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{MgCl}_2$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{FeCl}_2$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{FeCl}_3$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{ZnCl}_2$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\mathrm{FeCl}_3$<br/></span> </div> | <div class="solution">No Solution Available</div> | MarksBatch2_P2.db |
718 | paragraph-paminon-ndimethylaniline-is-added-to-a-strongly-acidic-solution-of-x-the-resulting-solution-is-treated-with-a-few-drops-of-aqueous-solution--2 | paragraph-paminon-ndimethylaniline-is-added-to-a-strongly-acidic-solution-of-x-the-resulting-solution-is-treated-with-a-few-drops-of-aqueous-solution-2-35554 | <div class="question"><strong>Paragraph:</strong><br/>p-amino-N, N-dimethylaniline is added to a strongly acidic solution of $X$. The resulting solution is treated with a few drops of aqueous solution of $Y$ to yield blue colouration due to the formation of methylene blue. Treatment of the aqueous solution of $Y$ with the reagent potassium hexacyanoferrate(II) leads to the formation of an intense blue precipitate. The precipitate dissolves an excess addition of the reagent. Similarly, treatment of the solution of $Y$ with the solution of potassium hexacyanoferrate(III) leads to a brown colouration due to the formation of $Z$.<strong>Question:</strong><br/>The compound $X$, is</div> | ['Chemistry', 'Amines', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{NaNO}_3$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{NaCl}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{Na}_2 \mathrm{SO}_4$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{Na}_2 \mathrm{~S}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\mathrm{Na}_2 \mathrm{~S}$</span> </div> | <div class="solution">No Solution Available</div> | MarksBatch2_P2.db |
719 | paragraph-paminon-ndimethylaniline-is-added-to-a-strongly-acidic-solution-of-x-the-resulting-solution-is-treated-with-a-few-drops-of-aqueous-solution--3 | paragraph-paminon-ndimethylaniline-is-added-to-a-strongly-acidic-solution-of-x-the-resulting-solution-is-treated-with-a-few-drops-of-aqueous-solution-3-95892 | <div class="question"><strong>Paragraph:</strong><br/>p-amino-N, N-dimethylaniline is added to a strongly acidic solution of $X$. The resulting solution is treated with a few drops of aqueous solution of $Y$ to yield blue colouration due to the formation of methylene blue. Treatment of the aqueous solution of $Y$ with the reagent potassium hexacyanoferrate(II) leads to the formation of an intense blue precipitate. The precipitate dissolves an excess addition of the reagent. Similarly, treatment of the solution of $Y$ with the solution of potassium hexacyanoferrate(III) leads to a brown colouration due to the formation of $Z$.<strong>Question:</strong><br/>The compound $Z$, is</div> | ['Chemistry', 'Amines', 'JEE Main'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{Mg}_2\left[\mathrm{Fe}(\mathrm{CN})_6\right]$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{Fe}\left[\mathrm{Fe}(\mathrm{CN})_6\right]$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{Fe}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]_3$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{K}_2 \mathrm{Zn}_3\left[\mathrm{Fe}(\mathrm{CN})_6\right]_2$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\mathrm{Fe}\left[\mathrm{Fe}(\mathrm{CN})_6\right]$<br/></span> </div> | <div class="solution">$p$-amino- $\mathrm{N}$, N-dimethylaniline reacts with sulphide ion $\left(\mathrm{S}^{2-}\right)$ in presence of $\mathrm{Fe}^{3+}$ ion to form blue coloured solution of methylene blue :<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/NZw4_QD8GSLGGMqrQZSpuv_AIQiOAXhksXIRa3V8Zsc.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
720 | paragraph-paminon-ndimethylaniline-is-added-to-a-strongly-acidic-solution-of-x-the-resulting-solution-is-treated-with-a-few-drops-of-aqueous-solution- | paragraph-paminon-ndimethylaniline-is-added-to-a-strongly-acidic-solution-of-x-the-resulting-solution-is-treated-with-a-few-drops-of-aqueous-solution-71735 | <div class="question"><strong>Paragraph:</strong><br/>p-amino-N, N-dimethylaniline is added to a strongly acidic solution of $X$. The resulting solution is treated with a few drops of aqueous solution of $Y$ to yield blue colouration due to the formation of methylene blue. Treatment of the aqueous solution of $Y$ with the reagent potassium hexacyanoferrate(II) leads to the formation of an intense blue precipitate. The precipitate dissolves an excess addition of the reagent. Similarly, treatment of the solution of $Y$ with the solution of potassium hexacyanoferrate(III) leads to a brown colouration due to the formation of $Z$.<strong>Question:</strong><br/>The compound $Z$, is</div> | ['Chemistry', 'Amines', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{Mg}_2\left[\mathrm{Fe}(\mathrm{CN})_6\right]$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{Fe}\left[\mathrm{Fe}(\mathrm{CN})_6\right]$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{Fe}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]_3$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{K}_2 \mathrm{Zn}_3\left[\mathrm{Fe}(\mathrm{CN})_6\right]_2$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\mathrm{Fe}\left[\mathrm{Fe}(\mathrm{CN})_6\right]$<br/></span> </div> | <div class="solution">$p$-amino- $\mathrm{N}$, N-dimethylaniline reacts with sulphide ion $\left(\mathrm{S}^{2-}\right)$ in presence of $\mathrm{Fe}^{3+}$ ion to form blue coloured solution of methylene blue :<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/NZw4_QD8GSLGGMqrQZSpuv_AIQiOAXhksXIRa3V8Zsc.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
721 | paragraph-phase-space-diagrams-are-useful-tools-in-analyzing-all-kinds-of-dynamical-problems-they-are-especially-useful-in-studying-the-changes-in-mot-1 | paragraph-phase-space-diagrams-are-useful-tools-in-analyzing-all-kinds-of-dynamical-problems-they-are-especially-useful-in-studying-the-changes-in-mot-1-33367 | <div class="question"><strong>Paragraph:</strong><br/>Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the changes in motion as initial position and momentum are changed. Here we consider some simple dynamical systems in one-dimension. For such systems, phase space is a plane in which position is plotted along horizontal axis and momentum is plotted along vertical axis. The phase space diagram is $x(t) v s p(t)$ curve in this plane. The arrow on the<br/>curve indicates the time flow. For example, the phase space diagram for a particle moving with constant velocity is a straight line as shown in the figure. We use the sign convention in which position or momentum upwards (or to right) is positive and downwards (or to left) is negative.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/XUS9yb1oVClHFXXo1R2Su7FpnIAGiALCHaAWRaCkIxo.original.fullsize.png"/><br/><strong>Question:</strong><br/>The phase space diagram for a ball thrown vertically up from ground is</div> | ['Physics', 'Motion In One Dimension', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/iI0Kxu2WnV4NkRO9yY3V7z6whEGe6AvixYB2vbO-hD8.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/DOfzCHyzibJNVnxn0HafBRyOgKJe6uLD1830_7T21VI.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/O1yAEKHii2lM3o6tCdd5OomqXot_8p1UEg0sH2_8QuA.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/h80ZqR_DLfd3NCpT3nZGdB647TUEv-dWcd5q3qSkx1k.original.fullsize.png"/><br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/h80ZqR_DLfd3NCpT3nZGdB647TUEv-dWcd5q3qSkx1k.original.fullsize.png"/><br/></span> </div> | <div class="solution">Momentum is first positive but decreasing. Displacement (or say position). is initially zero.<br/>It will first increase. At highest point, momentum is zero and displacement is maximum. After that momentum is downwards (negative) and increasing but displacement is decreasing. Only (d) option satisfies these conditions.<br/>Analysis of Question<br/>(i) Question is simple.<br/>(ii) Since all the graphs given in question are parabolic type, we need not to check the mathematical part of the question.</div> | MarksBatch2_P2.db |
722 | paragraph-phase-space-diagrams-are-useful-tools-in-analyzing-all-kinds-of-dynamical-problems-they-are-especially-useful-in-studying-the-changes-in-mot-2 | paragraph-phase-space-diagrams-are-useful-tools-in-analyzing-all-kinds-of-dynamical-problems-they-are-especially-useful-in-studying-the-changes-in-mot-2-16700 | <div class="question"><strong>Paragraph:</strong><br/>Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the changes in motion as initial position and momentum are changed. Here we consider some simple dynamical systems in one-dimension. For such systems, phase space is a plane in which position is plotted along horizontal axis and momentum is plotted along vertical axis. The phase space diagram is $x(t) v s p(t)$ curve in this plane. The arrow on the<br/>curve indicates the time flow. For example, the phase space diagram for a particle moving with constant velocity is a straight line as shown in the figure. We use the sign convention in which position or momentum upwards (or to right) is positive and downwards (or to left) is negative.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/XUS9yb1oVClHFXXo1R2Su7FpnIAGiALCHaAWRaCkIxo.original.fullsize.png"/><br/><strong>Question:</strong><br/>Consider the spring-mass system, with the mass submerged in water, as shown in the figure. The phase space diagram for one cycle of this system is<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/53Ml_Imd8sWvUpsp5WkZHm9H8FJc-nQ-pugQxJm97ok.original.fullsize.png"/><br/></div> | ['Physics', 'Oscillations', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ScSj_MoI5Vsl88sva79sD-8B0WCxi3NsGEbXVJF6aSk.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/sxdjVykv7RJmtA94RFRt8YswTOqvFAE_UO9XD0rEZDg.original.fullsize.png"/><br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/1uohWBNlMxXa1WJwPMqyZzuNWvjiQRx4QgWq1YHS0qo.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/1RyOg2mbKfACyAAqKJwVlK_79ZsVcgCMrL5fa53TRSY.original.fullsize.png"/><br/></span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/sxdjVykv7RJmtA94RFRt8YswTOqvFAE_UO9XD0rEZDg.original.fullsize.png"/><br/></span> </div> | <div class="solution">In all the given four figures, at mean position the position coordinate is zero. At the same time mass is starting from the extreme position in all fours cases. In figures (c) and (d), extreme position is more than the initial extreme position. But due to viscosity opposite should be the case. Hence, the answer should be either option (a) or option (b).<br/>Correct answer is (b), because mass starts from positive extreme position (from uppermost position). Then, it will move downwards or momentum should be negative.<br/>Analysis of Question<br/>Question is simple but (a) and (b) options are confusing.</div> | MarksBatch2_P2.db |
723 | paragraph-phase-space-diagrams-are-useful-tools-in-analyzing-all-kinds-of-dynamical-problems-they-are-especially-useful-in-studying-the-changes-in-mot | paragraph-phase-space-diagrams-are-useful-tools-in-analyzing-all-kinds-of-dynamical-problems-they-are-especially-useful-in-studying-the-changes-in-mot-15129 | <div class="question"><strong>Paragraph:</strong><br/>Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the changes in motion as initial position and momentum are changed. Here we consider some simple dynamical systems in one-dimension. For such systems, phase space is a plane in which position is plotted along horizontal axis and momentum is plotted along vertical axis. The phase space diagram is $x(t) v s p(t)$ curve in this plane. The arrow on the<br/>curve indicates the time flow. For example, the phase space diagram for a particle moving with constant velocity is a straight line as shown in the figure. We use the sign convention in which position or momentum upwards (or to right) is positive and downwards (or to left) is negative.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/XUS9yb1oVClHFXXo1R2Su7FpnIAGiALCHaAWRaCkIxo.original.fullsize.png"/><br/><strong>Question:</strong><br/>The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and $E_1$ and $E_2$ are the total mechanical energies respectively. Then,<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/9d_CDTvM8AdXVdLzqYCWwC2MYHrM0IHhSY55oxNI0tQ.original.fullsize.png"/><br/></div> | ['Physics', 'Oscillations', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$E_1=\sqrt{2} E_2$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$E_1=2 E_2$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$E_1=2 E_2$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$E_1=16 E_2$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$E_1=2 E_2$<br/></span> </div> | <div class="solution">$E=\frac{1}{2} m \omega^2 A^2$<br/>or<br/>$$<br/>\begin{aligned}<br/>E & \propto A^2 \\<br/>\frac{E_2}{E_1} & =\left(\frac{A_2}{A_1}\right)^2 \\<br/>& =\left(\frac{a}{2 a}\right)^2<br/>\end{aligned}<br/>$$<br/>or $\quad E_1=4 E_2$<br/>$\therefore$ Correct option is (c).<br/>Analysis of Question<br/>(i) Question is simple.<br/>(ii) Since, oscillator is same, $\omega_1=\omega_2$</div> | MarksBatch2_P2.db |
724 | paragraph-properties-such-as-boiling-point-freezing-point-and-vapour-pressure-of-a-pure-solvent-change-when-solute-molecules-are-added-to-get-homogene-1 | paragraph-properties-such-as-boiling-point-freezing-point-and-vapour-pressure-of-a-pure-solvent-change-when-solute-molecules-are-added-to-get-homogene-1-12719 | <div class="question"><strong>Paragraph:</strong><br/>Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added to get homogeneous solution. These are called colligative properties. Applications of colligative properties are very useful in day-to-day life. One of its examples is the use of ethylene glycol and water mixture as anti-freezing liquid in the radiator automobiles.<br/>A solution $M$ is prepared by mixing ethanol and water. The mole fraction of ethanol in the mixtrue is $0.9$<br/>Given Freezing point depression constant of water $\left(k^{\text {water }}\right)=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$<br/>Freezing point depression constant of ethanol $\left(k_f^{\text {ethanol }}\right)=2.0 \mathrm{Kkg} \mathrm{mol}^{-1}$<br/>Boiling point elevation constant of water $\left(k_b^{\text {water }}\right)=0.52 \mathrm{Kkg} \mathrm{mol}^{-1}$<br/>Boiling point elevation constant of ethanol $\left(k_b^{\text {ethanol }}\right)=1.2 \mathrm{Kkg} \mathrm{mol}^{-1}$<br/>Standard freezing point of water $=273 \mathrm{~K}$<br/>Standard freezing point of ethanol $=155.7 \mathrm{~K}$<br/>Standard boiling point of water $=373 \mathrm{~K}$<br/>Standard boiling point of ethanol $=351.5 \mathrm{~K}$<br/>Vapour pressure of pure water $=328 \mathrm{~mm}$ of $\mathrm{Hg}$<br/>Vapour pressure of pure ethanol $=40 \mathrm{~mm}$ of $\mathrm{Hg}$<br/>Molecular weight of water $=18 \mathrm{~g} \mathrm{~mol}^{-1}$<br/>Molecular weight of ethanol $=46 \mathrm{~g} \mathrm{~mol}^{-1}$<br/>In answering the following questions, consider the solutions to be ideal dilute solutions and solutes to be non-volatile and non-dissociative.<strong>Question:</strong><br/>The freezing point of the solution $M$ is</div> | ['Chemistry', 'Solutions', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$268.7 \mathrm{~K}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$268.5 \mathrm{~K}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$234.2 \mathrm{~K}$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$150.9 \mathrm{~K}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$150.9 \mathrm{~K}$</span> </div> | <div class="solution">Solution $M$ is mixture of ethanol and water.<br/>Mole fraction of ethanol is $0.9 \Rightarrow$ Solvent is $\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}$<br/>Mole fraction of water is $0.1 \Rightarrow \mathrm{H}_2 \mathrm{O}$ is solute<br/>Molality of $\mathrm{H}_2 \mathrm{O}=\frac{n_2}{n_1 M_1}=\frac{0.1}{0.9 \times 46} \times 1000=2.415$<br/>$$<br/>\Delta T_f=k_f \cdot m=2 \times 2.415=4.83<br/>$$<br/>or Freezing point of solution $=155.7-4.83=150.87 \mathrm{~K}$</div> | MarksBatch2_P2.db |
725 | paragraph-properties-such-as-boiling-point-freezing-point-and-vapour-pressure-of-a-pure-solvent-change-when-solute-molecules-are-added-to-get-homogene-2 | paragraph-properties-such-as-boiling-point-freezing-point-and-vapour-pressure-of-a-pure-solvent-change-when-solute-molecules-are-added-to-get-homogene-2-44306 | <div class="question"><strong>Paragraph:</strong><br/>Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added to get homogeneous solution. These are called colligative properties. Applications of colligative properties are very useful in day-to-day life. One of its examples is the use of ethylene glycol and water mixture as anti-freezing liquid in the radiator automobiles.<br/>A solution $M$ is prepared by mixing ethanol and water. The mole fraction of ethanol in the mixtrue is $0.9$<br/>Given Freezing point depression constant of water $\left(k^{\text {water }}\right)=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$<br/>Freezing point depression constant of ethanol $\left(k_f^{\text {ethanol }}\right)=2.0 \mathrm{Kkg} \mathrm{mol}^{-1}$<br/>Boiling point elevation constant of water $\left(k_b^{\text {water }}\right)=0.52 \mathrm{Kkg} \mathrm{mol}^{-1}$<br/>Boiling point elevation constant of ethanol $\left(k_b^{\text {ethanol }}\right)=1.2 \mathrm{Kkg} \mathrm{mol}^{-1}$<br/>Standard freezing point of water $=273 \mathrm{~K}$<br/>Standard freezing point of ethanol $=155.7 \mathrm{~K}$<br/>Standard boiling point of water $=373 \mathrm{~K}$<br/>Standard boiling point of ethanol $=351.5 \mathrm{~K}$<br/>Vapour pressure of pure water $=328 \mathrm{~mm}$ of $\mathrm{Hg}$<br/>Vapour pressure of pure ethanol $=40 \mathrm{~mm}$ of $\mathrm{Hg}$<br/>Molecular weight of water $=18 \mathrm{~g} \mathrm{~mol}^{-1}$<br/>Molecular weight of ethanol $=46 \mathrm{~g} \mathrm{~mol}^{-1}$<br/>In answering the following questions, consider the solutions to be ideal dilute solutions and solutes to be non-volatile and non-dissociative.<strong>Question:</strong><br/>Water is added to the solution $M$ such that the mole fraction of water in the solution becomes $0.9$ The boiling point of this solutions is</div> | ['Chemistry', 'Solutions', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$380.4 \mathrm{~K}$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$376.2 \mathrm{~K}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$375.5 \mathrm{~K}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$354.7 \mathrm{~K}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$376.2 \mathrm{~K}$<br/></span> </div> | <div class="solution">$\chi_{\mathrm{H}_2 \mathrm{O}}=0.9$ (solvent) $\chi_{\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}}=0.1$ (solute)<br/>$$<br/>\Delta T_b=k_b \times m=0.52 \times \frac{1.0 \times 1000}{0.9 \times 18}=3.2 \mathrm{~K}<br/>$$<br/>Boiling point, $T_b=373+3.2=376.2 \mathrm{~K}$</div> | MarksBatch2_P2.db |
726 | paragraph-properties-such-as-boiling-point-freezing-point-and-vapour-pressure-of-a-pure-solvent-change-when-solute-molecules-are-added-to-get-homogene | paragraph-properties-such-as-boiling-point-freezing-point-and-vapour-pressure-of-a-pure-solvent-change-when-solute-molecules-are-added-to-get-homogene-13012 | <div class="question"><strong>Paragraph:</strong><br/>Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added to get homogeneous solution. These are called colligative properties. Applications of colligative properties are very useful in day-to-day life. One of its examples is the use of ethylene glycol and water mixture as anti-freezing liquid in the radiator automobiles.<br/>A solution $M$ is prepared by mixing ethanol and water. The mole fraction of ethanol in the mixtrue is $0.9$<br/>Given Freezing point depression constant of water $\left(k^{\text {water }}\right)=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$<br/>Freezing point depression constant of ethanol $\left(k_f^{\text {ethanol }}\right)=2.0 \mathrm{Kkg} \mathrm{mol}^{-1}$<br/>Boiling point elevation constant of water $\left(k_b^{\text {water }}\right)=0.52 \mathrm{Kkg} \mathrm{mol}^{-1}$<br/>Boiling point elevation constant of ethanol $\left(k_b^{\text {ethanol }}\right)=1.2 \mathrm{Kkg} \mathrm{mol}^{-1}$<br/>Standard freezing point of water $=273 \mathrm{~K}$<br/>Standard freezing point of ethanol $=155.7 \mathrm{~K}$<br/>Standard boiling point of water $=373 \mathrm{~K}$<br/>Standard boiling point of ethanol $=351.5 \mathrm{~K}$<br/>Vapour pressure of pure water $=328 \mathrm{~mm}$ of $\mathrm{Hg}$<br/>Vapour pressure of pure ethanol $=40 \mathrm{~mm}$ of $\mathrm{Hg}$<br/>Molecular weight of water $=18 \mathrm{~g} \mathrm{~mol}^{-1}$<br/>Molecular weight of ethanol $=46 \mathrm{~g} \mathrm{~mol}^{-1}$<br/>In answering the following questions, consider the solutions to be ideal dilute solutions and solutes to be non-volatile and non-dissociative.<strong>Question:</strong><br/>The vapour pressure of the solution $M$ is</div> | ['Chemistry', 'Solutions', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$39.3 \mathrm{~mm} \mathrm{Hg}$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$36.0 \mathrm{~mm} \mathrm{Hg}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$29.5 \mathrm{~mm} \mathrm{Hg}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$28.8 \mathrm{~mm} \mathrm{Hg}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$36.0 \mathrm{~mm} \mathrm{Hg}$<br/></span> </div> | <div class="solution">Total vapour pressure, $p=p_A^{\circ} \chi_A$<br/>$$<br/>p=40 \times 0.9=36 \mathrm{~mm} \text { of } \mathrm{Hg}<br/>$$<br/>In the paragraph, it has been directed to take solute as non-volatile, thus $\mathrm{H}_2 \mathrm{O}$ do not contribute in the total vapour pressure.</div> | MarksBatch2_P2.db |
727 | paragraph-rconh-2-is-converted-into-rnh-2-by-means-of-hofmann-bromamide-degradation-im-g-src-h-ttp-s-c-d-n-q-u-es-t-i-o-n-p-oo-l-g-e-t-ma-r-k-s-a-pp-p-1 | paragraph-rconh-2-is-converted-into-rnh-2-by-means-of-hofmann-bromamide-degradation-im-g-src-h-ttp-s-c-d-n-q-u-es-t-i-o-n-p-oo-l-g-e-t-ma-r-k-s-a-pp-p-1-16630 | <div class="question"><strong>Paragraph:</strong><br/>$$<br/>\mathrm{RCONH}_2 \text { is converted into } \mathrm{RNH}_2 \text { by means of Hofmann bromamide degradation. }<br/>$$<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/kUvdLVZCCRDn5vZcz3oaK6cUZX7TS8jt4MnQjqIiZ1U.original.fullsize.png"/><br/><br/>In this reaction, $R \mathrm{CONHBr}$ is formed from which this reaction has derived its name. Electron donating group at phenyl activates the reaction. Hofmann degradation reaction is an intramolecular reaction.<strong>Question:</strong><br/>What are the constituent amines formed when the mixture of (i) and (ii) undergoes Hofmann bromamide degradation?<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/xUil9dp4OC-2i_JpT3k-Ay0mZhy3yc_KoxGe_XOoTO8.original.fullsize.png"/><br/></div> | ['Chemistry', 'Amines', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/9oEoYy5QRFL2XT7ezsHdF5ARJDl0lEN4arnP9U2UCIA.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/raLseyC7J4jpeBdxdouJO8i1ntB1EL77OiciIHqKM7A.original.fullsize.png"/><br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/XWvYR9onQwF915KtQ4fuwkz0nopYgxeL-dAMd-1wlrc.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/-f4PlSCzDHo1546w2x7iTwaj1AXy5kUxT2pDP5IEnWc.original.fullsize.png"/><br/></span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/raLseyC7J4jpeBdxdouJO8i1ntB1EL77OiciIHqKM7A.original.fullsize.png"/><br/></span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Oe_E6km97d_rshVwsJnXpBtvih6O1N6XCJ0vI3uSC5I.original.fullsize.png"/><br/><br/>$$<br/>\text { Since the overall reaction is intermolecular, hence there will be no effect on product formation. }<br/>$$</div> | MarksBatch2_P2.db |
728 | paragraph-rconh-2-is-converted-into-rnh-2-by-means-of-hofmann-bromamide-degradation-im-g-src-h-ttp-s-c-d-n-q-u-es-t-i-o-n-p-oo-l-g-e-t-ma-r-k-s-a-pp-p-2 | paragraph-rconh-2-is-converted-into-rnh-2-by-means-of-hofmann-bromamide-degradation-im-g-src-h-ttp-s-c-d-n-q-u-es-t-i-o-n-p-oo-l-g-e-t-ma-r-k-s-a-pp-p-2-55796 | <div class="question"><strong>Paragraph:</strong><br/>$$<br/>\mathrm{RCONH}_2 \text { is converted into } \mathrm{RNH}_2 \text { by means of Hofmann bromamide degradation. }<br/>$$<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/kUvdLVZCCRDn5vZcz3oaK6cUZX7TS8jt4MnQjqIiZ1U.original.fullsize.png"/><br/><br/>In this reaction, $R \mathrm{CONHBr}$ is formed from which this reaction has derived its name. Electron donating group at phenyl activates the reaction. Hofmann degradation reaction is an intramolecular reaction.<strong>Question:</strong><br/>Which is the rate determining step in Hofmann bromamide degradation?</div> | ['Chemistry', 'Amines', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Formation of (i)<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Formation of (ii)<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Formation of (iii)<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>Formation of (iv)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Formation of (iv)</span> </div> | <div class="solution">The rate determining step is probably elimination of $\mathrm{Br}^{-}$to form isocyanate because it is slower step of given conversion.</div> | MarksBatch2_P2.db |
729 | paragraph-rconh-2-is-converted-into-rnh-2-by-means-of-hofmann-bromamide-degradation-im-g-src-h-ttp-s-c-d-n-q-u-es-t-i-o-n-p-oo-l-g-e-t-ma-r-k-s-a-pp-p-3 | paragraph-rconh-2-is-converted-into-rnh-2-by-means-of-hofmann-bromamide-degradation-im-g-src-h-ttp-s-c-d-n-q-u-es-t-i-o-n-p-oo-l-g-e-t-ma-r-k-s-a-pp-p-3-22182 | <div class="question"><strong>Paragraph:</strong><br/>$$<br/>\mathrm{RCONH}_2 \text { is converted into } \mathrm{RNH}_2 \text { by means of Hofmann bromamide degradation. }<br/>$$<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/kUvdLVZCCRDn5vZcz3oaK6cUZX7TS8jt4MnQjqIiZ1U.original.fullsize.png"/><br/><br/>In this reaction, $R \mathrm{CONHBr}$ is formed from which this reaction has derived its name. Electron donating group at phenyl activates the reaction. Hofmann degradation reaction is an intramolecular reaction.<strong>Question:</strong><br/>What are the constituent amines formed when the mixture of (i) and (ii) undergoes Hofmann bromamide degradation?<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/xUil9dp4OC-2i_JpT3k-Ay0mZhy3yc_KoxGe_XOoTO8.original.fullsize.png"/><br/></div> | ['Chemistry', 'Amines', 'JEE Main'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/9oEoYy5QRFL2XT7ezsHdF5ARJDl0lEN4arnP9U2UCIA.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/raLseyC7J4jpeBdxdouJO8i1ntB1EL77OiciIHqKM7A.original.fullsize.png"/><br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/XWvYR9onQwF915KtQ4fuwkz0nopYgxeL-dAMd-1wlrc.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/-f4PlSCzDHo1546w2x7iTwaj1AXy5kUxT2pDP5IEnWc.original.fullsize.png"/><br/></span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/raLseyC7J4jpeBdxdouJO8i1ntB1EL77OiciIHqKM7A.original.fullsize.png"/><br/></span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Oe_E6km97d_rshVwsJnXpBtvih6O1N6XCJ0vI3uSC5I.original.fullsize.png"/><br/><br/>$$<br/>\text { Since the overall reaction is intermolecular, hence there will be no effect on product formation. }<br/>$$</div> | MarksBatch2_P2.db |
730 | paragraph-rconh-2-is-converted-into-rnh-2-by-means-of-hofmann-bromamide-degradation-im-g-src-h-ttp-s-c-d-n-q-u-es-t-i-o-n-p-oo-l-g-e-t-ma-r-k-s-a-pp-p | paragraph-rconh-2-is-converted-into-rnh-2-by-means-of-hofmann-bromamide-degradation-im-g-src-h-ttp-s-c-d-n-q-u-es-t-i-o-n-p-oo-l-g-e-t-ma-r-k-s-a-pp-p-22328 | <div class="question"><strong>Paragraph:</strong><br/>$$<br/>\mathrm{RCONH}_2 \text { is converted into } \mathrm{RNH}_2 \text { by means of Hofmann bromamide degradation. }<br/>$$<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/kUvdLVZCCRDn5vZcz3oaK6cUZX7TS8jt4MnQjqIiZ1U.original.fullsize.png"/><br/><br/>In this reaction, $R \mathrm{CONHBr}$ is formed from which this reaction has derived its name. Electron donating group at phenyl activates the reaction. Hofmann degradation reaction is an intramolecular reaction.<strong>Question:</strong><br/>How can the conversion of (i) to (ii) be brought about?</div> | ['Chemistry', 'Amines', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{KBr}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{KBr}+\mathrm{CH}_3 \mathrm{ONa}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{KBr}+\mathrm{KOH}$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{Br}_2+\mathrm{KOH}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\mathrm{Br}_2+\mathrm{KOH}$</span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/zDNTmjvVgpklMj_DLaJFK3heYy8d8GQqzVcSCiltWI4.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
731 | paragraph-read-the-following-passage-and-answer-the-questions-for-every-function-f-x-which-is-twice-differentiable-these-will-be-good-approximation-of-1 | paragraph-read-the-following-passage-and-answer-the-questions-for-every-function-f-x-which-is-twice-differentiable-these-will-be-good-approximation-of-1-74881 | <div class="question"><strong>Paragraph:</strong><br/>Read the following passage and answer the questions.<br/>For every function $f(x)$ which is twice differentiable, these will be good approximation of $\int_a^b f(x) d x \cong\left(\frac{b-a}{2}\right)\{f(a)+f(b)\}$. Now, if we take $c=\frac{a+b}{2}$, then using above again, we get $\int_a^b f(x) d x=\int_a^c f(x) d x+\int_c^b f(x) d x \cong \frac{b-a}{4}\{f(a)+f(b)+2 f(c)\}$ and so on.<br/>We get approximation for value of $\int_a^b f(x) d x$.<strong>Question:</strong><br/>If $f^{\prime \prime}(x) < 0, \forall x \in(a, b), c(c, f(c))$ is point of maxima where $c \in(a, b)$, then $f^{\prime}(c)$ is</div> | ['Mathematics', 'Application of Derivatives', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{f(b)-f(a)}{b-a}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$3\left(\frac{f(b)-f(a)}{b-a}\right)$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$2\left(\frac{f(b)-f(a)}{b-a}\right)$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>0</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>0</span> </div> | <div class="solution">$f^{\prime}(c)=0$.</div> | MarksBatch2_P2.db |
732 | paragraph-read-the-following-passage-and-answer-the-questions-for-every-function-f-x-which-is-twice-differentiable-these-will-be-good-approximation-of-2 | paragraph-read-the-following-passage-and-answer-the-questions-for-every-function-f-x-which-is-twice-differentiable-these-will-be-good-approximation-of-2-20665 | <div class="question"><strong>Paragraph:</strong><br/>Read the following passage and answer the questions.<br/>For every function $f(x)$ which is twice differentiable, these will be good approximation of $\int_a^b f(x) d x \cong\left(\frac{b-a}{2}\right)\{f(a)+f(b)\}$. Now, if we take $c=\frac{a+b}{2}$, then using above again, we get $\int_a^b f(x) d x=\int_a^c f(x) d x+\int_c^b f(x) d x \cong \frac{b-a}{4}\{f(a)+f(b)+2 f(c)\}$ and so on.<br/>We get approximation for value of $\int_a^b f(x) d x$.<strong>Question:</strong><br/>If $\lim _{t \rightarrow a} \frac{\int_a^t f(x) d x-\frac{(t-a)}{2}\{f(t)+f(a)\}}{(t-a)^3}=0$, then degree of polynomial function $f(x)$ at most is</div> | ['Mathematics', 'Limits', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>0<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>1<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>3<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>2</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>1<br/></span> </div> | <div class="solution">$$<br/>\begin{aligned}<br/>\lim _{t \rightarrow a} \frac{\int_a^t f(t) d t-\frac{(t-a)}{2}(f(t)+f(a))}{(t-a)^3} & =0 \\<br/>\Rightarrow \quad \lim _{h \rightarrow 0} \frac{\int_a^{a+h} f(t) d t-\frac{h}{2}(f(a+h)+f(a))}{h^3} & =0 \\<br/>\Rightarrow \quad \lim _{h \rightarrow 0} \frac{f(a+h)-\frac{1}{2}(f(a+h)+f(a))-\frac{h}{2}\left(f^{\prime}(a+h)\right)}{3 h^2} & =0<br/>\end{aligned}<br/>$$<br/>$f^{\prime}(a+h)-\frac{1}{2} f^{\prime}(a+h)$<br/>$\Rightarrow \quad \lim _{h \rightarrow 0} \frac{-\frac{1}{2} f^{\prime}(a+h)-\frac{h}{2} f^{\prime \prime}(a+h)}{6 h}=0$<br/>$\Rightarrow \quad \lim _{h \rightarrow 0} \frac{-\frac{h}{2} f^{\prime}(a+h)}{6 h}=0$<br/>$\Rightarrow \quad f^{\prime \prime}(a)=0, \forall a \in R$<br/>$\Rightarrow(x)$ must have maximum degree 1.</div> | MarksBatch2_P2.db |
733 | paragraph-read-the-following-passage-and-answer-the-questions-for-every-function-f-x-which-is-twice-differentiable-these-will-be-good-approximation-of | paragraph-read-the-following-passage-and-answer-the-questions-for-every-function-f-x-which-is-twice-differentiable-these-will-be-good-approximation-of-71334 | <div class="question"><strong>Paragraph:</strong><br/>Read the following passage and answer the questions.<br/>For every function $f(x)$ which is twice differentiable, these will be good approximation of $\int_a^b f(x) d x \cong\left(\frac{b-a}{2}\right)\{f(a)+f(b)\}$. Now, if we take $c=\frac{a+b}{2}$, then using above again, we get $\int_a^b f(x) d x=\int_a^c f(x) d x+\int_c^b f(x) d x \cong \frac{b-a}{4}\{f(a)+f(b)+2 f(c)\}$ and so on.<br/>We get approximation for value of $\int_a^b f(x) d x$.<strong>Question:</strong><br/>Good approximation of $\int_0^{\pi / 2} \sin x d x$, is</div> | ['Mathematics', 'Definite Integration', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{\pi}{4}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{\pi}{4}(\sqrt{2}+1)$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{\pi}{8}(\sqrt{2}+1)$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{\pi}{8}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{\pi}{8}(\sqrt{2}+1)$<br/></span> </div> | <div class="solution">$\int_0^{\pi / 2} \sin x d x=\frac{\frac{\pi}{2}-0}{4}\left(\sin 0+\sin \left(\frac{\pi}{2}\right)+2 \sin \left(\frac{0+\frac{\pi}{2}}{2}\right)\right)=\frac{\pi}{8}(1+\sqrt{2})$.</div> | MarksBatch2_P2.db |
734 | paragraph-read-the-following-passage-and-answer-the-questions-let-a-bc-d-be-a-square-of-side-length-2-units-c-2-is-the-circle-through-vertices-a-b-c-d-1 | paragraph-read-the-following-passage-and-answer-the-questions-let-a-bc-d-be-a-square-of-side-length-2-units-c-2-is-the-circle-through-vertices-a-b-c-d-1-90397 | <div class="question"><strong>Paragraph:</strong><br/>Read the following passage and answer the questions.<br/>Let $A B C D$ be a square of side length 2 units. $C_2$ is the circle through vertices $A, B, C, D$ and $C_1$ is the circle touching all the sides of square $A B C D$. $L$ is the line through $A$.<strong>Question:</strong><br/>A line $M$ through $A$ is drawn parallel to $B D$. Points $S$ moves such that its distances from the line $B D$ are the vertex $A$ are equal. If locus of $S$ cuts $M$ at $T_2$ and $T_3$ and $A C$ at $T_1$, then area of $\Delta T_1 T_2 T_3$ is</div> | ['Mathematics', 'Parabola', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{1}{2}$ sq unit<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{2}{3}$ sq unit<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>1 sq unit<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>2 sq unit</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>1 sq unit<br/></span> </div> | <div class="solution">$\because \quad A G=\sqrt{2}$<br/>$$<br/>\therefore \quad A T_1=T_1 G=\frac{1}{\sqrt{2}}<br/>$$<br/>\{ as $A$ is the focus, $T_1$ is the vertex and $B D$ is the directrix of parabola.\}<br/>Also, $T_2 T_3$ is latus rectum<br/>$$<br/>\begin{aligned}<br/>& \therefore \quad T_2 T_3=4 \cdot \frac{1}{\sqrt{2}} \\<br/>& \therefore \text { Area of } \Delta T_1 T_2 T_3=\frac{1}{2} \times \frac{1}{\sqrt{2}} \times \frac{4}{\sqrt{2}}=1 \text { sq unit }<br/>\end{aligned}<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Pxu686ffJomZ7_Tf427TB2KermtePPSHx--LU89pjaA.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
735 | paragraph-read-the-following-passage-and-answer-the-questions-let-a-bc-d-be-a-square-of-side-length-2-units-c-2-is-the-circle-through-vertices-a-b-c-d-2 | paragraph-read-the-following-passage-and-answer-the-questions-let-a-bc-d-be-a-square-of-side-length-2-units-c-2-is-the-circle-through-vertices-a-b-c-d-2-66029 | <div class="question"><strong>Paragraph:</strong><br/>Read the following passage and answer the questions.<br/>Let $A B C D$ be a square of side length 2 units. $C_2$ is the circle through vertices $A, B, C, D$ and $C_1$ is the circle touching all the sides of square $A B C D$. $L$ is the line through $A$.<strong>Question:</strong><br/>A circle touches the line $L$ and the circle $C_1$ externally such that both the circles are on the same side of the line, then the locus of centre of the circle is</div> | ['Mathematics', 'Parabola', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>ellipse<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>hyperbola<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>parabola<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>parts of straight line</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>parabola<br/></span> </div> | <div class="solution">Let $C$ be the centre of the required circle.<br/>Now, draw a line parallel to $L$ at a distance of $r_1$ (radius of $C_1$ ) from it. Now, $C P_1=A C$<br/>$\Rightarrow C$ lies on a parabola.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/T3E8jilQ7fAExrDkNa9zaAaWyOyYLzWpMUcoHIy2QN0.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
736 | paragraph-read-the-following-passage-and-answer-the-questions-let-a-bc-d-be-a-square-of-side-length-2-units-c-2-is-the-circle-through-vertices-a-b-c-d-3 | paragraph-read-the-following-passage-and-answer-the-questions-let-a-bc-d-be-a-square-of-side-length-2-units-c-2-is-the-circle-through-vertices-a-b-c-d-3-94566 | <div class="question"><strong>Paragraph:</strong><br/>Read the following passage and answer the questions.<br/>Let $A B C D$ be a square of side length 2 units. $C_2$ is the circle through vertices $A, B, C, D$ and $C_1$ is the circle touching all the sides of square $A B C D$. $L$ is the line through $A$.<strong>Question:</strong><br/>If $P$ is a point on $C_1$ and $Q$ is a point on $C_2$, then $\frac{P A^2+P B^2+P C^2+P D^2}{Q A^2+Q B^2+Q C^2+Q D^2}$ is equal to</div> | ['Mathematics', 'Circle', 'JEE Main'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$0.75$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$1.25$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>1<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$0.5$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$0.75$<br/></span> </div> | <div class="solution">$$<br/>\text { Here, equation of } C_2:(x-1)^2+(y-1)^2=(\sqrt{2})^2 \text { and } C_1:(x-1)^2+(y-1)^2=(1)^2<br/>$$<br/><br/>$$<br/>\begin{aligned}<br/>& \therefore P(1+\cos \theta, 1+\sin \theta) \\<br/>& \text { and } Q(1+\sqrt{2} \sin \theta, 1+\sqrt{2} \sin \theta) \\<br/>& \therefore P A^2+P B^2+P C^2+P D^2 \\<br/>& =\left\{(1+\cos \theta)^2+(1+\sin \theta)^2\right\} \\<br/>& +\left\{(\cos \theta-1)^2+(1+\sin \theta)^2\right\} \\<br/>& +\left\{(1+\cos \theta)^2+(1-\sin \theta)^2\right\} \\<br/>& +\left\{(1-\cos \theta)^2+(1-\sin \theta)^2\right\} \\<br/>& =16 \\<br/>& \therefore \quad \frac{\Sigma Q A^2}{\Sigma P A^2}=\frac{12}{16}=0.75 \\<br/>&<br/>\end{aligned}<br/>$$<br/>Hence (a) is the correct answer.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/SEWnUdfopYlFl_vklMsnqLI82c2868zLYyuLSPl5984.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
737 | paragraph-read-the-following-passage-and-answer-the-questions-let-a-bc-d-be-a-square-of-side-length-2-units-c-2-is-the-circle-through-vertices-a-b-c-d-4 | paragraph-read-the-following-passage-and-answer-the-questions-let-a-bc-d-be-a-square-of-side-length-2-units-c-2-is-the-circle-through-vertices-a-b-c-d-4-22987 | <div class="question"><strong>Paragraph:</strong><br/>Read the following passage and answer the questions.<br/>Let $A B C D$ be a square of side length 2 units. $C_2$ is the circle through vertices $A, B, C, D$ and $C_1$ is the circle touching all the sides of square $A B C D$. $L$ is the line through $A$.<strong>Question:</strong><br/>A circle touches the line $L$ and the circle $C_1$ externally such that both the circles are on the same side of the line, then the locus of centre of the circle is</div> | ['Mathematics', 'Parabola', 'JEE Main'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>ellipse<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>hyperbola<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>parabola<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>parts of straight line</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>parabola<br/></span> </div> | <div class="solution">Let $C$ be the centre of the required circle.<br/>Now, draw a line parallel to $L$ at a distance of $r_1$ (radius of $C_1$ ) from it. Now, $C P_1=A C$<br/>$\Rightarrow C$ lies on a parabola.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/T3E8jilQ7fAExrDkNa9zaAaWyOyYLzWpMUcoHIy2QN0.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
738 | paragraph-read-the-following-passage-and-answer-the-questions-let-a-bc-d-be-a-square-of-side-length-2-units-c-2-is-the-circle-through-vertices-a-b-c-d-5 | paragraph-read-the-following-passage-and-answer-the-questions-let-a-bc-d-be-a-square-of-side-length-2-units-c-2-is-the-circle-through-vertices-a-b-c-d-5-18949 | <div class="question"><strong>Paragraph:</strong><br/>Read the following passage and answer the questions.<br/>Let $A B C D$ be a square of side length 2 units. $C_2$ is the circle through vertices $A, B, C, D$ and $C_1$ is the circle touching all the sides of square $A B C D$. $L$ is the line through $A$.<strong>Question:</strong><br/>A line $M$ through $A$ is drawn parallel to $B D$. Points $S$ moves such that its distances from the line $B D$ are the vertex $A$ are equal. If locus of $S$ cuts $M$ at $T_2$ and $T_3$ and $A C$ at $T_1$, then area of $\Delta T_1 T_2 T_3$ is</div> | ['Mathematics', 'Parabola', 'JEE Main'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{1}{2}$ sq unit<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{2}{3}$ sq unit<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>1 sq unit<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>2 sq unit</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>1 sq unit<br/></span> </div> | <div class="solution">$\because \quad A G=\sqrt{2}$<br/>$$<br/>\therefore \quad A T_1=T_1 G=\frac{1}{\sqrt{2}}<br/>$$<br/>\{ as $A$ is the focus, $T_1$ is the vertex and $B D$ is the directrix of parabola.\}<br/>Also, $T_2 T_3$ is latus rectum<br/>$$<br/>\begin{aligned}<br/>& \therefore \quad T_2 T_3=4 \cdot \frac{1}{\sqrt{2}} \\<br/>& \therefore \text { Area of } \Delta T_1 T_2 T_3=\frac{1}{2} \times \frac{1}{\sqrt{2}} \times \frac{4}{\sqrt{2}}=1 \text { sq unit }<br/>\end{aligned}<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Pxu686ffJomZ7_Tf427TB2KermtePPSHx--LU89pjaA.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
739 | paragraph-read-the-following-passage-and-answer-the-questions-let-a-bc-d-be-a-square-of-side-length-2-units-c-2-is-the-circle-through-vertices-a-b-c-d | paragraph-read-the-following-passage-and-answer-the-questions-let-a-bc-d-be-a-square-of-side-length-2-units-c-2-is-the-circle-through-vertices-a-b-c-d-87608 | <div class="question"><strong>Paragraph:</strong><br/>Read the following passage and answer the questions.<br/>Let $A B C D$ be a square of side length 2 units. $C_2$ is the circle through vertices $A, B, C, D$ and $C_1$ is the circle touching all the sides of square $A B C D$. $L$ is the line through $A$.<strong>Question:</strong><br/>If $P$ is a point on $C_1$ and $Q$ is a point on $C_2$, then $\frac{P A^2+P B^2+P C^2+P D^2}{Q A^2+Q B^2+Q C^2+Q D^2}$ is equal to</div> | ['Mathematics', 'Circle', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$0.75$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$1.25$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>1<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$0.5$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$0.75$<br/></span> </div> | <div class="solution">$$<br/>\text { Here, equation of } C_2:(x-1)^2+(y-1)^2=(\sqrt{2})^2 \text { and } C_1:(x-1)^2+(y-1)^2=(1)^2<br/>$$<br/><br/>$$<br/>\begin{aligned}<br/>& \therefore P(1+\cos \theta, 1+\sin \theta) \\<br/>& \text { and } Q(1+\sqrt{2} \sin \theta, 1+\sqrt{2} \sin \theta) \\<br/>& \therefore P A^2+P B^2+P C^2+P D^2 \\<br/>& =\left\{(1+\cos \theta)^2+(1+\sin \theta)^2\right\} \\<br/>& +\left\{(\cos \theta-1)^2+(1+\sin \theta)^2\right\} \\<br/>& +\left\{(1+\cos \theta)^2+(1-\sin \theta)^2\right\} \\<br/>& +\left\{(1-\cos \theta)^2+(1-\sin \theta)^2\right\} \\<br/>& =16 \\<br/>& \therefore \quad \frac{\Sigma Q A^2}{\Sigma P A^2}=\frac{12}{16}=0.75 \\<br/>&<br/>\end{aligned}<br/>$$<br/>Hence (a) is the correct answer.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/SEWnUdfopYlFl_vklMsnqLI82c2868zLYyuLSPl5984.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
740 | paragraph-read-the-following-passage-and-answer-the-questions-question-the-value-of-3-2-0-3-2-0-is | paragraph-read-the-following-passage-and-answer-the-questions-question-the-value-of-3-2-0-3-2-0-is-91894 | <div class="question"><strong>Paragraph:</strong><br/>Read the following passage and answer the questions.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/88iLE50zA6etAHkOmNt74CAbkJliurfrRZp8CzupJk0.original.fullsize.png"/><br/><strong>Question:</strong><br/>The value of $\left[\begin{array}{lll}3 & 2 & 0\end{array}\right]\left[\begin{array}{l}3 \\ 2 \\ 0\end{array}\right]$ is</div> | ['Mathematics', 'Matrices', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$[5]$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\left[\frac{5}{2}\right]$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>[4]<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\left[\frac{3}{2}\right]$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$[5]$<br/></span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ZQgvpskrRTIhBmqoFgX30lBrLbKluyTOLvJb7_-5kd4.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
741 | paragraph-read-the-following-passage-and-answer-the-questions-question-the-value-of-the-elements-of-u-1-is | paragraph-read-the-following-passage-and-answer-the-questions-question-the-value-of-the-elements-of-u-1-is-46543 | <div class="question"><strong>Paragraph:</strong><br/>Read the following passage and answer the questions.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/88iLE50zA6etAHkOmNt74CAbkJliurfrRZp8CzupJk0.original.fullsize.png"/><br/><strong>Question:</strong><br/>The value of the elements of $U^{-1}$ is</div> | ['Mathematics', 'Matrices', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$-1$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>0<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>1<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>3</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$-1$<br/></span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/YBHdmRS2Jayt5PH1g06WziEPbMaRY-1B-tsUnQ-177g.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
742 | paragraph-read-the-following-passage-and-answer-the-questions-question-the-value-of-u-is | paragraph-read-the-following-passage-and-answer-the-questions-question-the-value-of-u-is-68616 | <div class="question"><strong>Paragraph:</strong><br/>Read the following passage and answer the questions.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/88iLE50zA6etAHkOmNt74CAbkJliurfrRZp8CzupJk0.original.fullsize.png"/><br/><strong>Question:</strong><br/>The value of $|U|$ is</div> | ['Mathematics', 'Matrices', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>3<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$-3$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{3}{2}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>2</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>3<br/></span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/wgH9BbHmJlVwdCzbsjL7tQqY-vkRnukiLSB1oxMNbTc.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
743 | paragraph-redox-reaction-play-a-pivotal-role-in-chemistry-and-biology-the-values-of-standard-redox-potential-e-of-two-halfcell-reactions-decide-which--1 | paragraph-redox-reaction-play-a-pivotal-role-in-chemistry-and-biology-the-values-of-standard-redox-potential-e-of-two-halfcell-reactions-decide-which-1-19742 | <div class="question"><strong>Paragraph:</strong><br/>Redox reaction play a pivotal role in chemistry and biology. The values of standard redox potential $\left(E^{\circ}\right)$ of two half-cell reactions decide which way the reaction is expected to proceed. A simple example is a Daniel cell in which zinc goes into solution and copper gets deposited. Given below are a set of half-cell reactions (acidic medium) along with their $E^{\circ}(V$ with respect to normal hydrogen electrode) values. Using this data obtain the correct explanations to Questions 14-19.<br/>$$<br/>\begin{array}{cl}<br/>\mathrm{I}_2+2 e^{-} \longrightarrow 2 \mathrm{I}^{-} & E^{\circ}=0.54 \\<br/>\mathrm{Cl}_2+2 e^{-} \longrightarrow 2 \mathrm{Cl}^{-} & E^{\circ}=1.36 \\<br/>\mathrm{Mn}^{3+}+e^{-} \longrightarrow \mathrm{Mn}^{2+} & E^{\circ}=1.50 \\<br/>\mathrm{Fe}^{3+}+e^{-} \longrightarrow \mathrm{Fe}^{2+} & E^{\circ}=0.77 \\<br/>\mathrm{O}_2+4 \mathrm{H}^{+}+4 e^{-} \longrightarrow 2 \mathrm{H}_2 \mathrm{O} & E^{\circ}=1.23<br/>\end{array}<br/>$$<strong>Question:</strong><br/>Among the following, identify the correct statement</div> | ['Chemistry', 'Redox Reactions', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Chloride ion is oxidised by $\mathrm{O}_2$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{Fe}^{2+}$ is oxidised by iodine<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>Iodide ion is oxidised by chlorine<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{Mn}^{2+}$ is oxidised by chlorine</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Iodide ion is oxidised by chlorine<br/></span> </div> | <div class="solution">$2 \mathrm{I}^{-}+\mathrm{Cl}_2 \longrightarrow \mathrm{I}_2+2 \mathrm{Cl}^{-}$<br/>$$<br/>E_{\text {cell }}^{\circ}=1.36-0.54=0.82 \mathrm{~V}<br/>$$<br/>$E_{\text {cell }}^{\circ}$ is $+v e$ cell reactions is feasible.</div> | MarksBatch2_P2.db |
744 | paragraph-redox-reaction-play-a-pivotal-role-in-chemistry-and-biology-the-values-of-standard-redox-potential-e-of-two-halfcell-reactions-decide-which--2 | paragraph-redox-reaction-play-a-pivotal-role-in-chemistry-and-biology-the-values-of-standard-redox-potential-e-of-two-halfcell-reactions-decide-which-2-12867 | <div class="question"><strong>Paragraph:</strong><br/>Redox reaction play a pivotal role in chemistry and biology. The values of standard redox potential $\left(E^{\circ}\right)$ of two half-cell reactions decide which way the reaction is expected to proceed. A simple example is a Daniel cell in which zinc goes into solution and copper gets deposited. Given below are a set of half-cell reactions (acidic medium) along with their $E^{\circ}(V$ with respect to normal hydrogen electrode) values. Using this data obtain the correct explanations to Questions 14-19.<br/>$$<br/>\begin{array}{cl}<br/>\mathrm{I}_2+2 e^{-} \longrightarrow 2 \mathrm{I}^{-} & E^{\circ}=0.54 \\<br/>\mathrm{Cl}_2+2 e^{-} \longrightarrow 2 \mathrm{Cl}^{-} & E^{\circ}=1.36 \\<br/>\mathrm{Mn}^{3+}+e^{-} \longrightarrow \mathrm{Mn}^{2+} & E^{\circ}=1.50 \\<br/>\mathrm{Fe}^{3+}+e^{-} \longrightarrow \mathrm{Fe}^{2+} & E^{\circ}=0.77 \\<br/>\mathrm{O}_2+4 \mathrm{H}^{+}+4 e^{-} \longrightarrow 2 \mathrm{H}_2 \mathrm{O} & E^{\circ}=1.23<br/>\end{array}<br/>$$<strong>Question:</strong><br/>Sodium fusion extract, obtained from aniline, on treatment with iron (II) sulphate and $\mathrm{H}_2 \mathrm{SO}_4$ in presence of air gives a prussian blue precipitate. The blue colour is due to the formation of</div> | ['Chemistry', 'Redox Reactions', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{Fe}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]_3$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{Fe}_3\left[\mathrm{Fe}(\mathrm{CN})_6\right]_2$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{Fe}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]_2$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$$<br/>\mathrm{Fe}_3\left[\mathrm{Fe}(\mathrm{CN})_6\right]_3<br/>$$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\mathrm{Fe}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]_3$<br/></span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/iMwLX8MdIS0emG5pSZDSPnOA9F7gf0vj-JxCA5ieavY.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
745 | paragraph-redox-reaction-play-a-pivotal-role-in-chemistry-and-biology-the-values-of-standard-redox-potential-e-of-two-halfcell-reactions-decide-which--3 | paragraph-redox-reaction-play-a-pivotal-role-in-chemistry-and-biology-the-values-of-standard-redox-potential-e-of-two-halfcell-reactions-decide-which-3-25629 | <div class="question"><strong>Paragraph:</strong><br/>Redox reaction play a pivotal role in chemistry and biology. The values of standard redox potential $\left(E^{\circ}\right)$ of two half-cell reactions decide which way the reaction is expected to proceed. A simple example is a Daniel cell in which zinc goes into solution and copper gets deposited. Given below are a set of half-cell reactions (acidic medium) along with their $E^{\circ}(V$ with respect to normal hydrogen electrode) values. Using this data obtain the correct explanations to Questions 14-19.<br/>$$<br/>\begin{array}{cl}<br/>\mathrm{I}_2+2 e^{-} \longrightarrow 2 \mathrm{I}^{-} & E^{\circ}=0.54 \\<br/>\mathrm{Cl}_2+2 e^{-} \longrightarrow 2 \mathrm{Cl}^{-} & E^{\circ}=1.36 \\<br/>\mathrm{Mn}^{3+}+e^{-} \longrightarrow \mathrm{Mn}^{2+} & E^{\circ}=1.50 \\<br/>\mathrm{Fe}^{3+}+e^{-} \longrightarrow \mathrm{Fe}^{2+} & E^{\circ}=0.77 \\<br/>\mathrm{O}_2+4 \mathrm{H}^{+}+4 e^{-} \longrightarrow 2 \mathrm{H}_2 \mathrm{O} & E^{\circ}=1.23<br/>\end{array}<br/>$$<strong>Question:</strong><br/>Sodium fusion extract, obtained from aniline, on treatment with iron (II) sulphate and $\mathrm{H}_2 \mathrm{SO}_4$ in presence of air gives a prussian blue precipitate. The blue colour is due to the formation of</div> | ['Chemistry', 'Redox Reactions', 'JEE Main'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{Fe}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]_3$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{Fe}_3\left[\mathrm{Fe}(\mathrm{CN})_6\right]_2$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{Fe}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]_2$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$$<br/>\mathrm{Fe}_3\left[\mathrm{Fe}(\mathrm{CN})_6\right]_3<br/>$$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\mathrm{Fe}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]_3$<br/></span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/iMwLX8MdIS0emG5pSZDSPnOA9F7gf0vj-JxCA5ieavY.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
746 | paragraph-redox-reaction-play-a-pivotal-role-in-chemistry-and-biology-the-values-of-standard-redox-potential-e-of-two-halfcell-reactions-decide-which- | paragraph-redox-reaction-play-a-pivotal-role-in-chemistry-and-biology-the-values-of-standard-redox-potential-e-of-two-halfcell-reactions-decide-which-92486 | <div class="question"><strong>Paragraph:</strong><br/>Redox reaction play a pivotal role in chemistry and biology. The values of standard redox potential $\left(E^{\circ}\right)$ of two half-cell reactions decide which way the reaction is expected to proceed. A simple example is a Daniel cell in which zinc goes into solution and copper gets deposited. Given below are a set of half-cell reactions (acidic medium) along with their $E^{\circ}(V$ with respect to normal hydrogen electrode) values. Using this data obtain the correct explanations to Questions 14-19.<br/>$$<br/>\begin{array}{cl}<br/>\mathrm{I}_2+2 e^{-} \longrightarrow 2 \mathrm{I}^{-} & E^{\circ}=0.54 \\<br/>\mathrm{Cl}_2+2 e^{-} \longrightarrow 2 \mathrm{Cl}^{-} & E^{\circ}=1.36 \\<br/>\mathrm{Mn}^{3+}+e^{-} \longrightarrow \mathrm{Mn}^{2+} & E^{\circ}=1.50 \\<br/>\mathrm{Fe}^{3+}+e^{-} \longrightarrow \mathrm{Fe}^{2+} & E^{\circ}=0.77 \\<br/>\mathrm{O}_2+4 \mathrm{H}^{+}+4 e^{-} \longrightarrow 2 \mathrm{H}_2 \mathrm{O} & E^{\circ}=1.23<br/>\end{array}<br/>$$<strong>Question:</strong><br/>While $\mathrm{Fe}^{3+}$ is stable, $\mathrm{Mn}^{3+}$ is not stable in acid solution because</div> | ['Chemistry', 'Redox Reactions', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{O}_2$ oxidises $\mathrm{Mn}^{2+}$ to $\mathrm{Mn}^{3+}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{O}_2$ oxidises both $\mathrm{Mn}^{2+}$ and $\mathrm{Fe}^{2+}$ to $\mathrm{Fe}^{3+}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{Fe}^{3+}$ oxidises $\mathrm{H}_2 \mathrm{O}$ to $\mathrm{O}_2$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{Mn}^{3+}$ oxidises $\mathrm{H}_2 \mathrm{O}$ to $\mathrm{O}_2$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\mathrm{Mn}^{3+}$ oxidises $\mathrm{H}_2 \mathrm{O}$ to $\mathrm{O}_2$</span> </div> | <div class="solution">$$<br/>\begin{aligned}<br/>& {\left[\mathrm{Mn}^{3+}+e^{-}\right.}\left.\longrightarrow \mathrm{Mn}^{2+}\right] \times 4 \\<br/>& 2 \mathrm{H}_2 \mathrm{O} \longrightarrow 4 \mathrm{H}^{+}+\mathrm{O}_2+4 e^{-} \\<br/>& 4 \mathrm{Mn}^{2+}+2 \mathrm{H}_2 \mathrm{O} \longrightarrow 4 \mathrm{Mn}^{2+}+4 \mathrm{H}^{+}+\mathrm{O}_2 \\<br/>& E_{\text {cell }}^{\circ}= 1.50-1.23=0.27 \mathrm{~V} \\<br/>& E_{\text {cell }}^{\circ} \text { is + ve }<br/>\end{aligned}<br/>$$</div> | MarksBatch2_P2.db |
747 | paragraph-reimertiemann-reaction-introduces-an-aldehyde-group-on-to-the-aromatic-ring-of-phenol-ortho-to-the-hydroxyl-group-this-reaction-involves-ele-1 | paragraph-reimertiemann-reaction-introduces-an-aldehyde-group-on-to-the-aromatic-ring-of-phenol-ortho-to-the-hydroxyl-group-this-reaction-involves-ele-1-18345 | <div class="question"><strong>Paragraph:</strong><br/>Reimer-Tiemann reaction introduces an aldehyde group, on to the aromatic ring of phenol, ortho to the hydroxyl group. This reaction involves electrophilic aromatic substitution. This is a general method for the synthesis of substituted salicylaldehydes as depicted below.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Du2opTwjmV3M-NwcVEb4w_x6hSMB0KtJP7732UoYD-0.original.fullsize.png"/><br/><strong>Question:</strong><br/>Which one of the following reagents is used the above reaction?</div> | ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>aq. $\mathrm{NaOH}+\mathrm{CH}_3 \mathrm{Cl}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>aq. $\mathrm{NaOH}+\mathrm{CH}_2 \mathrm{Cl}_2$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>aq. $\mathrm{NaOH}+\mathrm{CHCl}_3$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>aq. $\mathrm{NaOH}+\mathrm{CCl}_4$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>aq. $\mathrm{NaOH}+\mathrm{CHCl}_3$<br/></span> </div> | <div class="solution">aq. $\mathrm{NaOH}+\mathrm{CHCl}_3$<br/>$$<br/>\mathrm{Cl}_3 \mathrm{C}-\mathrm{H} \underset{-\mathrm{H}_2 \mathrm{O}}{\stackrel{\mathrm{OH}^{-}}{\longrightarrow}} \mathrm{Cl}_3 \mathrm{C}^{-} \underset{-\mathrm{Cl}^{-}}{\longrightarrow} \mathrm{Cl}_2 \mathrm{C}:<br/>$$</div> | MarksBatch2_P2.db |
748 | paragraph-reimertiemann-reaction-introduces-an-aldehyde-group-on-to-the-aromatic-ring-of-phenol-ortho-to-the-hydroxyl-group-this-reaction-involves-ele-2 | paragraph-reimertiemann-reaction-introduces-an-aldehyde-group-on-to-the-aromatic-ring-of-phenol-ortho-to-the-hydroxyl-group-this-reaction-involves-ele-2-66537 | <div class="question"><strong>Paragraph:</strong><br/>Reimer-Tiemann reaction introduces an aldehyde group, on to the aromatic ring of phenol, ortho to the hydroxyl group. This reaction involves electrophilic aromatic substitution. This is a general method for the synthesis of substituted salicylaldehydes as depicted below.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Du2opTwjmV3M-NwcVEb4w_x6hSMB0KtJP7732UoYD-0.original.fullsize.png"/><br/><strong>Question:</strong><br/>The electrophile in this reaction is</div> | ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>: CHCL<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>${ }^{+} \mathrm{CHCl}_2$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$: \mathrm{CCl}_2$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\cdot \mathrm{CCl}_3$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$: \mathrm{CCl}_2$<br/></span> </div> | <div class="solution">In Reimer-Tiemann reaction<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/IOBozXMEqhNuMBg0Q6L_JIJOJLYs23aag8wBtoC3OBU.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
749 | paragraph-reimertiemann-reaction-introduces-an-aldehyde-group-on-to-the-aromatic-ring-of-phenol-ortho-to-the-hydroxyl-group-this-reaction-involves-ele-3 | paragraph-reimertiemann-reaction-introduces-an-aldehyde-group-on-to-the-aromatic-ring-of-phenol-ortho-to-the-hydroxyl-group-this-reaction-involves-ele-3-33624 | <div class="question"><strong>Paragraph:</strong><br/>Reimer-Tiemann reaction introduces an aldehyde group, on to the aromatic ring of phenol, ortho to the hydroxyl group. This reaction involves electrophilic aromatic substitution. This is a general method for the synthesis of substituted salicylaldehydes as depicted below.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Du2opTwjmV3M-NwcVEb4w_x6hSMB0KtJP7732UoYD-0.original.fullsize.png"/><br/><strong>Question:</strong><br/>The structure of the intermediate $\mathrm{I}$ is</div> | ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Main'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ufEUk1j8s6jfvsoJhfg8lv47ygbrWsRJyTN4VSxj5HE.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/d-XGjxXmeveuzoYrGaxk9voyVW1aNHidwq3e9QB66Ow.original.fullsize.png"/><br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/OXLhm9FBFe0UEFkzFWnzJkWIDQBqymao0aq0olvvTCo.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/sGD7l_cZ4zJCRD1c5LAJLAQTuZTxGWsDqfBQ_5VC-Hc.original.fullsize.png"/><br/></span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/d-XGjxXmeveuzoYrGaxk9voyVW1aNHidwq3e9QB66Ow.original.fullsize.png"/><br/></span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/wItlqDuGitnTqt9mqZGYafaNfHHbw4_W8zFcogYiWAo.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
750 | paragraph-reimertiemann-reaction-introduces-an-aldehyde-group-on-to-the-aromatic-ring-of-phenol-ortho-to-the-hydroxyl-group-this-reaction-involves-ele-4 | paragraph-reimertiemann-reaction-introduces-an-aldehyde-group-on-to-the-aromatic-ring-of-phenol-ortho-to-the-hydroxyl-group-this-reaction-involves-ele-4-70758 | <div class="question"><strong>Paragraph:</strong><br/>Reimer-Tiemann reaction introduces an aldehyde group, on to the aromatic ring of phenol, ortho to the hydroxyl group. This reaction involves electrophilic aromatic substitution. This is a general method for the synthesis of substituted salicylaldehydes as depicted below.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Du2opTwjmV3M-NwcVEb4w_x6hSMB0KtJP7732UoYD-0.original.fullsize.png"/><br/><strong>Question:</strong><br/>Which one of the following reagents is used the above reaction?</div> | ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Main'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>aq. $\mathrm{NaOH}+\mathrm{CH}_3 \mathrm{Cl}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>aq. $\mathrm{NaOH}+\mathrm{CH}_2 \mathrm{Cl}_2$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>aq. $\mathrm{NaOH}+\mathrm{CHCl}_3$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>aq. $\mathrm{NaOH}+\mathrm{CCl}_4$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>aq. $\mathrm{NaOH}+\mathrm{CHCl}_3$<br/></span> </div> | <div class="solution">aq. $\mathrm{NaOH}+\mathrm{CHCl}_3$<br/>$$<br/>\mathrm{Cl}_3 \mathrm{C}-\mathrm{H} \underset{-\mathrm{H}_2 \mathrm{O}}{\stackrel{\mathrm{OH}^{-}}{\longrightarrow}} \mathrm{Cl}_3 \mathrm{C}^{-} \underset{-\mathrm{Cl}^{-}}{\longrightarrow} \mathrm{Cl}_2 \mathrm{C}:<br/>$$</div> | MarksBatch2_P2.db |
751 | paragraph-reimertiemann-reaction-introduces-an-aldehyde-group-on-to-the-aromatic-ring-of-phenol-ortho-to-the-hydroxyl-group-this-reaction-involves-ele | paragraph-reimertiemann-reaction-introduces-an-aldehyde-group-on-to-the-aromatic-ring-of-phenol-ortho-to-the-hydroxyl-group-this-reaction-involves-ele-55570 | <div class="question"><strong>Paragraph:</strong><br/>Reimer-Tiemann reaction introduces an aldehyde group, on to the aromatic ring of phenol, ortho to the hydroxyl group. This reaction involves electrophilic aromatic substitution. This is a general method for the synthesis of substituted salicylaldehydes as depicted below.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Du2opTwjmV3M-NwcVEb4w_x6hSMB0KtJP7732UoYD-0.original.fullsize.png"/><br/><strong>Question:</strong><br/>The structure of the intermediate $\mathrm{I}$ is</div> | ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ufEUk1j8s6jfvsoJhfg8lv47ygbrWsRJyTN4VSxj5HE.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/d-XGjxXmeveuzoYrGaxk9voyVW1aNHidwq3e9QB66Ow.original.fullsize.png"/><br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/OXLhm9FBFe0UEFkzFWnzJkWIDQBqymao0aq0olvvTCo.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/sGD7l_cZ4zJCRD1c5LAJLAQTuZTxGWsDqfBQ_5VC-Hc.original.fullsize.png"/><br/></span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/d-XGjxXmeveuzoYrGaxk9voyVW1aNHidwq3e9QB66Ow.original.fullsize.png"/><br/></span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/wItlqDuGitnTqt9mqZGYafaNfHHbw4_W8zFcogYiWAo.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
752 | paragraph-scientists-are-working-hard-to-develop-nuclear-fusion-reactor-nuclei-of-heavy-hydrogen-1-2-h-known-as-deuteron-and-denoted-by-d-can-be-thoug-1 | paragraph-scientists-are-working-hard-to-develop-nuclear-fusion-reactor-nuclei-of-heavy-hydrogen-1-2-h-known-as-deuteron-and-denoted-by-d-can-be-thoug-1-28663 | <div class="question"><strong>Paragraph:</strong><br/>Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, ${ }_1^2 \mathrm{H}$ known as deuteron and denoted by $D$ can be thought of as a candidate for fusion reactor. The $D$ - $D$ reaction is ${ }_1^2 \mathrm{H}+{ }_1^2 \mathrm{H} \rightarrow{ }_2^3 \mathrm{He}+n+$ energy. In the core of fusion reactor. A gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of ${ }_1^4 \mathrm{H}$ nuclei and electrons is known as plasma. The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually, the temperatures in the reactor core are too high and no material wall can be used to confine the plasma. Special techniques are used which confine the plasma for a time $t_0$ before the particles fly away from the core. If n is the density (number/volume) of deutrons, the product t $_0$ is called Lawson number. In one of the criteria, $a$ reactor is termed successful if Lawson number is greater than $5 \times 10^{14} \mathrm{scm}^{-3}$.<br/>It may be helpful to use the following : Boltzmann constant $k=8.6 \times 10^{-5} \mathrm{eV} / \mathrm{K}$; $\frac{e^2}{4 \pi \varepsilon_0}=1.44 \times 10^{-9} \mathrm{eVm}$<strong>Question:</strong><br/>In the core of nuclear fusion reactor, the gas becomes plasma because of</div> | ['Physics', 'Nuclear Physics', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>strong nuclear force acting between the deuterons<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Coulomb fore acting between the deuterons<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Coulomb force acting between deuteron-electron pairs<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>the high temperature maintained inside the reactor core</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>the high temperature maintained inside the reactor core</span> </div> | <div class="solution">No Solution Available</div> | MarksBatch2_P2.db |
753 | paragraph-scientists-are-working-hard-to-develop-nuclear-fusion-reactor-nuclei-of-heavy-hydrogen-1-2-h-known-as-deuteron-and-denoted-by-d-can-be-thoug-2 | paragraph-scientists-are-working-hard-to-develop-nuclear-fusion-reactor-nuclei-of-heavy-hydrogen-1-2-h-known-as-deuteron-and-denoted-by-d-can-be-thoug-2-40676 | <div class="question"><strong>Paragraph:</strong><br/>Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, ${ }_1^2 \mathrm{H}$ known as deuteron and denoted by $D$ can be thought of as a candidate for fusion reactor. The $D$ - $D$ reaction is ${ }_1^2 \mathrm{H}+{ }_1^2 \mathrm{H} \rightarrow{ }_2^3 \mathrm{He}+n+$ energy. In the core of fusion reactor. A gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of ${ }_1^4 \mathrm{H}$ nuclei and electrons is known as plasma. The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually, the temperatures in the reactor core are too high and no material wall can be used to confine the plasma. Special techniques are used which confine the plasma for a time $t_0$ before the particles fly away from the core. If n is the density (number/volume) of deutrons, the product t $_0$ is called Lawson number. In one of the criteria, $a$ reactor is termed successful if Lawson number is greater than $5 \times 10^{14} \mathrm{scm}^{-3}$.<br/>It may be helpful to use the following : Boltzmann constant $k=8.6 \times 10^{-5} \mathrm{eV} / \mathrm{K}$; $\frac{e^2}{4 \pi \varepsilon_0}=1.44 \times 10^{-9} \mathrm{eVm}$<strong>Question:</strong><br/>Results of calculations for four different designs of a fusion reactor using D-D reaction are given below. Which of these is most promising based on Lawson criterion?</div> | ['Physics', 'Nuclear Physics', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Deuteron density $=20 \times 10^{12} \mathrm{~cm}^{-3}$, confinement time $=5.0 \times 10^{-3} \mathrm{~s}$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>Deuteron density $=8.0 \times 10^{14} \mathrm{~cm}^{-3}$, confinement time $=9.0 \times 10^{-1} \mathrm{~s}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Deuteron density $=4.0 \times 10^{23} \mathrm{~cm}^{-3}$, confinement time $=1.0 \times 10^{-11} \mathrm{~s}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Deuteron density $=1.0 \times 10^{24} \mathrm{~cm}^{-3}$, confinement time $=4.0 \times 10^{-12} \mathrm{~s}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Deuteron density $=8.0 \times 10^{14} \mathrm{~cm}^{-3}$, confinement time $=9.0 \times 10^{-1} \mathrm{~s}$<br/></span> </div> | <div class="solution">As given in the paragraph, a reactor is termed successful, if<br/>$$<br/>n t_0>5 \times 10^{14} \mathrm{scm}^{-3}<br/>$$</div> | MarksBatch2_P2.db |
754 | paragraph-scientists-are-working-hard-to-develop-nuclear-fusion-reactor-nuclei-of-heavy-hydrogen-1-2-h-known-as-deuteron-and-denoted-by-d-can-be-thoug | paragraph-scientists-are-working-hard-to-develop-nuclear-fusion-reactor-nuclei-of-heavy-hydrogen-1-2-h-known-as-deuteron-and-denoted-by-d-can-be-thoug-54985 | <div class="question"><strong>Paragraph:</strong><br/>Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, ${ }_1^2 \mathrm{H}$ known as deuteron and denoted by $D$ can be thought of as a candidate for fusion reactor. The $D$ - $D$ reaction is ${ }_1^2 \mathrm{H}+{ }_1^2 \mathrm{H} \rightarrow{ }_2^3 \mathrm{He}+n+$ energy. In the core of fusion reactor. A gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of ${ }_1^4 \mathrm{H}$ nuclei and electrons is known as plasma. The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually, the temperatures in the reactor core are too high and no material wall can be used to confine the plasma. Special techniques are used which confine the plasma for a time $t_0$ before the particles fly away from the core. If n is the density (number/volume) of deutrons, the product t $_0$ is called Lawson number. In one of the criteria, $a$ reactor is termed successful if Lawson number is greater than $5 \times 10^{14} \mathrm{scm}^{-3}$.<br/>It may be helpful to use the following : Boltzmann constant $k=8.6 \times 10^{-5} \mathrm{eV} / \mathrm{K}$; $\frac{e^2}{4 \pi \varepsilon_0}=1.44 \times 10^{-9} \mathrm{eVm}$<strong>Question:</strong><br/>Assume that two deuteron nuclei in the core of fusion reactor at temperature $T$ are moving towards each other, each with kinetic energy $1.5 \mathrm{kT}$, when the separation between them is large enough to neglect Coulomb potential energy. Also neglect any interaction from other particles in the core. The minimum temperature $T$ required for them to reach a separation of $4 \times 10^{-15} \mathrm{~m}$ is in the range</div> | ['Physics', 'Nuclear Physics', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$1.0 \times 10^9 \mathrm{~K} < T < 2.0 \times 10^9 \mathrm{~K}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$20 \times 10^9 \mathrm{~K} < T < 3.0 \times 10^9 \mathrm{~K}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$3.0 \times 10^9 \mathrm{~K} < T < 4.0 \times 10^9 \mathrm{~K}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$4.0 \times 10^9 \mathrm{~K} < T < 5.0 \times 10^9 \mathrm{~K}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$1.0 \times 10^9 \mathrm{~K} < T < 2.0 \times 10^9 \mathrm{~K}$</span> </div> | <div class="solution">From conservation of mechanical energy, we have<br/>$$<br/>\begin{gathered}<br/>U_i+K_i=U_f+U_f \\<br/>0+2(1.5 k T)=\frac{1}{4 \pi \varepsilon_0} \cdot \frac{(e)(e)}{d}+0<br/>\end{gathered}<br/>$$<br/>Substituting the values, we get<br/>$$<br/>T=1.4 \times 10^9 \mathrm{~K}<br/>$$</div> | MarksBatch2_P2.db |
755 | paragraph-tangents-are-drawn-from-the-point-p-3-4-to-the-ellipse-9-x-2-4-y-2-1-touching-the-ellipse-at-points-a-and-b-question-the-coordinates-of-a-an | paragraph-tangents-are-drawn-from-the-point-p-3-4-to-the-ellipse-9-x-2-4-y-2-1-touching-the-ellipse-at-points-a-and-b-question-the-coordinates-of-a-an-60424 | <div class="question"><strong>Paragraph:</strong><br/>Tangents are drawn from the point $P(3,4)$ to the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ touching the ellipse at points $A$ and $B$.<strong>Question:</strong><br/>The coordinates of $A$ and $B$ are</div> | ['Mathematics', 'Ellipse', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$(3,0)$ and $(0,2)$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\left(-\frac{8}{5}, \frac{2 \sqrt{161}}{15}\right)$ and $\left(-\frac{9}{5}, \frac{8}{5}\right)$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\left(-\frac{8}{5}, \frac{2 \sqrt{161}}{15}\right)$ and $(0,2)$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$(3,0)$ and $\left(-\frac{9}{5}, \frac{8}{5}\right)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$(3,0)$ and $\left(-\frac{9}{5}, \frac{8}{5}\right)$</span> </div> | <div class="solution">$$<br/>\text { Figure is self explanatory }<br/>$$<br/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/jDX6GkEhtNdY7zYO8pXOklILC_QwTFTGY_kNUs2S2r4.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
756 | paragraph-tangents-are-drawn-from-the-point-p-3-4-to-the-ellipse-9-x-2-4-y-2-1-touching-the-ellipse-at-points-a-and-b-question-the-equation-of-the-loc | paragraph-tangents-are-drawn-from-the-point-p-3-4-to-the-ellipse-9-x-2-4-y-2-1-touching-the-ellipse-at-points-a-and-b-question-the-equation-of-the-loc-63661 | <div class="question"><strong>Paragraph:</strong><br/>Tangents are drawn from the point $P(3,4)$ to the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ touching the ellipse at points $A$ and $B$.<strong>Question:</strong><br/>The equation of the locus of the point whose distance from the point $P$ and the line $A B$ are equal, is</div> | ['Mathematics', 'Ellipse', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$9 x^2+y^2-6 x y-54 x-62 y$<br/>$$<br/>+241=0<br/>$$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$x^2+9 y^2+6 x y-54 x+62 y$<br/>$$<br/>-241=0<br/>$$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$9 x^2+9 y^2-6 x y-54 x-62 y$<br/>$$<br/>-241=0<br/>$$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$x^2+y^2-2 x y+27 x+31 y$<br/>$$<br/>-120=0<br/>$$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$9 x^2+y^2-6 x y-54 x-62 y$<br/>$$<br/>+241=0<br/>$$<br/></span> </div> | <div class="solution">Equation of $A B$ is $y-0=-\frac{1}{3}(x-3)$<br/>$$<br/>\begin{gathered}<br/>x+3 y-3=0 \\<br/>|x+3 y-3|^2=10\left[(x-3)^2+(y-4)^2\right]<br/>\end{gathered}<br/>$$<br/>(Look at coefficient of $x^2$ and $y^2$ in the<br/>answers)</div> | MarksBatch2_P2.db |
757 | paragraph-tangents-are-drawn-from-the-point-p-3-4-to-the-ellipse-9-x-2-4-y-2-1-touching-the-ellipse-at-points-a-and-b-question-the-orthocentre-of-the--1 | paragraph-tangents-are-drawn-from-the-point-p-3-4-to-the-ellipse-9-x-2-4-y-2-1-touching-the-ellipse-at-points-a-and-b-question-the-orthocentre-of-the-1-38147 | <div class="question"><strong>Paragraph:</strong><br/>Tangents are drawn from the point $P(3,4)$ to the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ touching the ellipse at points $A$ and $B$.<strong>Question:</strong><br/>The orthocentre of the triangle $P A B$ is</div> | ['Mathematics', 'Straight Lines', 'JEE Main'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\left(5, \frac{8}{7}\right)$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\left(\frac{7}{5}, \frac{25}{8}\right)$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\left(\frac{11}{5}, \frac{8}{5}\right)$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\left(\frac{8}{25}, \frac{7}{5}\right)$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\left(\frac{11}{5}, \frac{8}{5}\right)$<br/></span> </div> | <div class="solution">$$<br/>\text { Equation of } A B \text { is }<br/>$$<br/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/vGNDL6PX8Om2ubizKilLEdDE0M3SMgzemqgZ4ITooP0.original.fullsize.png"/><br/><br/><br/>$$<br/>\begin{aligned}<br/>y-0 & =\frac{\frac{8}{5}}{-\frac{9}{5}-3}(x-3)=\frac{8}{-24}(x-3) \\<br/>\Rightarrow \quad y & =-\frac{1}{3}(x-3) \\<br/>\Rightarrow \quad x & +3 y=3<br/>\end{aligned}<br/>$$<br/>Equation of the straight line perpendicular to $A B$ through $P$ is $3 x-y=5$.<br/>Equation of $P A$ is $x-3=0$.<br/>The equation of straight line perpendicular to $P A$ through $B\left(\frac{-9}{5}, \frac{8}{5}\right)$. is $y=\frac{8}{5}$.<br/>Hence, the orthocentre is $\left(\frac{11}{5}, \frac{8}{5}\right)$.</div> | MarksBatch2_P2.db |
758 | paragraph-tangents-are-drawn-from-the-point-p-3-4-to-the-ellipse-9-x-2-4-y-2-1-touching-the-ellipse-at-points-a-and-b-question-the-orthocentre-of-the- | paragraph-tangents-are-drawn-from-the-point-p-3-4-to-the-ellipse-9-x-2-4-y-2-1-touching-the-ellipse-at-points-a-and-b-question-the-orthocentre-of-the-21076 | <div class="question"><strong>Paragraph:</strong><br/>Tangents are drawn from the point $P(3,4)$ to the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ touching the ellipse at points $A$ and $B$.<strong>Question:</strong><br/>The orthocentre of the triangle $P A B$ is</div> | ['Mathematics', 'Straight Lines', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\left(5, \frac{8}{7}\right)$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\left(\frac{7}{5}, \frac{25}{8}\right)$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\left(\frac{11}{5}, \frac{8}{5}\right)$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\left(\frac{8}{25}, \frac{7}{5}\right)$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\left(\frac{11}{5}, \frac{8}{5}\right)$<br/></span> </div> | <div class="solution">$$<br/>\text { Equation of } A B \text { is }<br/>$$<br/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/vGNDL6PX8Om2ubizKilLEdDE0M3SMgzemqgZ4ITooP0.original.fullsize.png"/><br/><br/><br/>$$<br/>\begin{aligned}<br/>y-0 & =\frac{\frac{8}{5}}{-\frac{9}{5}-3}(x-3)=\frac{8}{-24}(x-3) \\<br/>\Rightarrow \quad y & =-\frac{1}{3}(x-3) \\<br/>\Rightarrow \quad x & +3 y=3<br/>\end{aligned}<br/>$$<br/>Equation of the straight line perpendicular to $A B$ through $P$ is $3 x-y=5$.<br/>Equation of $P A$ is $x-3=0$.<br/>The equation of straight line perpendicular to $P A$ through $B\left(\frac{-9}{5}, \frac{8}{5}\right)$. is $y=\frac{8}{5}$.<br/>Hence, the orthocentre is $\left(\frac{11}{5}, \frac{8}{5}\right)$.</div> | MarksBatch2_P2.db |
759 | paragraph-the-capacitor-of-capacitance-c-can-be-charged-with-the-help-of-a-resistance-r-by-a-voltage-source-v-by-closing-switch-s-1-while-keeping-swit-1 | paragraph-the-capacitor-of-capacitance-c-can-be-charged-with-the-help-of-a-resistance-r-by-a-voltage-source-v-by-closing-switch-s-1-while-keeping-swit-1-96412 | <div class="question"><strong>Paragraph:</strong><br/>The capacitor of capacitance $C$ can be charged (with the help of a resistance $R$ ) by a voltage source $V$, by closing switch $S_1$ while keeping switch $S_2$ open. The capacitor can be connected in series with an inductor $L$ by closing switch $S_2$ and opening $S_1$.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/0Y1I8mvhYVnowTpUifCLeg2xPE10yRn1Ap7tEzxaL24.original.fullsize.png"/><br/><strong>Question:</strong><br/>Initially, the capacitor was uncharged. Now, switch $S_1$ is closed and $S_2$ is kept open. If time constant of this circuit is $\tau$, then</div> | ['Physics', 'Alternating Current', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>after time interval $\tau$, charge on the capacitor is $C V / 2$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>after time interval $2 \tau$, charge on the capacitor is $C V /\left(1-e^{-2}\right)$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>the work done by the voltage source will be half on the heat dissipated when the capacitor is fully charged<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>after time interval $2 \tau$, charge on the capacitor is $C V\left(1-e^{-1}\right)$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>after time interval $2 \tau$, charge on the capacitor is $C V /\left(1-e^{-2}\right)$<br/></span> </div> | <div class="solution">Charge on capacitor at time $t$ is $q=q_0\left(1-e^{-t / \tau}\right)$<br/>$\begin{array}{ll}\text { Here, } & q_0=C V \text { and } t=2 \tau \\ \therefore & q=C V\left(1-e^{-2 \tau / \tau}\right)=C V\left(1-e^{-2}\right)\end{array}$</div> | MarksBatch2_P2.db |
760 | paragraph-the-capacitor-of-capacitance-c-can-be-charged-with-the-help-of-a-resistance-r-by-a-voltage-source-v-by-closing-switch-s-1-while-keeping-swit-2 | paragraph-the-capacitor-of-capacitance-c-can-be-charged-with-the-help-of-a-resistance-r-by-a-voltage-source-v-by-closing-switch-s-1-while-keeping-swit-2-15669 | <div class="question"><strong>Paragraph:</strong><br/>The capacitor of capacitance $C$ can be charged (with the help of a resistance $R$ ) by a voltage source $V$, by closing switch $S_1$ while keeping switch $S_2$ open. The capacitor can be connected in series with an inductor $L$ by closing switch $S_2$ and opening $S_1$.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/0Y1I8mvhYVnowTpUifCLeg2xPE10yRn1Ap7tEzxaL24.original.fullsize.png"/><br/><strong>Question:</strong><br/>After the capacitor gets fully charged, $S_1$ is opened and $S_2$ is closed so that the inductor is connected in series with the capacitor. Then,</div> | ['Physics', 'Alternating Current', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>at $t=0$, energy stored in the circuit is purely in the form of magnetic energy<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>at any time $t>0$, current in the circuit is in the same direction<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>at $t>0$, there is no exchange of energy between the inductor and capacitor<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>at any time $t>0$, maximum instantaneous current in the circuit may $V \sqrt{\frac{C}{L}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>at any time $t>0$, maximum instantaneous current in the circuit may $V \sqrt{\frac{C}{L}}$</span> </div> | <div class="solution">From conservation of energy, $\frac{1}{2} L I_{\max }^2=\frac{1}{2} C V^2$<br/>$$<br/>\therefore \quad I_{\max }=V \sqrt{\frac{C}{L}}<br/>$$</div> | MarksBatch2_P2.db |
761 | paragraph-the-capacitor-of-capacitance-c-can-be-charged-with-the-help-of-a-resistance-r-by-a-voltage-source-v-by-closing-switch-s-1-while-keeping-swit-3 | paragraph-the-capacitor-of-capacitance-c-can-be-charged-with-the-help-of-a-resistance-r-by-a-voltage-source-v-by-closing-switch-s-1-while-keeping-swit-3-91957 | <div class="question"><strong>Paragraph:</strong><br/>The capacitor of capacitance $C$ can be charged (with the help of a resistance $R$ ) by a voltage source $V$, by closing switch $S_1$ while keeping switch $S_2$ open. The capacitor can be connected in series with an inductor $L$ by closing switch $S_2$ and opening $S_1$.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/0Y1I8mvhYVnowTpUifCLeg2xPE10yRn1Ap7tEzxaL24.original.fullsize.png"/><br/><strong>Question:</strong><br/>Initially, the capacitor was uncharged. Now, switch $S_1$ is closed and $S_2$ is kept open. If time constant of this circuit is $\tau$, then</div> | ['Physics', 'Alternating Current', 'JEE Main'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>after time interval $\tau$, charge on the capacitor is $C V / 2$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>after time interval $2 \tau$, charge on the capacitor is $C V /\left(1-e^{-2}\right)$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>the work done by the voltage source will be half on the heat dissipated when the capacitor is fully charged<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>after time interval $2 \tau$, charge on the capacitor is $C V\left(1-e^{-1}\right)$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>after time interval $2 \tau$, charge on the capacitor is $C V /\left(1-e^{-2}\right)$<br/></span> </div> | <div class="solution">Charge on capacitor at time $t$ is $q=q_0\left(1-e^{-t / \tau}\right)$<br/>$\begin{array}{ll}\text { Here, } & q_0=C V \text { and } t=2 \tau \\ \therefore & q=C V\left(1-e^{-2 \tau / \tau}\right)=C V\left(1-e^{-2}\right)\end{array}$</div> | MarksBatch2_P2.db |
762 | paragraph-the-capacitor-of-capacitance-c-can-be-charged-with-the-help-of-a-resistance-r-by-a-voltage-source-v-by-closing-switch-s-1-while-keeping-swit | paragraph-the-capacitor-of-capacitance-c-can-be-charged-with-the-help-of-a-resistance-r-by-a-voltage-source-v-by-closing-switch-s-1-while-keeping-swit-55687 | <div class="question"><strong>Paragraph:</strong><br/>The capacitor of capacitance $C$ can be charged (with the help of a resistance $R$ ) by a voltage source $V$, by closing switch $S_1$ while keeping switch $S_2$ open. The capacitor can be connected in series with an inductor $L$ by closing switch $S_2$ and opening $S_1$.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/0Y1I8mvhYVnowTpUifCLeg2xPE10yRn1Ap7tEzxaL24.original.fullsize.png"/><br/><strong>Question:</strong><br/>If the total charge stored in the $L C$ circuit is $Q_0$, then for $t \geq 0$</div> | ['Physics', 'Alternating Current', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>the charge on the capacitor is $Q=Q_0 \cos \left(\frac{\pi}{2}+\frac{t}{\sqrt{L C}}\right)$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>the charge on the capacitor is $Q=Q_0 \cos \left(\frac{\pi}{2}-\frac{t}{\sqrt{L C}}\right)$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>the charge on the capacitor is $Q=-L C \frac{d^2 Q}{d t^2}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>the charge on the capacitor is $Q=-\frac{1}{\sqrt{L C}} \frac{d^2 Q}{d t^2}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>the charge on the capacitor is $Q=-L C \frac{d^2 Q}{d t^2}$<br/></span> </div> | <div class="solution">Comparing the LC oscillations with normal SHM, we get<br/>$$<br/>\frac{d^2 Q}{d t^2}=-\omega^2 Q<br/>$$<br/>Here,<br/>$$<br/>\begin{aligned}<br/>\omega^2 & =\frac{1}{L C} \\<br/>Q & =-L C \frac{d^2 Q}{d t^2}<br/>\end{aligned}<br/>$$<br/>$$<br/>\therefore \quad Q=-L C \frac{d^2 Q}{d t^2}<br/>$$</div> | MarksBatch2_P2.db |
763 | paragraph-the-circle-x-2-y-2-8-x-0-and-hyperbola-9-x-2-4-y-2-1-intersect-at-the-points-a-and-b-question-equation-of-a-common-tangent-with-positive-slo | paragraph-the-circle-x-2-y-2-8-x-0-and-hyperbola-9-x-2-4-y-2-1-intersect-at-the-points-a-and-b-question-equation-of-a-common-tangent-with-positive-slo-19992 | <div class="question"><strong>Paragraph:</strong><br/>The circle $x^2+y^2-8 x=0$ and hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$ intersect at the points $A$ and $B$.<strong>Question:</strong><br/>Equation of a common tangent with positive slope to the circle as well as to the hyperbola is</div> | ['Mathematics', 'Hyperbola', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$2 x-\sqrt{5} y-20=0$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$2 x-\sqrt{5} y+4=0$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$3 x-4 y+8=0$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$4 x-3 y+4=0$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$2 x-\sqrt{5} y+4=0$<br/></span> </div> | <div class="solution">Equation of tangent to hyperbola having slope $m$ is<br/>$$<br/>y=m x+\sqrt{9 m^2-4}<br/>$$<br/>Equation of tangent to circle is<br/>$$<br/>y=m(x-4)+\sqrt{16 m^2+16}<br/>$$<br/>Eqs. (i) and (ii) will be identical for $m=\frac{2}{\sqrt{5}}$ satisfy.<br/>$\therefore$ Equation of common tangent is $2 x-\sqrt{5} y+4=0$</div> | MarksBatch2_P2.db |
764 | paragraph-the-circle-x-2-y-2-8-x-0-and-hyperbola-9-x-2-4-y-2-1-intersect-at-the-points-a-and-b-question-equation-of-the-circle-with-a-b-as-its-diamete | paragraph-the-circle-x-2-y-2-8-x-0-and-hyperbola-9-x-2-4-y-2-1-intersect-at-the-points-a-and-b-question-equation-of-the-circle-with-a-b-as-its-diamete-85278 | <div class="question"><strong>Paragraph:</strong><br/>The circle $x^2+y^2-8 x=0$ and hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$ intersect at the points $A$ and $B$.<strong>Question:</strong><br/>Equation of the circle with $A B$ as its diameter is</div> | ['Mathematics', 'Circle', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$x^2+y^2-12 x+24=0$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$x^2+y^2+12 x+24=0$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$x^2+y^2+24 x-12=0$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$x^2+y^2-24 x-12=0$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$x^2+y^2-12 x+24=0$<br/></span> </div> | <div class="solution">The equation of the hyperbola is $\frac{x^2}{9}-\frac{y^2}{4}=1$ and that of circle is<br/>$$<br/>x^2+y^2-8 x=0<br/>$$<br/>For their points of intersection<br/>$$<br/>\frac{x^2}{9}+\frac{x^2-8 x}{4}=1<br/>$$<br/><br/>$$<br/>\begin{array}{ll}<br/>\Rightarrow & 4 x^2+9 x^2-72 x=36 \\<br/>\Rightarrow & 13 x^2-72 x-36=0<br/>\end{array}<br/>$$<br/><br/>$$<br/>\begin{aligned}<br/>& \Rightarrow \quad 13 x^2-78 x+6 x-36=0 \\<br/>& \Rightarrow \quad 13 x(x-6)+6(x-6)=0 \\<br/>& \Rightarrow \quad x=6, x=-\frac{13}{6} \\<br/>& x=-\frac{13}{6} \text { not acceptable } \\<br/>&<br/>\end{aligned}<br/>$$<br/>Now, for $x=6, y=\pm 2 \sqrt{3}$<br/>Required equation is<br/>$$<br/>\begin{aligned}<br/>& (x-6)^2+(y+2 \sqrt{3})(y-2 \sqrt{3})=0 \\<br/>& \Rightarrow \quad x^2-12 x+y^2+24=0 \\<br/>& \Rightarrow \quad x^2+y^2-12 x+24=0<br/>\end{aligned}<br/>$$</div> | MarksBatch2_P2.db |
765 | paragraph-the-concentration-of-potassium-ions-inside-a-biological-cell-is-at-least-twenty-times-higher-than-the-outside-the-resulting-potential-differ-1 | paragraph-the-concentration-of-potassium-ions-inside-a-biological-cell-is-at-least-twenty-times-higher-than-the-outside-the-resulting-potential-differ-1-56820 | <div class="question"><strong>Paragraph:</strong><br/>The concentration of potassium ions inside a biological cell is at least twenty times higher than the outside. The resulting potential difference across the cell is important in several processes such as transmission of nerve impulses and maintaining the ion balance. A simple model for such a concentration cell involving a metal $\mathrm{M}$ is :<br/>$$<br/>M(s) \mid M^{+}(\alpha q ; 0.05 \text { molar }) \| M^{+}(a q ; 1 \text { molar }) \mid M(s)<br/>$$<br/>For the above electrolytic cell the magnitude of the cell potential $\left|E_{\text {cell }}\right|=70 \mathrm{mV}$.<strong>Question:</strong><br/>For the above cell</div> | ['Chemistry', 'Electrochemistry', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$E_{\text {cell }} < 0 ; \Delta G>0$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$E_{\text {cell }}>0 ; \Delta G < 0$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$E_{\text {cell }} < 0 ; \Delta G^{\circ}>0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$E_{\text {cell }}>0 ; \Delta G^{\circ} < 0$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$E_{\text {cell }}>0 ; \Delta G < 0$</span> </div> | <div class="solution">The given cell is electrolytic concentration cell, So $E_{\text {cell }}^{\circ}=0$<br/>Anode :<br/>$$<br/>\begin{gathered}<br/>M(s) \longrightarrow M^{+}(a q)+e^{-} \\<br/>\text {Cathode }: \quad M^{+}(a q)+e^{-} \longrightarrow M(s) \\<br/>\hline M^{+}(a q) \text { cathode } \rightleftharpoons M^{+}(a q) \text { anode } \\<br/>E_{\text {cell }}=E_{\text {cell }}^{\circ}-\frac{0.0591}{1} \log \frac{\left[M^{+}\right]_{\text {anodic }}}{\left[M^{+}\right]_{\text {cathodic }}} \\<br/>=0-\frac{0.0591}{1} \log \frac{0.05}{1} \\<br/>E_{\text {cell }}=70 \mathrm{mV}(+\text { ve }) \\<br/>\text { Hence, } \Delta G=-n F E_{\text {cell }}=-\text { ve }<br/>\end{gathered}<br/>$$</div> | MarksBatch2_P2.db |
766 | paragraph-the-concentration-of-potassium-ions-inside-a-biological-cell-is-at-least-twenty-times-higher-than-the-outside-the-resulting-potential-differ | paragraph-the-concentration-of-potassium-ions-inside-a-biological-cell-is-at-least-twenty-times-higher-than-the-outside-the-resulting-potential-differ-54443 | <div class="question"><strong>Paragraph:</strong><br/>The concentration of potassium ions inside a biological cell is at least twenty times higher than the outside. The resulting potential difference across the cell is important in several processes such as transmission of nerve impulses and maintaining the ion balance. A simple model for such a concentration cell involving a metal $\mathrm{M}$ is :<br/>$$<br/>M(s) \mid M^{+}(\alpha q ; 0.05 \text { molar }) \| M^{+}(a q ; 1 \text { molar }) \mid M(s)<br/>$$<br/>For the above electrolytic cell the magnitude of the cell potential $\left|E_{\text {cell }}\right|=70 \mathrm{mV}$.<strong>Question:</strong><br/>If the $0.05$ molar solution of $M^{+}$is replaced by a $0.0025$ molar $M^{+}$ solution, then the magnitude of the cell potential would be</div> | ['Chemistry', 'Electrochemistry', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$35 \mathrm{mV}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$70 \mathrm{mV}$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$140 \mathrm{mV}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$700 \mathrm{mV}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$140 \mathrm{mV}$<br/></span> </div> | <div class="solution">$E_{\text {cell }}=E_{\text {cell }}^{\circ}-\frac{0.0591}{1} \log \frac{0.0025}{1}$ $E_{\text {cell }}=140 \mathrm{mV}$ Electrochemistry Straight conceptual III</div> | MarksBatch2_P2.db |
767 | paragraph-the-coordination-number-of-ni-2-is-4-nicl-2-kcn-excess-a-cyano-complex-nicl-2-conc-hcl-excess-b-chloro-complex-question-predict-the-magnetic-1 | paragraph-the-coordination-number-of-ni-2-is-4-nicl-2-kcn-excess-a-cyano-complex-nicl-2-conc-hcl-excess-b-chloro-complex-question-predict-the-magnetic-1-50011 | <div class="question"><strong>Paragraph:</strong><br/>The coordination number of $\mathrm{Ni}^{2+}$ is 4 .<br/>$\mathrm{NiCl}_2+\mathrm{KCN}$ (excess) $\rightarrow A$ (cyano complex)<br/>$\mathrm{NiCl}_2+$ conc. $\mathrm{HCl}$ (excess) $\rightarrow B$ (chloro complex)<strong>Question:</strong><br/>Predict the magnetic nature of $A$ and $B$ are</div> | ['Chemistry', 'Coordination Compounds', 'JEE Main'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>both are diamagnetic<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$A$ is diamagnetic and $B$ is paramagnetic with one unpaired electron<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$A$ is diamagnetic and $B$ is paramagnetic with two unpaired electrons<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>both are paramagnetic</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$A$ is diamagnetic and $B$ is paramagnetic with two unpaired electrons<br/></span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/bxniP2faO05oymhcV10_WdIk3gLHeD2fmQyg8NeBIyg.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/tnP_t0NK4QmcgilDBfKM3tt5vf6rtViHlqmfSkxpHDE.original.fullsize.png"/><br/><br/>In it unpaired orbital is not present, so it is diamagnetic in character (square planar shape) In chloro complex $\mathrm{K}_2\left[\mathrm{Ni}(\mathrm{Cl})_4\right]$, complex ion is $\left[\mathrm{Ni}^2\left(\mathrm{Cl}_4\right)\right]^{2-}$ and $\mathrm{Ni}$ is present $\mathrm{Ni}^{2+}$ or $\mathrm{Ni}(\mathrm{II})$, so<br/>$$<br/>\mathrm{Ni}^2+=1 s^2, 2 s^2 2 p^6, 3 s^2 3 p^6 3 d^8, 4 s^0<br/>$$<br/>In $\left.\left[\mathrm{Ni}_{\left(\mathrm{Cl}_4\right)}\right)\right]^2$ ion, $\mathrm{Ni}^{2+}$ is present as follows due to weaker ligand character is $\mathrm{Cl}^{-}$ion. $\left(\mathrm{Cl}^{-}\right.$is weak field ligand). So, it is unable to pair up the electron and $\mathrm{Ni}^{2+}$ needs four empty orbitals to accommodate four $\mathrm{Cl}^{-}$ligand. Thus, $\left(\mathrm{NiCl}_4\right)^{2-}$ shows $s p^3$-hybridisation (Tetrahedral shapes)<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/VMTOLX6FBBnXc5tD6S5F5HPhSdWbXV3aR3-3XVqDn38.original.fullsize.png"/><br/><br/>Hence, due to presence of unpaired orbitals, it is paramagnetic in character.</div> | MarksBatch2_P2.db |
768 | paragraph-the-coordination-number-of-ni-2-is-4-nicl-2-kcn-excess-a-cyano-complex-nicl-2-conc-hcl-excess-b-chloro-complex-question-predict-the-magnetic | paragraph-the-coordination-number-of-ni-2-is-4-nicl-2-kcn-excess-a-cyano-complex-nicl-2-conc-hcl-excess-b-chloro-complex-question-predict-the-magnetic-49674 | <div class="question"><strong>Paragraph:</strong><br/>The coordination number of $\mathrm{Ni}^{2+}$ is 4 .<br/>$\mathrm{NiCl}_2+\mathrm{KCN}$ (excess) $\rightarrow A$ (cyano complex)<br/>$\mathrm{NiCl}_2+$ conc. $\mathrm{HCl}$ (excess) $\rightarrow B$ (chloro complex)<strong>Question:</strong><br/>Predict the magnetic nature of $A$ and $B$ are</div> | ['Chemistry', 'Coordination Compounds', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>both are diamagnetic<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$A$ is diamagnetic and $B$ is paramagnetic with one unpaired electron<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$A$ is diamagnetic and $B$ is paramagnetic with two unpaired electrons<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>both are paramagnetic</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$A$ is diamagnetic and $B$ is paramagnetic with two unpaired electrons<br/></span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/bxniP2faO05oymhcV10_WdIk3gLHeD2fmQyg8NeBIyg.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/tnP_t0NK4QmcgilDBfKM3tt5vf6rtViHlqmfSkxpHDE.original.fullsize.png"/><br/><br/>In it unpaired orbital is not present, so it is diamagnetic in character (square planar shape) In chloro complex $\mathrm{K}_2\left[\mathrm{Ni}(\mathrm{Cl})_4\right]$, complex ion is $\left[\mathrm{Ni}^2\left(\mathrm{Cl}_4\right)\right]^{2-}$ and $\mathrm{Ni}$ is present $\mathrm{Ni}^{2+}$ or $\mathrm{Ni}(\mathrm{II})$, so<br/>$$<br/>\mathrm{Ni}^2+=1 s^2, 2 s^2 2 p^6, 3 s^2 3 p^6 3 d^8, 4 s^0<br/>$$<br/>In $\left.\left[\mathrm{Ni}_{\left(\mathrm{Cl}_4\right)}\right)\right]^2$ ion, $\mathrm{Ni}^{2+}$ is present as follows due to weaker ligand character is $\mathrm{Cl}^{-}$ion. $\left(\mathrm{Cl}^{-}\right.$is weak field ligand). So, it is unable to pair up the electron and $\mathrm{Ni}^{2+}$ needs four empty orbitals to accommodate four $\mathrm{Cl}^{-}$ligand. Thus, $\left(\mathrm{NiCl}_4\right)^{2-}$ shows $s p^3$-hybridisation (Tetrahedral shapes)<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/VMTOLX6FBBnXc5tD6S5F5HPhSdWbXV3aR3-3XVqDn38.original.fullsize.png"/><br/><br/>Hence, due to presence of unpaired orbitals, it is paramagnetic in character.</div> | MarksBatch2_P2.db |
769 | paragraph-the-coordination-number-of-ni-2-is-4-nicl-2-kcn-excess-a-cyano-complex-nicl-2-conc-hcl-excess-b-chloro-complex-question-the-hybridization-of | paragraph-the-coordination-number-of-ni-2-is-4-nicl-2-kcn-excess-a-cyano-complex-nicl-2-conc-hcl-excess-b-chloro-complex-question-the-hybridization-of-12331 | <div class="question"><strong>Paragraph:</strong><br/>The coordination number of $\mathrm{Ni}^{2+}$ is 4 .<br/>$\mathrm{NiCl}_2+\mathrm{KCN}$ (excess) $\rightarrow A$ (cyano complex)<br/>$\mathrm{NiCl}_2+$ conc. $\mathrm{HCl}$ (excess) $\rightarrow B$ (chloro complex)<strong>Question:</strong><br/>The hybridization of $A$ and $B$ are</div> | ['Chemistry', 'Coordination Compounds', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$d s p^2, s p^3$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$s p^3, s p^3$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$d s p^2, d s p^2$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$s p^3 d^2, d^2 s p^3$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$d s p^2, s p^3$<br/></span> </div> | <div class="solution">Hybridisation of $\mathrm{Ni}$ in $\mathrm{K}_2\left[\mathrm{Ni}(\mathrm{CN})_4\right]$ is $d s p^2$ and in $\mathrm{K}_2\left[\mathrm{Ni}^2\left(\mathrm{Cl}_4\right)\right]$ is $s p^3$ (Detail see in question no. 25).</div> | MarksBatch2_P2.db |
770 | paragraph-the-coordination-number-of-ni-2-is-4-nicl-2-kcn-excess-a-cyano-complex-nicl-2-conc-hcl-excess-b-chloro-complex-question-the-iupac-name-of-a--1 | paragraph-the-coordination-number-of-ni-2-is-4-nicl-2-kcn-excess-a-cyano-complex-nicl-2-conc-hcl-excess-b-chloro-complex-question-the-iupac-name-of-a-1-52023 | <div class="question"><strong>Paragraph:</strong><br/>The coordination number of $\mathrm{Ni}^{2+}$ is 4 .<br/>$\mathrm{NiCl}_2+\mathrm{KCN}$ (excess) $\rightarrow A$ (cyano complex)<br/>$\mathrm{NiCl}_2+$ conc. $\mathrm{HCl}$ (excess) $\rightarrow B$ (chloro complex)<strong>Question:</strong><br/>The IUPAC name of $A$ and $B$ are</div> | ['Chemistry', 'Coordination Compounds', 'JEE Main'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>Potassium tetracyanonickelate (II), potassium tetrachloronickelate (II)<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Tetracyanopotassiumnickelate (II), tetrorachloropotassiumnickelate (II)<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Tetracyanonickel (II), tetrachloronickel (II)<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Potassium tetracyanonickel (II), potassium tetrachloronickel (II)</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Potassium tetracyanonickelate (II), potassium tetrachloronickelate (II)<br/></span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Bn02GMAdWZA8GFgxTA7dU8trtiKgKX_w7sLhSq02ZGE.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
771 | paragraph-the-coordination-number-of-ni-2-is-4-nicl-2-kcn-excess-a-cyano-complex-nicl-2-conc-hcl-excess-b-chloro-complex-question-the-iupac-name-of-a- | paragraph-the-coordination-number-of-ni-2-is-4-nicl-2-kcn-excess-a-cyano-complex-nicl-2-conc-hcl-excess-b-chloro-complex-question-the-iupac-name-of-a-87176 | <div class="question"><strong>Paragraph:</strong><br/>The coordination number of $\mathrm{Ni}^{2+}$ is 4 .<br/>$\mathrm{NiCl}_2+\mathrm{KCN}$ (excess) $\rightarrow A$ (cyano complex)<br/>$\mathrm{NiCl}_2+$ conc. $\mathrm{HCl}$ (excess) $\rightarrow B$ (chloro complex)<strong>Question:</strong><br/>The IUPAC name of $A$ and $B$ are</div> | ['Chemistry', 'Coordination Compounds', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>Potassium tetracyanonickelate (II), potassium tetrachloronickelate (II)<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Tetracyanopotassiumnickelate (II), tetrorachloropotassiumnickelate (II)<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Tetracyanonickel (II), tetrachloronickel (II)<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Potassium tetracyanonickel (II), potassium tetrachloronickel (II)</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Potassium tetracyanonickelate (II), potassium tetrachloronickelate (II)<br/></span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Bn02GMAdWZA8GFgxTA7dU8trtiKgKX_w7sLhSq02ZGE.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
772 | paragraph-the-figure-shows-a-surface-x-y-separating-two-transparent-media-medium1-and-medium2-the-lines-ab-and-c-d-represent-wavefronts-of-a-light-wav-1 | paragraph-the-figure-shows-a-surface-x-y-separating-two-transparent-media-medium1-and-medium2-the-lines-ab-and-c-d-represent-wavefronts-of-a-light-wav-1-93050 | <div class="question"><strong>Paragraph:</strong><br/>The figure shows a surface $X Y$ separating two transparent media, medium-1 and medium-2. The lines $a b$ and $c d$ represent wavefronts of a light wave travelling in medium-1 and incident on $X Y$. The lines ef and $g h$ represent wavefronts of the light wave in medium-2 after refraction.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/tm_QoNKNACdV0vkT1URUx9Z9uiV2_apI_Zxl1TkT2TA.original.fullsize.png"/><br/><strong>Question:</strong><br/>Light travels as a</div> | ['Physics', 'Ray Optics', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>parallel beam in each medium<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>convergent beam in each medium<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>divergent beam in each medium<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>divergent beam in one medium and convergent beam in the other medium</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>parallel beam in each medium<br/></span> </div> | <div class="solution">Wavefronts are parallel in both media. Therefore, light which is perpendicular to wavefront travels as a parallel beam in each medium. Hence, the correct option is (a).</div> | MarksBatch2_P2.db |
773 | paragraph-the-figure-shows-a-surface-x-y-separating-two-transparent-media-medium1-and-medium2-the-lines-ab-and-c-d-represent-wavefronts-of-a-light-wav-2 | paragraph-the-figure-shows-a-surface-x-y-separating-two-transparent-media-medium1-and-medium2-the-lines-ab-and-c-d-represent-wavefronts-of-a-light-wav-2-27371 | <div class="question"><strong>Paragraph:</strong><br/>The figure shows a surface $X Y$ separating two transparent media, medium-1 and medium-2. The lines $a b$ and $c d$ represent wavefronts of a light wave travelling in medium-1 and incident on $X Y$. The lines ef and $g h$ represent wavefronts of the light wave in medium-2 after refraction.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/tm_QoNKNACdV0vkT1URUx9Z9uiV2_apI_Zxl1TkT2TA.original.fullsize.png"/><br/><strong>Question:</strong><br/>The phases of the light wave at $c, d, e$ and $f$ are $\phi_c, \phi_d, \phi_e$ and $\phi_f$, respectively. It is given that $\phi_c \neq \phi_f$.</div> | ['Physics', 'Ray Optics', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\phi_c$ cannot be equal to $\phi_d$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\phi_d$ can be equal to $\phi_e$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\left(\phi_d-\phi_f\right)$ is equal to $\left(\phi_c-\phi_e\right)$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\left(\phi_d-\phi_c\right)$ is not equal to $\left(\phi_f-\phi_e\right)$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\left(\phi_d-\phi_f\right)$ is equal to $\left(\phi_c-\phi_e\right)$<br/></span> </div> | <div class="solution">All points on a wavefront are at the same phase.<br/>$$<br/>\begin{array}{rlrl}<br/>\therefore & \phi_d & =\phi_c \text { and } \phi_f=\phi_e \\<br/>& \therefore & \phi_d-\phi_f & =\phi_c-\phi_e<br/>\end{array}<br/>$$<br/>Hence, the correct option is (c).</div> | MarksBatch2_P2.db |
774 | paragraph-the-figure-shows-a-surface-x-y-separating-two-transparent-media-medium1-and-medium2-the-lines-ab-and-c-d-represent-wavefronts-of-a-light-wav | paragraph-the-figure-shows-a-surface-x-y-separating-two-transparent-media-medium1-and-medium2-the-lines-ab-and-c-d-represent-wavefronts-of-a-light-wav-77246 | <div class="question"><strong>Paragraph:</strong><br/>The figure shows a surface $X Y$ separating two transparent media, medium-1 and medium-2. The lines $a b$ and $c d$ represent wavefronts of a light wave travelling in medium-1 and incident on $X Y$. The lines ef and $g h$ represent wavefronts of the light wave in medium-2 after refraction.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/tm_QoNKNACdV0vkT1URUx9Z9uiV2_apI_Zxl1TkT2TA.original.fullsize.png"/><br/><strong>Question:</strong><br/>Speed of light is</div> | ['Physics', 'Ray Optics', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>the same in medium-1 and medium-2<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>larger in medium-1 than in medium-2<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>larger in medium-2 than in medium-1<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>different at $b$ and $d$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>larger in medium-1 than in medium-2<br/></span> </div> | <div class="solution">In medium-2 wavefront bends away from the normal after refraction. Therefore, ray of light which is perpendicular to wavefront bends towards the normal in medium-2 during refraction. So, medium-2 is denser or its speed in medium-1 is more. Hence, option (b) is correct.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/kmERJkMOW5BgYYxAZ08NF8h5YO7pGDXY_swArSgnZ38.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
775 | paragraph-the-hydrogenlike-species-li-2-is-in-a-spherically-symmetric-state-s-1-with-one-radial-node-upon-absorbing-light-the-ion-undergoes-transition-1 | paragraph-the-hydrogenlike-species-li-2-is-in-a-spherically-symmetric-state-s-1-with-one-radial-node-upon-absorbing-light-the-ion-undergoes-transition-1-24930 | <div class="question"><strong>Paragraph:</strong><br/>The hydrogen-like species $\mathrm{Li}^{2+}$ is in a spherically symmetric state $S_1$ with one radial node. Upon absorbing light the ion undergoes transition to a state $S_2$. The state $S_2$ has one radial node and its energy is equal to the ground state energy of the hydrogen atom.<strong>Question:</strong><br/>The state $S_1$ is</div> | ['Chemistry', 'Structure of Atom', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$1 s$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$2 \mathrm{~s}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$2 p$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$3 \mathrm{~s}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$2 \mathrm{~s}$<br/></span> </div> | <div class="solution">Given : Hydrogen like species, $\mathrm{Li}^{2+}$<br/>Spherically symmetric state, $S_1 \Rightarrow s$-orbital<br/>$S_1$ has radial node $1 \Rightarrow 2 s \quad$ (No. of radial node $=1=n-l-1$, so $n=2$ ) Species undergoes state $S_2$<br/>$S_2$ has energy equal to the ground state energy of $\mathrm{H}$-atom $=-13.6 \mathrm{eV}$<br/>So, $\quad-13.6=-13.6\left(\frac{3^2}{n^2}\right)$<br/>$n=3$<br/>Again radial node $=1=n-1-1$<br/>or $1=3-l-1 \quad$ so $\quad l=1$<br/>It suggests $S_2$ is $3 p$</div> | MarksBatch2_P2.db |
776 | paragraph-the-hydrogenlike-species-li-2-is-in-a-spherically-symmetric-state-s-1-with-one-radial-node-upon-absorbing-light-the-ion-undergoes-transition-2 | paragraph-the-hydrogenlike-species-li-2-is-in-a-spherically-symmetric-state-s-1-with-one-radial-node-upon-absorbing-light-the-ion-undergoes-transition-2-78778 | <div class="question"><strong>Paragraph:</strong><br/>The hydrogen-like species $\mathrm{Li}^{2+}$ is in a spherically symmetric state $S_1$ with one radial node. Upon absorbing light the ion undergoes transition to a state $S_2$. The state $S_2$ has one radial node and its energy is equal to the ground state energy of the hydrogen atom.<strong>Question:</strong><br/>The orbtial angular momentum quantum number of the state $S_2$ is</div> | ['Chemistry', 'Structure of Atom', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>0<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>1<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>2<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>3</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>1<br/></span> </div> | <div class="solution">For $p$-orbital, orbital angular momentum quantum number $=1$ Atomic structure Conceptual data analysis IV</div> | MarksBatch2_P2.db |
777 | paragraph-the-hydrogenlike-species-li-2-is-in-a-spherically-symmetric-state-s-1-with-one-radial-node-upon-absorbing-light-the-ion-undergoes-transition | paragraph-the-hydrogenlike-species-li-2-is-in-a-spherically-symmetric-state-s-1-with-one-radial-node-upon-absorbing-light-the-ion-undergoes-transition-53790 | <div class="question"><strong>Paragraph:</strong><br/>The hydrogen-like species $\mathrm{Li}^{2+}$ is in a spherically symmetric state $S_1$ with one radial node. Upon absorbing light the ion undergoes transition to a state $S_2$. The state $S_2$ has one radial node and its energy is equal to the ground state energy of the hydrogen atom.<strong>Question:</strong><br/>Energy of the state $S_1$ in units of the hydrogen atom ground state energy is</div> | ['Chemistry', 'Structure of Atom', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$0.75$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$1.50$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$2.25$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$4.50$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$2.25$<br/></span> </div> | <div class="solution">Energy of state, $S_1=-13.6\left(\frac{3^2}{2^2}\right) \mathrm{eV} /$ atom $=\frac{9}{4}$ of energy of $\mathrm{H}$-atom in ground state $=2.25$ of energy of $\mathrm{H}$-atom in ground state</div> | MarksBatch2_P2.db |
778 | paragraph-the-key-feature-of-bohrs-theory-of-spectrum-of-hydrogen-atom-is-the-quantization-of-angular-momentum-when-an-electron-is-revolving-around-a--1 | paragraph-the-key-feature-of-bohrs-theory-of-spectrum-of-hydrogen-atom-is-the-quantization-of-angular-momentum-when-an-electron-is-revolving-around-a-1-54595 | <div class="question"><strong>Paragraph:</strong><br/>The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr's quantization condition.<strong>Question:</strong><br/>In a CO molecule, the distance between $\mathrm{C}$ (mass $=12 \mathrm{amu}$ ) and $\mathrm{O}$ (mass = $16 \mathrm{amu}$ ), where $1 \mathrm{amu}=\frac{5}{3} \times 10^{-27} \mathrm{~kg}$, is close to</div> | ['Physics', 'Atomic Physics', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$2.4 \times 10^{-10} \mathrm{~m}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$1.9 \times 10^{-10} \mathrm{~m}$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$1.3 \times 10^{-10} \mathrm{~m}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$4.4 \times 10^{-11} \mathrm{~m}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$1.3 \times 10^{-10} \mathrm{~m}$<br/></span> </div> | <div class="solution">$I=\mu r^2$ ( where $\mu=$ reduced mass) $\mu=\frac{m_1 m_2}{m_1+m_2}=\frac{48}{7} \mathrm{amu}$ $=11.43 \times 10^{-27} \mathrm{~kg}$<br/>Substituting in $I=\mu r^2$ we get,<br/>$$<br/>\begin{aligned}<br/>r & =\sqrt{\frac{I}{\mu}}=\sqrt{\frac{1.87 \times 10^{-46}}{11.43 \times 10^{-27}}} \\<br/>& =1.28 \times 10^{-10} \mathrm{~m}<br/>\end{aligned}<br/>$$<br/>$\therefore$ The correct answer is (c).</div> | MarksBatch2_P2.db |
779 | paragraph-the-key-feature-of-bohrs-theory-of-spectrum-of-hydrogen-atom-is-the-quantization-of-angular-momentum-when-an-electron-is-revolving-around-a--2 | paragraph-the-key-feature-of-bohrs-theory-of-spectrum-of-hydrogen-atom-is-the-quantization-of-angular-momentum-when-an-electron-is-revolving-around-a-2-94332 | <div class="question"><strong>Paragraph:</strong><br/>The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr's quantization condition.<strong>Question:</strong><br/>It is found that the excitation frequency from ground to the first excited state of rotation for the $\mathrm{CO}$ molecule is close to $\frac{4}{\pi} \times 10^{11} \mathrm{~Hz}$. Then the moment of inertia of CO molecule about its centre of mass is close to (Take $h=2 \pi \times 10^{-34} J-s$ )</div> | ['Physics', 'Atomic Physics', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$2.76 \times 10^{-46} \mathrm{~kg}-\mathrm{m}^2$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$1.87 \times 10^{-46} \mathrm{~kg}-\mathrm{m}^2$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$4.67 \times 10^{-47} \mathrm{~kg}-\mathrm{m}^2$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$1.17 \times 10^{-47} \mathrm{~kg}-\mathrm{m}^2$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$1.87 \times 10^{-46} \mathrm{~kg}-\mathrm{m}^2$<br/></span> </div> | <div class="solution">$$<br/>\begin{gathered}<br/>h v=K_2-K_1=\frac{3 h^2}{8 \pi^2 I} \\<br/>\therefore I=\frac{3 h}{8 \pi^2 f}=\frac{3 \times 2 \pi \times 10^{-34} \times \pi}{8 \times \pi^2 \times 4 \times 10^{11}}<br/>\end{gathered}<br/>$$<br/>$$<br/>=1.87 \times 10^{-46} \mathrm{~kg}-\mathrm{m}^2<br/>$$<br/>$\therefore$ The correct answer is (b).</div> | MarksBatch2_P2.db |
780 | paragraph-the-key-feature-of-bohrs-theory-of-spectrum-of-hydrogen-atom-is-the-quantization-of-angular-momentum-when-an-electron-is-revolving-around-a- | paragraph-the-key-feature-of-bohrs-theory-of-spectrum-of-hydrogen-atom-is-the-quantization-of-angular-momentum-when-an-electron-is-revolving-around-a-14575 | <div class="question"><strong>Paragraph:</strong><br/>The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr's quantization condition.<strong>Question:</strong><br/>A diatomic molecule has moment of inertia I. By Bohr's quantization condition its rotational energy in the $n$th level ( $n=0$ is not allowed) is</div> | ['Physics', 'Atomic Physics', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{1}{n^2}\left(\frac{h^2}{8 \pi^2 I}\right)$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{1}{n}\left(\frac{h^2}{8 \pi^2 I}\right)$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$n\left(\frac{h^2}{8 \pi^2 I}\right)$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$n^2\left(\frac{h^2}{8 \pi^2 I}\right)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$n^2\left(\frac{h^2}{8 \pi^2 I}\right)$</span> </div> | <div class="solution">$$<br/>\begin{aligned}<br/>L=I \omega & =\frac{n h}{2 \pi} \therefore \omega=\frac{n h}{2 \pi I} \\<br/>K & =\frac{1}{2} I \omega^2=\frac{1}{2} I\left(\frac{n h}{2 \pi I}\right)^2 \\<br/>& =\frac{n^2 h^2}{8 \pi^2 I}<br/>\end{aligned}<br/>$$<br/>$\therefore$ The correct answer is (d).</div> | MarksBatch2_P2.db |
781 | paragraph-the-noble-gases-have-closedshell-electronic-configuration-and-are-monoatomic-gases-under-normal-conditions-the-low-boiling-points-of-the-lig-1 | paragraph-the-noble-gases-have-closedshell-electronic-configuration-and-are-monoatomic-gases-under-normal-conditions-the-low-boiling-points-of-the-lig-1-76653 | <div class="question"><strong>Paragraph:</strong><br/>The noble gases have closed-shell electronic configuration and are monoatomic gases under normal conditions. The low boiling points of the lighter noble gases are due to weak dispersion forces between the atoms and the absence of other interatomic interactions.<br/>The direct reaction of xenon with fluorine leads to a series of compounds with oxidation numbers $+2,+4$ and $+6 . \mathrm{XeF}_4$ reacts violently with water to give $\mathrm{XeO}_3$. The compounds of xenon exhibit rich stereochemistry and their geometries can be deduced considering the total number of electron pairs in the valence shell.<strong>Question:</strong><br/>Argon is used in are welding because of its</div> | ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>low reactivity with metal<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>ability to lower the melting point of metal<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>flammability<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>high calorific value</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>low reactivity with metal<br/></span> </div> | <div class="solution">Argon is used in arc welding to cause the inert atmosphere around without interaction with metal.</div> | MarksBatch2_P2.db |
782 | paragraph-the-noble-gases-have-closedshell-electronic-configuration-and-are-monoatomic-gases-under-normal-conditions-the-low-boiling-points-of-the-lig-2 | paragraph-the-noble-gases-have-closedshell-electronic-configuration-and-are-monoatomic-gases-under-normal-conditions-the-low-boiling-points-of-the-lig-2-24083 | <div class="question"><strong>Paragraph:</strong><br/>The noble gases have closed-shell electronic configuration and are monoatomic gases under normal conditions. The low boiling points of the lighter noble gases are due to weak dispersion forces between the atoms and the absence of other interatomic interactions.<br/>The direct reaction of xenon with fluorine leads to a series of compounds with oxidation numbers $+2,+4$ and $+6 . \mathrm{XeF}_4$ reacts violently with water to give $\mathrm{XeO}_3$. The compounds of xenon exhibit rich stereochemistry and their geometries can be deduced considering the total number of electron pairs in the valence shell.<strong>Question:</strong><br/>The structure of $\mathrm{XeO}_3$ is</div> | ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>linear<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>planar<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>pyramidal<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$T$-shaped</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>pyramidal<br/></span> </div> | <div class="solution">$\mathrm{XeO}_3$ total $e^{-}$pairs $=4(3 p b+1 l p)$ $s p^3$-hybridisation $\Rightarrow$ pyramidal shape.</div> | MarksBatch2_P2.db |
783 | paragraph-the-noble-gases-have-closedshell-electronic-configuration-and-are-monoatomic-gases-under-normal-conditions-the-low-boiling-points-of-the-lig | paragraph-the-noble-gases-have-closedshell-electronic-configuration-and-are-monoatomic-gases-under-normal-conditions-the-low-boiling-points-of-the-lig-29621 | <div class="question"><strong>Paragraph:</strong><br/>The noble gases have closed-shell electronic configuration and are monoatomic gases under normal conditions. The low boiling points of the lighter noble gases are due to weak dispersion forces between the atoms and the absence of other interatomic interactions.<br/>The direct reaction of xenon with fluorine leads to a series of compounds with oxidation numbers $+2,+4$ and $+6 . \mathrm{XeF}_4$ reacts violently with water to give $\mathrm{XeO}_3$. The compounds of xenon exhibit rich stereochemistry and their geometries can be deduced considering the total number of electron pairs in the valence shell.<strong>Question:</strong><br/>$\mathrm{XeF}_4$ and $\mathrm{XeF}_6$ are expected to be</div> | ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>oxidising<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>reducing<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>unreactive<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>strongly basic</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>oxidising<br/></span> </div> | <div class="solution">$\mathrm{XeF}_4$ oxidises potassium iodide<br/>$$<br/>\mathrm{XeF}_4+4 \mathrm{I}^{-} \longrightarrow 2 \mathrm{I}_2+4 \mathrm{~F}^{-1}+\mathrm{Xe}<br/>$$<br/>$\mathrm{XeF}_6$ oxidises hydrogen like other xenon fluorides.</div> | MarksBatch2_P2.db |
784 | paragraph-the-nuclear-charge-ze-is-nonuniformly-distributed-within-a-nucleus-of-radius-r-the-charge-density-r-charge-per-unit-volume-is-dependent-only-1 | paragraph-the-nuclear-charge-ze-is-nonuniformly-distributed-within-a-nucleus-of-radius-r-the-charge-density-r-charge-per-unit-volume-is-dependent-only-1-20772 | <div class="question"><strong>Paragraph:</strong><br/>The nuclear charge $(\mathrm{Ze})$ is non-uniformly distributed within a nucleus of radius $R$. The charge density $\rho(r)$ [charge per unit volume] is dependent only on the radial distance $r$ from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/jlFKxAkJt_03DKXWqhIFlKSRLGpw3OZjlz0a8gNGa4M.original.fullsize.png"/><br/><strong>Question:</strong><br/>The electric field within the nucleus is generally observed to be linearly dependent on $r$. This implies</div> | ['Physics', 'Electrostatics', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$a=0$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$a=\frac{R}{2}$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$a=R$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$a=\frac{2 R}{3}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$a=R$<br/></span> </div> | <div class="solution">In case of solid sphere of charge of uniform volume density.<br/>$$<br/>E=\frac{1}{4 \pi \varepsilon_0} \cdot \frac{q}{R^3} \cdot r \text { or } E \propto r<br/>$$<br/>Thus, for $E$ to be linearly dependent on $r$, volume charge density should be constant.<br/>or $\quad a=R$<br/>$\therefore$ correct option is (c).<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/VsVVtDqMKnBK3h17v1qy70Lf_sV00VrHsuOzxggW71w.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
785 | paragraph-the-nuclear-charge-ze-is-nonuniformly-distributed-within-a-nucleus-of-radius-r-the-charge-density-r-charge-per-unit-volume-is-dependent-only-2 | paragraph-the-nuclear-charge-ze-is-nonuniformly-distributed-within-a-nucleus-of-radius-r-the-charge-density-r-charge-per-unit-volume-is-dependent-only-2-13276 | <div class="question"><strong>Paragraph:</strong><br/>The nuclear charge $(\mathrm{Ze})$ is non-uniformly distributed within a nucleus of radius $R$. The charge density $\rho(r)$ [charge per unit volume] is dependent only on the radial distance $r$ from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/jlFKxAkJt_03DKXWqhIFlKSRLGpw3OZjlz0a8gNGa4M.original.fullsize.png"/><br/><strong>Question:</strong><br/>The electric field at $r=R$ is</div> | ['Physics', 'Electrostatics', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>independent of $a$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>directly proportional to $a$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>directly proportional to $a^2$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>inversely proportional to $a$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>independent of $a$<br/></span> </div> | <div class="solution">At $r=R$, from Gauss's law<br/>or<br/>$$<br/>\begin{aligned}<br/>E\left(4 \pi R^2\right) & =\frac{q_{\text {net }}}{\varepsilon_0}=\frac{Z e}{\varepsilon_0} \\<br/>E & =\frac{1}{4 \pi \varepsilon_0} \cdot \frac{Z e}{R^2}<br/>\end{aligned}<br/>$$<br/>$E$ is independent of ' $a$ '<br/>$\therefore$ correct option is (a).</div> | MarksBatch2_P2.db |
786 | paragraph-the-nuclear-charge-ze-is-nonuniformly-distributed-within-a-nucleus-of-radius-r-the-charge-density-r-charge-per-unit-volume-is-dependent-only-3 | paragraph-the-nuclear-charge-ze-is-nonuniformly-distributed-within-a-nucleus-of-radius-r-the-charge-density-r-charge-per-unit-volume-is-dependent-only-3-17566 | <div class="question"><strong>Paragraph:</strong><br/>The nuclear charge $(\mathrm{Ze})$ is non-uniformly distributed within a nucleus of radius $R$. The charge density $\rho(r)$ [charge per unit volume] is dependent only on the radial distance $r$ from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/jlFKxAkJt_03DKXWqhIFlKSRLGpw3OZjlz0a8gNGa4M.original.fullsize.png"/><br/><strong>Question:</strong><br/>The electric field at $r=R$ is</div> | ['Physics', 'Electrostatics', 'JEE Main'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>independent of $a$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>directly proportional to $a$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>directly proportional to $a^2$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>inversely proportional to $a$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>independent of $a$<br/></span> </div> | <div class="solution">At $r=R$, from Gauss's law<br/>or<br/>$$<br/>\begin{aligned}<br/>E\left(4 \pi R^2\right) & =\frac{q_{\text {net }}}{\varepsilon_0}=\frac{Z e}{\varepsilon_0} \\<br/>E & =\frac{1}{4 \pi \varepsilon_0} \cdot \frac{Z e}{R^2}<br/>\end{aligned}<br/>$$<br/>$E$ is independent of ' $a$ '<br/>$\therefore$ correct option is (a).</div> | MarksBatch2_P2.db |
787 | paragraph-the-nuclear-charge-ze-is-nonuniformly-distributed-within-a-nucleus-of-radius-r-the-charge-density-r-charge-per-unit-volume-is-dependent-only | paragraph-the-nuclear-charge-ze-is-nonuniformly-distributed-within-a-nucleus-of-radius-r-the-charge-density-r-charge-per-unit-volume-is-dependent-only-69092 | <div class="question"><strong>Paragraph:</strong><br/>The nuclear charge $(\mathrm{Ze})$ is non-uniformly distributed within a nucleus of radius $R$. The charge density $\rho(r)$ [charge per unit volume] is dependent only on the radial distance $r$ from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/jlFKxAkJt_03DKXWqhIFlKSRLGpw3OZjlz0a8gNGa4M.original.fullsize.png"/><br/><strong>Question:</strong><br/>For $a=0$, the value of $d$ (maximum value of $\rho$ as shown in the figure) is</div> | ['Physics', 'Electrostatics', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{3 Z e}{4 \pi R^3}$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{3 Z e}{\pi R^3}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{4 Z e}{3 \pi R^3}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{Z e}{3 \pi R^3}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{3 Z e}{\pi R^3}$<br/></span> </div> | <div class="solution">For $a=0$<br/>$$<br/>\begin{aligned}<br/>& \rho(r)=\left(-\frac{d}{R} \cdot r+d\right) \\<br/>& \text { Now } \int_0^R\left(4 \pi r^2\right)\left(d-\frac{d}{R} r\right) d r=\text { net charge }=Z e<br/>\end{aligned}<br/>$$<br/>Solving this equation, we get $d=\frac{3 Z e}{\pi R^3}$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/LyvPQp1nkAouhegtu45_JVyeZAs0gj3wpNxj90T5ADo.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
788 | paragraph-there-are-n-urns-each-containing-n-1-balls-such-that-the-ith-urn-contains-i-white-balls-and-n-1-i-red-balls-let-u-i-be-the-event-of-selectin-1 | paragraph-there-are-n-urns-each-containing-n-1-balls-such-that-the-ith-urn-contains-i-white-balls-and-n-1-i-red-balls-let-u-i-be-the-event-of-selectin-1-47960 | <div class="question"><strong>Paragraph:</strong><br/>There are $n$ urns each containing $(n+1)$ balls such that the ith urn contains $i$ white balls and $(n+1-i)$ red balls. Let $u_i$ be the event of selecting ith urn, $i=1,2,3, \ldots, n$ and $W$ denotes the event of getting a white balls.<strong>Question:</strong><br/>If $P\left(u_i\right)=c$, where $c$ is a constant, then $P\left(u_i / W\right)$ is equal to</div> | ['Mathematics', 'Probability', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{2}{n+1}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{1}{n+1}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{n}{n+1}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{1}{2}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{2}{n+1}$<br/></span> </div> | <div class="solution">$P\left(\frac{u_i}{W}\right)=\frac{\frac{n}{n+1}}{\frac{\Sigma i}{n+1}}=\frac{2}{n+1}$</div> | MarksBatch2_P2.db |
789 | paragraph-there-are-n-urns-each-containing-n-1-balls-such-that-the-ith-urn-contains-i-white-balls-and-n-1-i-red-balls-let-u-i-be-the-event-of-selectin-2 | paragraph-there-are-n-urns-each-containing-n-1-balls-such-that-the-ith-urn-contains-i-white-balls-and-n-1-i-red-balls-let-u-i-be-the-event-of-selectin-2-52096 | <div class="question"><strong>Paragraph:</strong><br/>There are $n$ urns each containing $(n+1)$ balls such that the ith urn contains $i$ white balls and $(n+1-i)$ red balls. Let $u_i$ be the event of selecting ith urn, $i=1,2,3, \ldots, n$ and $W$ denotes the event of getting a white balls.<strong>Question:</strong><br/>If $n$ is even and $E$ denotes the event of choosing even numbered urn $\left(P\left(u_i\right)=\frac{1}{n}\right)$, then the value of $P(W / E)$ is</div> | ['Mathematics', 'Probability', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{n+2}{2 n+1}$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{n+2}{2(n+1)}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{n}{n+1}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{1}{n+1}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{n+2}{2(n+1)}$<br/></span> </div> | <div class="solution">$P(W / E)=\frac{2+4+6+\ldots}{\frac{n(n+1)}{2}}=\frac{n+2}{2(n+1)}$</div> | MarksBatch2_P2.db |
790 | paragraph-there-are-n-urns-each-containing-n-1-balls-such-that-the-ith-urn-contains-i-white-balls-and-n-1-i-red-balls-let-u-i-be-the-event-of-selectin-3 | paragraph-there-are-n-urns-each-containing-n-1-balls-such-that-the-ith-urn-contains-i-white-balls-and-n-1-i-red-balls-let-u-i-be-the-event-of-selectin-3-47711 | <div class="question"><strong>Paragraph:</strong><br/>There are $n$ urns each containing $(n+1)$ balls such that the ith urn contains $i$ white balls and $(n+1-i)$ red balls. Let $u_i$ be the event of selecting ith urn, $i=1,2,3, \ldots, n$ and $W$ denotes the event of getting a white balls.<strong>Question:</strong><br/>If $P\left(u_i\right) \propto i$, where $i=1,2,3, \ldots, n$, then $\lim _{n \rightarrow \infty} P(W)$ is equal to</div> | ['Mathematics', 'Probability', 'JEE Main'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>1<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{2}{3}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{1}{4}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{3}{4}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{2}{3}$<br/></span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/P2FXcCfLyF2E7Scmlez396yBvjhkeK-dJUDHezmuJrc.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
791 | paragraph-there-are-n-urns-each-containing-n-1-balls-such-that-the-ith-urn-contains-i-white-balls-and-n-1-i-red-balls-let-u-i-be-the-event-of-selectin | paragraph-there-are-n-urns-each-containing-n-1-balls-such-that-the-ith-urn-contains-i-white-balls-and-n-1-i-red-balls-let-u-i-be-the-event-of-selectin-92672 | <div class="question"><strong>Paragraph:</strong><br/>There are $n$ urns each containing $(n+1)$ balls such that the ith urn contains $i$ white balls and $(n+1-i)$ red balls. Let $u_i$ be the event of selecting ith urn, $i=1,2,3, \ldots, n$ and $W$ denotes the event of getting a white balls.<strong>Question:</strong><br/>If $P\left(u_i\right) \propto i$, where $i=1,2,3, \ldots, n$, then $\lim _{n \rightarrow \infty} P(W)$ is equal to</div> | ['Mathematics', 'Probability', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>1<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{2}{3}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{1}{4}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{3}{4}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{2}{3}$<br/></span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/P2FXcCfLyF2E7Scmlez396yBvjhkeK-dJUDHezmuJrc.original.fullsize.png"/><br/></div> | MarksBatch2_P2.db |
792 | paragraph-there-are-some-deposits-of-nitrates-and-phosphates-in-earths-crust-nitrates-are-more-soluble-in-water-nitrates-are-difficult-to-reduce-under-1 | paragraph-there-are-some-deposits-of-nitrates-and-phosphates-in-earths-crust-nitrates-are-more-soluble-in-water-nitrates-are-difficult-to-reduce-under-1-83986 | <div class="question"><strong>Paragraph:</strong><br/>There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under the laboratory conditions but microbes do it easily. Ammonia forms large number of complexes with transition metal ions. Hybridisation easily explains the ease of sigma donation capability of $\mathrm{NH}_3$ and $\mathrm{PH}_3$. Phosphine is a flammable gas and is prepared from white phosphorus.<strong>Question:</strong><br/>Among the following, the correct statement is</div> | ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>between $\mathrm{NH}_3$ and $\mathrm{PH}_3, \mathrm{NH}_3$ is a better electron donor because the lone pair of electrons occupies spherical 's' orbital and is less directional<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>between $\mathrm{NH}_3$ and $\mathrm{PH}_3, \mathrm{PH}_3$ is a better electron donor because the lone pair of electrons occupies $\mathrm{sp}^3$ orbital and is more directional<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>between $\mathrm{NH}_3$ and $\mathrm{PH}_3, \mathrm{NH}_3$ is a better electron donor because the lone pair of electrons occupies $\mathrm{sp}^3$ orbital and is more directional<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>between $\mathrm{NH}_3$ and $\mathrm{PH}_3, \mathrm{PH}_3$ is a better electron donor because the lone pair of electrons occupies spherical ' $s$ ' orbital and is less directional</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>between $\mathrm{NH}_3$ and $\mathrm{PH}_3, \mathrm{NH}_3$ is a better electron donor because the lone pair of electrons occupies $\mathrm{sp}^3$ orbital and is more directional<br/></span> </div> | <div class="solution">$\mathrm{NH}_3$ is better electron donor because the lone pair of electrons occupies $\mathrm{sp}^3$-orbital and is more directional.</div> | MarksBatch2_P2.db |
793 | paragraph-there-are-some-deposits-of-nitrates-and-phosphates-in-earths-crust-nitrates-are-more-soluble-in-water-nitrates-are-difficult-to-reduce-under-2 | paragraph-there-are-some-deposits-of-nitrates-and-phosphates-in-earths-crust-nitrates-are-more-soluble-in-water-nitrates-are-difficult-to-reduce-under-2-56171 | <div class="question"><strong>Paragraph:</strong><br/>There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under the laboratory conditions but microbes do it easily. Ammonia forms large number of complexes with transition metal ions. Hybridisation easily explains the ease of sigma donation capability of $\mathrm{NH}_3$ and $\mathrm{PH}_3$. Phosphine is a flammable gas and is prepared from white phosphorus.<strong>Question:</strong><br/>White phosphorus on reaction with $\mathrm{NaOH}$ gives $\mathrm{PH}_3$ as one of the products. This is a</div> | ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>dimerisation reaction<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>disproportionation reaction<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>condensation reaction<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>precipitation reaction</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>disproportionation reaction<br/></span> </div> | <div class="solution">White phosphorus on reaction with $\mathrm{NaOH}$ gives $\mathrm{PH}_3$ as one of the product in disproportionation reaction<br/>$$<br/>\mathrm{P}_4+3 \mathrm{NaOH}+3 \mathrm{H}_2 \mathrm{O} \longrightarrow 3 \mathrm{NaH}_2 \mathrm{PO}_2+\mathrm{PH}_3<br/>$$</div> | MarksBatch2_P2.db |
794 | paragraph-there-are-some-deposits-of-nitrates-and-phosphates-in-earths-crust-nitrates-are-more-soluble-in-water-nitrates-are-difficult-to-reduce-under | paragraph-there-are-some-deposits-of-nitrates-and-phosphates-in-earths-crust-nitrates-are-more-soluble-in-water-nitrates-are-difficult-to-reduce-under-16619 | <div class="question"><strong>Paragraph:</strong><br/>There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under the laboratory conditions but microbes do it easily. Ammonia forms large number of complexes with transition metal ions. Hybridisation easily explains the ease of sigma donation capability of $\mathrm{NH}_3$ and $\mathrm{PH}_3$. Phosphine is a flammable gas and is prepared from white phosphorus.<strong>Question:</strong><br/>Among the following, the correct statement is</div> | ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>phosphates have no biological significance in humans<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>between nitrates and phosphates, phosphates are less abundant in earth's crust<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>between nitrates and phosphates, nitrates are less abundant in earth's crust<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>oxidation of nitrates is possible in soil</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>between nitrates and phosphates, nitrates are less abundant in earth's crust<br/></span> </div> | <div class="solution">Due to greater solubility and nature to be prone to microbial action, nitrates are less abundant in earth's crust.</div> | MarksBatch2_P2.db |
795 | paragraph-tollens-reagent-is-used-for-the-detection-of-aldehyde-when-a-solution-of-agno-3-is-added-to-glucose-with-nh-4-oh-then-gluconic-acid-is-forme-1 | paragraph-tollens-reagent-is-used-for-the-detection-of-aldehyde-when-a-solution-of-agno-3-is-added-to-glucose-with-nh-4-oh-then-gluconic-acid-is-forme-1-55157 | <div class="question"><strong>Paragraph:</strong><br/>Tollen's reagent is used for the detection of aldehyde when a solution of $\mathrm{AgNO}_3$ is added to glucose with $\mathrm{NH}_4 \mathrm{OH}$ then gluconic acid is formed<br/>$\begin{array}{rr}\mathrm{Ag}^{+}+e^{-} \rightarrow \mathrm{Ag} & E_{\text {red }}^{\circ}=0.8 \mathrm{~V} \\ \mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O} \rightarrow \text { Gluconic acid }\left(\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_7\right)+2 \mathrm{H}^{+}+2 e^{-} ; & -E_{\mathrm{red}}^{\circ}=-0.05 \mathrm{~V} \\ \mathrm{Ag}\left(\mathrm{NH}_3\right)_2^{+}+e^{-} \rightarrow \mathrm{Ag}(s)+2 \mathrm{NH}_3 ; & E_{\mathrm{red}}^{\circ}=0.337 \mathrm{~V}\end{array}$<br/>[Use $2.303 \times \frac{R T}{F}=0.0592$ and $\frac{F}{R T}=38.92$ at $298 \mathrm{~K}$ ]<strong>Question:</strong><br/>When ammonia is added to the solution, $\mathrm{pH}$ is raised to 11 . Which half-cell reaction is affected by $\mathrm{pH}$ and by how much?</div> | ['Chemistry', 'Electrochemistry', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$E_{\text {oxd }}$ will increase by a factor of $0.65$ from $E_{\text {oxd }}^{\circ}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$E_{\text {oxd }}$ will decrease by a factor of $0.65$ from $E_{\text {oxd }}^{\circ}$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$E_{\text {red }}$ will increase by a factor of $0.65$ from $E_{\text {red }}^{\circ}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$E_{\text {red }}$ will decrease by a factor of $0.65$ from $E_{\text {red }}^{\circ}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$E_{\text {red }}$ will increase by a factor of $0.65$ from $E_{\text {red }}^{\circ}$<br/></span> </div> | <div class="solution">On increasing concentration of $\mathrm{NH}_3$, the concentration of $\mathrm{H}^{+}$ion decreases, therefore<br/>$$<br/>\begin{aligned}<br/>E_{\mathrm{red}} & =E_{\mathrm{red}}^{\circ}-\frac{0.0592}{n} \log _{10}\left[\mathrm{H}^{+}\right]^2 \\<br/>& =0-\frac{0.0592}{2} \times 2 \log _{10} 10^{-11} \quad\left(\because \mathrm{pH}=11 ; \therefore\left[\mathrm{H}^{+}\right]=10^{-11} \mathrm{M}\right) \\<br/>& =-0.0592 \times 11=0.6512 \mathrm{~V}=0.65 \mathrm{~V}<br/>\end{aligned}<br/>$$<br/>$E_{\text {red }}$ increased by a factor of $0.65$ from $E_{\text {red }}^{\circ}$.</div> | MarksBatch2_P2.db |
796 | paragraph-tollens-reagent-is-used-for-the-detection-of-aldehyde-when-a-solution-of-agno-3-is-added-to-glucose-with-nh-4-oh-then-gluconic-acid-is-forme-2 | paragraph-tollens-reagent-is-used-for-the-detection-of-aldehyde-when-a-solution-of-agno-3-is-added-to-glucose-with-nh-4-oh-then-gluconic-acid-is-forme-2-20513 | <div class="question"><strong>Paragraph:</strong><br/>Tollen's reagent is used for the detection of aldehyde when a solution of $\mathrm{AgNO}_3$ is added to glucose with $\mathrm{NH}_4 \mathrm{OH}$ then gluconic acid is formed<br/>$\begin{array}{rr}\mathrm{Ag}^{+}+e^{-} \rightarrow \mathrm{Ag} & E_{\text {red }}^{\circ}=0.8 \mathrm{~V} \\ \mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O} \rightarrow \text { Gluconic acid }\left(\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_7\right)+2 \mathrm{H}^{+}+2 e^{-} ; & -E_{\mathrm{red}}^{\circ}=-0.05 \mathrm{~V} \\ \mathrm{Ag}\left(\mathrm{NH}_3\right)_2^{+}+e^{-} \rightarrow \mathrm{Ag}(s)+2 \mathrm{NH}_3 ; & E_{\mathrm{red}}^{\circ}=0.337 \mathrm{~V}\end{array}$<br/>[Use $2.303 \times \frac{R T}{F}=0.0592$ and $\frac{F}{R T}=38.92$ at $298 \mathrm{~K}$ ]<strong>Question:</strong><br/>Ammonia is always added in this reaction. Which of the following must be incorrect?</div> | ['Chemistry', 'Electrochemistry', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{NH}_3$ combines with $\mathrm{Ag}^{+}$to form a complex<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{Ag}\left(\mathrm{NH}_3\right)_2^{+}$is a stronger oxidising reagent than $\mathrm{Ag}^{+}$.<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>In absence of $\mathrm{NH}_3$ silver salt of gluconic acid is formed.<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{NH}_3$ has affected the standard reduction potential of glucose/gluconic acid electrode.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\mathrm{NH}_3$ has affected the standard reduction potential of glucose/gluconic acid electrode.</span> </div> | <div class="solution">Ammonia has no effect on the standard reduction potential.</div> | MarksBatch2_P2.db |
797 | paragraph-tollens-reagent-is-used-for-the-detection-of-aldehyde-when-a-solution-of-agno-3-is-added-to-glucose-with-nh-4-oh-then-gluconic-acid-is-forme | paragraph-tollens-reagent-is-used-for-the-detection-of-aldehyde-when-a-solution-of-agno-3-is-added-to-glucose-with-nh-4-oh-then-gluconic-acid-is-forme-29027 | <div class="question"><strong>Paragraph:</strong><br/>Tollen's reagent is used for the detection of aldehyde when a solution of $\mathrm{AgNO}_3$ is added to glucose with $\mathrm{NH}_4 \mathrm{OH}$ then gluconic acid is formed<br/>$\begin{array}{rr}\mathrm{Ag}^{+}+e^{-} \rightarrow \mathrm{Ag} & E_{\text {red }}^{\circ}=0.8 \mathrm{~V} \\ \mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O} \rightarrow \text { Gluconic acid }\left(\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_7\right)+2 \mathrm{H}^{+}+2 e^{-} ; & -E_{\mathrm{red}}^{\circ}=-0.05 \mathrm{~V} \\ \mathrm{Ag}\left(\mathrm{NH}_3\right)_2^{+}+e^{-} \rightarrow \mathrm{Ag}(s)+2 \mathrm{NH}_3 ; & E_{\mathrm{red}}^{\circ}=0.337 \mathrm{~V}\end{array}$<br/>[Use $2.303 \times \frac{R T}{F}=0.0592$ and $\frac{F}{R T}=38.92$ at $298 \mathrm{~K}$ ]<strong>Question:</strong><br/>$2 \mathrm{Ag}^{+}+\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O} \rightarrow 2 \mathrm{Ag}(\mathrm{s})+\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_4+2 \mathrm{H}^{+}$. Find $\ln \mathrm{K}$ of this reaction.</div> | ['Chemistry', 'Electrochemistry', 'JEE Advanced', 'JEE Advanced 2006'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$66.13$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$58.38$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$28.30$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$46.29$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$58.38$<br/></span> </div> | <div class="solution">Cell reaction,<br/>(i) $\mathrm{Ag}^{+}+e^{-} \longrightarrow \mathrm{Ag}(\mathrm{s}), E_{\mathrm{red}}^{\circ}=0.8 \mathrm{~V}$<br/>(ii) $\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O} \longrightarrow \mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_7+2 \mathrm{H}^{+}+2 e^{-}, E_{\text {oxid }}=-0.05 \mathrm{~V}$<br/>Hence, for reaction<br/>$$<br/>\begin{aligned}<br/>2 \mathrm{Ag}^{+}+\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O} & \longrightarrow 2 \mathrm{Ag}(s)+\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O} 7+2 \mathrm{H}^{+} \\<br/>E_{\text {cell }}^{\circ} & =(0.8-0.05)=0.75 \mathrm{~V} \\<br/>E_{\text {cell }}^{\circ} & =E_{\text {anode }}^{\circ}-E_{\text {cathode }}^{\circ}=[-0.05-(-0.8)]_{\mathrm{V}}<br/>\end{aligned}<br/>$$<br/>On the basis of oxidised electrode potential $=0.75 \mathrm{~V}$<br/>By Nernst equation, $E_{\text {cell }}=E_{\text {cell }}^{\circ}-\frac{2.303 R T}{n F} \log _{10} K$<br/>At equilibrium, $E_{\text {cell }}=0$<br/><br/>$$<br/>\begin{aligned}<br/>E_{\text {cell }}^{\circ} & =\frac{2.303 R T}{n F} \log _{10} K \\<br/>0.75 & =\frac{0.0592}{2} \log _{10} K \\<br/>\log _{10} K & =\frac{2 \times 0.75}{0.0592}=25.33<br/>\end{aligned}<br/>$$<br/>or In $K=2.303 \times \log _{10} K=2.303 \times 25.33=58.35$</div> | MarksBatch2_P2.db |
798 | paragraph-two-aliphatic-aldehydes-p-and-q-react-in-the-presence-of-aqueous-k-2-co-3-to-give-compound-r-which-upon-treatment-with-hcn-provides-compound-1 | paragraph-two-aliphatic-aldehydes-p-and-q-react-in-the-presence-of-aqueous-k-2-co-3-to-give-compound-r-which-upon-treatment-with-hcn-provides-compound-1-59304 | <div class="question"><strong>Paragraph:</strong><br/>Two aliphatic aldehydes $\mathrm{P}$ and $\mathrm{Q}$ react in the presence of aqueous $\mathrm{K}_2 \mathrm{CO}_3$ to give compound R, which upon treatment with HCN provides compound $\mathrm{S}$. On acidification and heating, S gives the product shown below :<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/fNKC7BRqyIG0XUhPQ9I2Jk7TQZkubA1XHiW9jOv0YY0.original.fullsize.png"/><br/><strong>Question:</strong><br/>$$<br/>\text { The compound } R \text { is }<br/>$$</div> | ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/u_YwwvUlHeiPhW65xViBpGcBxqt8HU514eXHCbA3geQ.original.fullsize.png"/><br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/IDJssAH1ncINmZ5akVkIM_FUNloUGOu8t4BpmySVkyA.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/OGVZ0Fw5frdcrCcs2tsy0DkdyE4HH1ZMpVo4t5yffvY.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Oi9S2vlqWFuLp344kRTeSO0M0ZhRfPe7Noo9mqLWyDE.original.fullsize.png"/><br/></span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/u_YwwvUlHeiPhW65xViBpGcBxqt8HU514eXHCbA3geQ.original.fullsize.png"/><br/></span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ub0i1Roguh0VykvMYjTBnPZBFg5b20aVJPzytT7IND8.original.fullsize.png"/><br/><br/>Some inferences from above data<br/>- $a q \mathrm{~K}_2 \mathrm{CO}_3$ can facilitate aldol condensation to aliphatic aldehydes.<br/>- HCN can lead to cyanohydrin formation<br/>- $\mathrm{H}^{+}, \Delta$ can lead to hydrolysis of cyanide to acid and following esterification. So $S$ is cyanohydrin.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/PSYRzrrQMjFhPEo-HPgMnRsEh0hKBpYpzHThIfd51OA.original.fullsize.png"/><br/><br/>Carbonyl compounds (Aldol condensation) Conceptual reaction and mechanistic understanding IV</div> | MarksBatch2_P2.db |
799 | paragraph-two-aliphatic-aldehydes-p-and-q-react-in-the-presence-of-aqueous-k-2-co-3-to-give-compound-r-which-upon-treatment-with-hcn-provides-compound-2 | paragraph-two-aliphatic-aldehydes-p-and-q-react-in-the-presence-of-aqueous-k-2-co-3-to-give-compound-r-which-upon-treatment-with-hcn-provides-compound-2-86714 | <div class="question"><strong>Paragraph:</strong><br/>Two aliphatic aldehydes $\mathrm{P}$ and $\mathrm{Q}$ react in the presence of aqueous $\mathrm{K}_2 \mathrm{CO}_3$ to give compound R, which upon treatment with HCN provides compound $\mathrm{S}$. On acidification and heating, S gives the product shown below :<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/fNKC7BRqyIG0XUhPQ9I2Jk7TQZkubA1XHiW9jOv0YY0.original.fullsize.png"/><br/><strong>Question:</strong><br/>The compounds $P$ and $Q$ respectively are</div> | ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/XY3JBMOyrm-KVvXIZxh5pV6xAvBhHJWZiMIlukGMOKU.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/C2l-Yu0JxplE9MQVK9s1Xi5LEJUy4GkVnyKS90ZuwTA.original.fullsize.png"/><br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/NhiFPpUESgSYDDhaq0k91PHm239pKR3rWBeZPstpShM.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ERVwJ12xZZSGOLlgQrDC59mU5Ps2L_8iJbdy6bnzhII.original.fullsize.png"/><br/></span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/C2l-Yu0JxplE9MQVK9s1Xi5LEJUy4GkVnyKS90ZuwTA.original.fullsize.png"/><br/></span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ub0i1Roguh0VykvMYjTBnPZBFg5b20aVJPzytT7IND8.original.fullsize.png"/><br/><br/>Some inferences from above data<br/>- $a q \mathrm{~K}_2 \mathrm{CO}_3$ can facilitate aldol condensation to aliphatic aldehydes.<br/>- HCN can lead to cyanohydrin formation<br/>- $\mathrm{H}^{+}, \Delta$ can lead to hydrolysis of cyanide to acid and following esterification. So $S$ is cyanohydrin.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/PSYRzrrQMjFhPEo-HPgMnRsEh0hKBpYpzHThIfd51OA.original.fullsize.png"/><br/><br/>Carbonyl compounds (Aldol condensation) Conceptual reaction and mechanistic understanding IV</div> | MarksBatch2_P2.db |
800 | paragraph-two-aliphatic-aldehydes-p-and-q-react-in-the-presence-of-aqueous-k-2-co-3-to-give-compound-r-which-upon-treatment-with-hcn-provides-compound-3 | paragraph-two-aliphatic-aldehydes-p-and-q-react-in-the-presence-of-aqueous-k-2-co-3-to-give-compound-r-which-upon-treatment-with-hcn-provides-compound-3-44304 | <div class="question"><strong>Paragraph:</strong><br/>Two aliphatic aldehydes $\mathrm{P}$ and $\mathrm{Q}$ react in the presence of aqueous $\mathrm{K}_2 \mathrm{CO}_3$ to give compound R, which upon treatment with HCN provides compound $\mathrm{S}$. On acidification and heating, S gives the product shown below :<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/fNKC7BRqyIG0XUhPQ9I2Jk7TQZkubA1XHiW9jOv0YY0.original.fullsize.png"/><br/><strong>Question:</strong><br/>The compounds $P$ and $Q$ respectively are</div> | ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Main'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/XY3JBMOyrm-KVvXIZxh5pV6xAvBhHJWZiMIlukGMOKU.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/C2l-Yu0JxplE9MQVK9s1Xi5LEJUy4GkVnyKS90ZuwTA.original.fullsize.png"/><br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/NhiFPpUESgSYDDhaq0k91PHm239pKR3rWBeZPstpShM.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ERVwJ12xZZSGOLlgQrDC59mU5Ps2L_8iJbdy6bnzhII.original.fullsize.png"/><br/></span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/C2l-Yu0JxplE9MQVK9s1Xi5LEJUy4GkVnyKS90ZuwTA.original.fullsize.png"/><br/></span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ub0i1Roguh0VykvMYjTBnPZBFg5b20aVJPzytT7IND8.original.fullsize.png"/><br/><br/>Some inferences from above data<br/>- $a q \mathrm{~K}_2 \mathrm{CO}_3$ can facilitate aldol condensation to aliphatic aldehydes.<br/>- HCN can lead to cyanohydrin formation<br/>- $\mathrm{H}^{+}, \Delta$ can lead to hydrolysis of cyanide to acid and following esterification. So $S$ is cyanohydrin.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/PSYRzrrQMjFhPEo-HPgMnRsEh0hKBpYpzHThIfd51OA.original.fullsize.png"/><br/><br/>Carbonyl compounds (Aldol condensation) Conceptual reaction and mechanistic understanding IV</div> | MarksBatch2_P2.db |
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