index
int64 1
560
| question_number
stringclasses 99
values | question_type
stringclasses 4
values | question_text
stringlengths 0
813
⌀ | marks
int64 0
25
⌀ | related_topics
sequencelengths 0
8
⌀ | related_chapter
stringclasses 30
values | figure_paths
sequencelengths 0
3
⌀ | sub_parts
listlengths 0
5
⌀ | options
dict | or_question
dict | vi_candidate
bool 1
class | assertion
stringclasses 23
values | reason
stringclasses 23
values | case_study_text
stringclasses 9
values | sub_questions
listlengths 0
4
⌀ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 1 | standard | A thin plastic rod is bent into a circular ring of radius R. It is uniformly charged with charge density $\lambda$. The magnitude of the electric field at its centre is : | 1 | [
"Electric Charges",
"Electric Field",
"Electric Field due to continuous charge distribution"
] | Electric Charges and Fields | null | null | {
"A": "$\\frac{\\lambda}{2\\varepsilon_0R}$",
"B": "Zero",
"C": "$\\frac{\\lambda}{4\\pi\\varepsilon_0R}$",
"D": "$\\frac{\\lambda}{4\\varepsilon_0R}$"
} | null | false | null | null | null | null |
2 | 2 | standard | Ten capacitors, each of capacitance 1 $\mu$F, are connected in parallel to a source of 100 V. The total energy stored in the system is equal to : | 1 | [
"Capacitors",
"Combination of capacitors",
"Energy stored in a capacitor"
] | Electrostatic Potential and Capacitance | null | null | {
"A": "$10^{-2}$ J",
"B": "$10^{-3}$ J",
"C": "$0.5 \\times 10^{-3}$ J",
"D": "$5.0 \\times 10^{-2}$ J"
} | null | false | null | null | null | null |
3 | 3 | standard | Consider the circuit shown in the figure. The potential difference between points A and B is : | 1 | [
"Electric current",
"Ohm's law",
"Kirchhoff's rules"
] | Current Electricity | [
"img\\img_1.jpeg"
] | null | {
"A": "6 V",
"B": "8 V",
"C": "9 V",
"D": "12 V"
} | null | false | null | null | null | null |
4 | 4 | standard | A loop carrying a current I clockwise is placed in x – y plane, in a uniform magnetic field directed along z-axis. The tendency of the loop will be to : | 1 | [
"Magnetic field",
"Force on a current-carrying conductor in a uniform magnetic field",
"Torque on a current loop"
] | Moving Charges and Magnetism | null | null | {
"A": "move along x-axis",
"B": "move along y-axis",
"C": "shrink",
"D": "expand"
} | null | false | null | null | null | null |
5 | 5 | standard | A 10 cm long wire lies along y-axis. It carries a current of 1.0 A in positive y-direction. A magnetic field $\vec{B} = (5 \text{ mT}) \hat{j} - (8 \text{ mT})\hat{k}$ exists in the region. The force on the wire is : | 1 | [
"Magnetic field",
"Force on a current-carrying conductor in a uniform magnetic field"
] | Moving Charges and Magnetism | null | null | {
"A": "$(0.8 \\text{ mN}) \\hat{i}$",
"B": "$-(0.8 \\text{ mN}) \\hat{i}$",
"C": "$(80 \\text{ mN}) \\hat{i}$",
"D": "$-(80 \\text{ mN}) \\hat{i}$"
} | null | false | null | null | null | null |
6 | 6 | standard | A galvanometer of resistance GΩ is converted into an ammeter of range O to I A. If the current through the galvanometer is 0.1% of I A, the resistance of the ammeter is : | 1 | [
"Moving Coil Galvanometer",
"Ammeter Conversion",
"Shunt Resistance"
] | Moving Charges and Magnetism | null | null | {
"A": "$\\frac{G}{999} \\Omega$",
"B": "$\\frac{G}{1000} \\Omega$",
"C": "$\\frac{G}{1001} \\Omega$",
"D": "$\\frac{G}{100-1} \\Omega$"
} | null | false | null | null | null | null |
7 | 7 | standard | The reactance of a capacitor of capacitance C connected to an ac source of frequency ω is ‘X'. If the capacitance of the capacitor is doubled and the frequency of the source is tripled, the reactance will become : | 1 | [
"Capacitive Reactance",
"Alternating Current Circuits"
] | Alternating Current | null | null | {
"A": "$\\frac{X}{6}$",
"B": "$6X$",
"C": "$\\frac{2}{3}X$",
"D": "$\\frac{3}{2}X$"
} | null | false | null | null | null | null |
8 | 8 | standard | In the four regions, I, II, III and IV, the electric fields are described as :
Region I : Eₓ = E₀ sin (kz – ωt)
Region II : Eₓ = E₀
Region III: Eₓ = E₀ sin kz
Region IV: Eₓ = E₀ cos kz
The displacement current will exist in the region : | 1 | [
"Displacement Current",
"Electromagnetic Waves"
] | Electromagnetic Waves | null | null | {
"A": "I",
"B": "IV",
"C": "II",
"D": "III"
} | null | false | null | null | null | null |
9 | 9 | standard | The transition of electron that gives rise to the formation of the second spectral line of the Balmer series in the spectrum of hydrogen atom corresponds to : | 1 | [
"Hydrogen Spectrum",
"Balmer Series",
"Atomic Transitions"
] | Atoms | null | null | {
"A": "n<0xE1><0xB5> = 2 and n<0xE2><0x82><0x81> = 3",
"B": "n<0xE1><0xB5> = 3 and n<0xE2><0x82><0x81> = 4",
"C": "n<0xE1><0xB5> = 2 and n<0xE2><0x82><0x81> = 4",
"D": "n<0xE1><0xB5> = 2 and n<0xE2><0x82><0x81> = ∞"
} | null | false | null | null | null | null |
10 | 10 | standard | Ge is doped with As. Due to doping, | 1 | [
"Semiconductors",
"Doping",
"Extrinsic Semiconductors",
"n-type Semiconductor"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | null | null | {
"A": "the structure of Ge lattice is distorted.",
"B": "the number of conduction electrons increases.",
"C": "the number of holes increases.",
"D": "the number of conduction electrons decreases."
} | null | false | null | null | null | null |
11 | 11 | standard | Two beams, A and B whose photon energies are 3.3 eV and 11.3 eV respectively, illuminate a metallic surface (work function 2.3 eV) successively. The ratio of maximum speed of electrons emitted due to beam A to that due to beam B is : | 1 | [
"Photoelectric Effect",
"Einstein's Photoelectric Equation",
"Kinetic Energy of Photoelectrons"
] | Dual Nature of Radiation and Matter | null | null | {
"A": "3",
"B": "9",
"C": "$\\frac{1}{3}$",
"D": "$\\frac{1}{9}$"
} | null | false | null | null | null | null |
12 | 12. | standard | The waves associated with a moving electron and a moving proton have the same wavelength \(\lambda\). It implies that they have the same : | 1 | [
"de-Broglie relation",
"momentum"
] | Dual Nature of Radiation and Matter | null | null | {
"A": "momentum",
"B": "angular momentum",
"C": "speed",
"D": "energy"
} | null | false | null | null | null | null |
13 | 13. | assertion_reason | null | 1 | [
"Photoelectric effect",
"Einstein's photoelectric equation"
] | Dual Nature of Radiation and Matter | null | null | {
"A": "Both Assertion and Reason are true and Reason is the correct explanation of Assertion",
"B": "Both Assertion and Reason are true but Reason is not the correct explanation of Assertion",
"C": "Assertion is true but Reason is false",
"D": "Both Assertion and Reason are false"
} | null | null | In photoelectric effect, the kinetic energy of the emitted photoelectrons increases with increase in the intensity of the incident light. | Photoelectric current depends on the wavelength of the incident light. | null | null |
14 | 14. | assertion_reason | null | 1 | [
"Mutual induction",
"Magnetic flux"
] | Electromagnetic Induction | null | null | {
"A": "Both Assertion and Reason are true and Reason is the correct explanation of Assertion",
"B": "Both Assertion and Reason are true but Reason is not the correct explanation of Assertion",
"C": "Assertion is true but Reason is false",
"D": "Both Assertion and Reason are false"
} | null | null | The mutual inductance between two coils is maximum when the coils are wound on each other. | The flux linkage between two coils is maximum when they are wound on each other. | null | null |
15 | 15. | assertion_reason | null | 1 | [
"Force between two parallel current-carrying conductors",
"Ampere's law"
] | Moving Charges and Magnetism | null | null | {
"A": "Both Assertion and Reason are true and Reason is the correct explanation of Assertion",
"B": "Both Assertion and Reason are true but Reason is not the correct explanation of Assertion",
"C": "Assertion is true but Reason is false",
"D": "Both Assertion and Reason are false"
} | null | null | Two long parallel wires, freely suspended and connected in series to a battery, move apart. | Two wires carrying current in opposite directions repel each other. | null | null |
16 | 16. | assertion_reason | null | 1 | [
"Reflection of light",
"Spherical mirrors",
"Image formation"
] | Ray Optics and Optical Instruments | null | null | {
"A": "Both Assertion and Reason are true and Reason is the correct explanation of Assertion",
"B": "Both Assertion and Reason are true but Reason is not the correct explanation of Assertion",
"C": "Assertion is true but Reason is false",
"D": "Both Assertion and Reason are false"
} | null | null | Plane and convex mirrors cannot produce real images under any circumstance. | A virtual image cannot serve as an object to produce a real image. | null | null |
17 | 17 | standard | Find the temperature at which the resistance of a wire made of silver will be twice its resistance at 20°C. Take 20°C as the reference temperature and temperature coefficient of resistance of silver at 20°C = 4.0 × 10⁻³ K⁻¹. | 2 | [
"Temperature dependence of resistance",
"Electrical resistivity and conductivity"
] | Current Electricity | null | null | null | null | false | null | null | null | null |
18 | 18 | standard | Monochromatic light of frequency 5.0 × 10¹⁴ Hz passes from air into a medium of refractive index 1.5. Find the wavelength of the light (i) reflected, and (ii) refracted at the interface of the two media. | 2 | [
"Refraction of light",
"Reflection of light",
"Wave optics"
] | Ray Optics and Optical Instruments | null | [
{
"part": "(i)",
"text": "reflected"
},
{
"part": "(ii)",
"text": "refracted at the interface of the two media"
}
] | null | {
"figure_paths": null,
"marks": 2,
"options": null,
"or_question": null,
"question_number": "18",
"question_text": "A plano-convex lens of focal length 16 cm is made of a material of refractive index 1.4. Calculate the radius of the curved surface of the lens.",
"question_type": "standard",
"related_chapter": "Ray Optics and Optical Instruments",
"related_topics": [
"Refraction at spherical surfaces",
"Lenses",
"Thin lens formula",
"Lens maker’s formula"
],
"sub_parts": null,
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
19 | 19 | standard | An object is placed 30 cm in front of a concave mirror of radius of curvature 40 cm. Find the (i) position of the image formed and (ii) magnification of the image. | 2 | [
"Reflection of light",
"Spherical mirrors",
"Mirror formula",
"Magnification"
] | Ray Optics and Optical Instruments | null | [
{
"part": "(i)",
"text": "position of the image formed"
},
{
"part": "(ii)",
"text": "magnification of the image"
}
] | null | null | false | null | null | null | null |
20 | 20 | standard | Consider a neutron (mass m) of kinetic energy E and a photon of the same energy. Let λₙ and λₚ be the de Broglie wavelength of neutron and the wavelength of photon respectively. Obtain an expression for λₙ / λₚ. | 2 | [
"Dual nature of radiation",
"Matter waves",
"de-Broglie relation",
"Photoelectric effect"
] | Dual Nature of Radiation and Matter | null | null | null | null | false | null | null | null | null |
21 | 21 | standard | Plot a graph showing the variation of current with voltage for the material GaAs. On the graph, mark the region where : (a) resistance is negative, and (b) Ohm's law is obeyed. | 2 | [
"Electric current",
"Ohm's law",
"V-I characteristics",
"Semiconductors"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | null | [
{
"part": "(a)",
"text": "resistance is negative"
},
{
"part": "(b)",
"text": "Ohm's law is obeyed"
}
] | null | null | false | null | null | null | null |
22 | 22. | standard | A cube of side 0.1 m is placed, as shown in the figure, in a region where electric field $\vec{E} = 500 x \hat{i}$ exists. Here x is in meters and E in NC$^{-1}$. Calculate : | 3 | [
"Electric flux",
"Gauss's theorem"
] | Electric Charges and Fields | [
"img\\img_2.jpeg"
] | [
{
"part": "(a)",
"text": "the flux passing through the cube, and"
},
{
"part": "(b)",
"text": "the charge within the cube."
}
] | null | null | false | null | null | null | null |
23 | 23. | standard | Define 'current density'. Is it a scalar or a vector ? An electric field $\vec{E}$ is maintained in a metallic conductor. If n be the number of electrons (mass m, charge – e) per unit volume in the conductor and $\tau$ its relaxation time, show that the current density $\vec{j} = \alpha \vec{E}$, where $\alpha = \left( \frac{ne^2}{m} \right) \tau$. | 3 | [
"Current density",
"Drift velocity",
"Ohm's law"
] | Current Electricity | null | [
{
"part": "(a)",
"text": "Define 'current density'."
},
{
"part": "(a)",
"text": "Is it a scalar or a vector ?"
},
{
"part": "(a)",
"text": "An electric field $\\vec{E}$ is maintained in a metallic conductor. If n be the number of electrons (mass m, charge – e) per unit volume in the conductor and $\\tau$ its relaxation time, show that the current density $\\vec{j} = \\alpha \\vec{E}$, where $\\alpha = \\left( \\frac{ne^2}{m} \\right) \\tau$."
}
] | null | {
"figure_paths": null,
"marks": 3,
"options": null,
"or_question": null,
"question_number": "23.",
"question_text": "What is a Wheatstone bridge ? Obtain the necessary conditions under which the Wheatstone bridge is balanced.",
"question_type": "standard",
"related_chapter": "Current Electricity",
"related_topics": [
"Wheatstone bridge",
"Kirchhoff's rules"
],
"sub_parts": [
{
"part": "(b)",
"text": "What is a Wheatstone bridge ?"
},
{
"part": "(b)",
"text": "Obtain the necessary conditions under which the Wheatstone bridge is balanced."
}
],
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
24 | 24. | standard | A proton with kinetic energy $1.3384 \times 10^{-14}$ J moving horizontally from north to south, enters a uniform magnetic field B of 2.0 mT directed eastward. Calculate : | 3 | [
"Force on a moving charge in magnetic field",
"Motion in a magnetic field"
] | Moving Charges and Magnetism | null | [
{
"part": "(a)",
"text": "the speed of the proton"
},
{
"part": "(b)",
"text": "the magnitude of acceleration of the proton"
},
{
"part": "(c)",
"text": "the radius of the path traced by the proton"
}
] | null | null | false | null | null | null | null |
25 | 25. | standard | An inductor, a capacitor and a resistor are connected in series with an ac source v = $v_m$ sin $\omega$t. Derive an expression for the average power dissipated in the circuit. Also obtain the expression for the resonant frequency of the circuit. | 3 | [
"AC Circuits",
"Average Power",
"Resonance"
] | Alternating Current | null | null | null | null | false | null | null | null | null |
26 | 26. | standard | (a) “The wavelength of the electromagnetic wave is often correlated with the characteristic size of the system that radiates.” Give two examples to justify this statement. | 3 | [
"Electromagnetic Waves",
"Radiation"
] | Electromagnetic Waves | null | [
{
"part": "a",
"text": "“The wavelength of the electromagnetic wave is often correlated with the characteristic size of the system that radiates.” Give two examples to justify this statement."
},
{
"part": "b",
"text": "(i) Long distance radio broadcasts use short-wave bands. Why ?"
},
{
"part": "b",
"text": "(ii) Optical and radio telescopes are built on the ground, but X-ray astronomy is possible only from satellites orbiting the Earth. Why ?"
}
] | null | null | false | null | null | null | null |
27 | 27. | standard | Write the drawbacks of Rutherford's atomic model. How did Bohr remove them ? Show that different orbits in Bohr's atom are not equally spaced. | 3 | [
"Rutherford's Atomic Model",
"Bohr's Model",
"Atomic Spectra"
] | Atoms | null | null | null | null | false | null | null | null | null |
28 | 28. | standard | (a) State any two properties of a nucleus.
(b) Why is the density of a nucleus much more than that of an atom ?
(c) Show that the density of the nuclear matter is the same for all nuclei. | 3 | [
"Nucleus",
"Nuclear Density"
] | Nuclei | null | [
{
"part": "a",
"text": "State any two properties of a nucleus."
},
{
"part": "b",
"text": "Why is the density of a nucleus much more than that of an atom ?"
},
{
"part": "c",
"text": "Show that the density of the nuclear matter is the same for all nuclei."
}
] | null | null | false | null | null | null | null |
29 | 29 | case_study | null | 15 | [
"Lenses",
"Focal Length",
"Refractive Index",
"Power of a Lens",
"Combination of Lenses"
] | Ray Optics and Optical Instruments | null | null | null | null | null | null | null | A lens is a transparent medium bounded by two surfaces, with one or both surfaces being spherical. The focal length of a lens is determined by the radii of curvature of its two surfaces and the refractive index of its medium with respect to that of the surrounding medium. The power of a lens is reciprocal of its focal length. If a number of lenses are kept in contact, the power of the combination is the algebraic sum of the powers of the individual lenses. | [] |
30 | (i) | standard | A double-convex lens, with each face having same radius of curvature R, is made of glass of refractive index n. Its power is : | 1 | [
"Refraction of light",
"Lenses",
"Power of a lens",
"Lens maker’s formula"
] | Ray Optics and Optical Instruments | null | null | {
"A": "$\\frac{2 (n - 1)}{R}$",
"B": "$\\frac{(2n - 1)}{R}$",
"C": "$\\frac{(n - 1)}{2R}$",
"D": "$\\frac{(2n – 1)}{2R}$"
} | null | false | null | null | null | null |
31 | (ii) | standard | A double-convex lens of power P, with each face having same radius of curvature, is cut into two equal parts perpendicular to its principal axis. The power of one part of the lens will be : | 1 | [
"Refraction of light",
"Lenses",
"Power of a lens",
"Combination of thin lenses in contact"
] | Ray Optics and Optical Instruments | null | null | {
"A": "2P",
"B": "P",
"C": "4P",
"D": "$\\frac{P}{2}$"
} | null | false | null | null | null | null |
32 | (iii) | standard | The above two parts are kept in contact with each other as shown in the figure. The power of the combination will be : | 1 | [
"Refraction of light",
"Lenses",
"Power of a lens",
"Combination of thin lenses in contact"
] | Ray Optics and Optical Instruments | [
"img\\img_3.jpeg"
] | null | {
"A": "$\\frac{P}{2}$",
"B": "P",
"C": "2P",
"D": "$\\frac{P}{4}$"
} | null | false | null | null | null | null |
33 | (iv) | standard | A double-convex lens of power P, with each face having same radius of curvature, is cut along its principal axis. The two parts are arranged as shown in the figure. The power of the combination will be : | 1 | [
"Refraction of light",
"Lenses",
"Power of a lens",
"Combination of thin lenses in contact"
] | Ray Optics and Optical Instruments | [
"img\\img_4.jpeg"
] | null | {
"A": "Zero",
"B": "P",
"C": "2P",
"D": "$\\frac{P}{2}$"
} | {
"figure_paths": null,
"marks": 1,
"options": {
"A": "6.6 D",
"B": "15 D",
"C": "$\\frac{1}{15}$ D",
"D": "$\\frac{1}{80}$ D"
},
"or_question": null,
"question_number": "(iv)",
"question_text": "Two convex lenses of focal lengths 60 cm and 20 cm are held coaxially in contact with each other. The power of the combination is :",
"question_type": "standard",
"related_chapter": "Ray Optics and Optical Instruments",
"related_topics": [
"Refraction of light",
"Lenses",
"Power of a lens",
"Combination of thin lenses in contact"
],
"sub_parts": null,
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
34 | 30 | case_study | null | 3 | [
"Semiconductor diode",
"Rectifier",
"Forward bias",
"Reverse bias",
"Half-wave rectifier",
"Full-wave rectifier"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | null | null | null | null | null | null | null | Junction Diode as a Rectifier :
The process of conversion of an ac voltage into a dc voltage is called rectification and the device which performs this conversion is called a rectifier. The characteristics of a p-n junction diode reveal that when a p-n junction diode is forward biased, it offers a low resistance and when it is reverse biased, it offers a high resistance. Hence, a p-n junction diode conducts only when it is forward biased. This property of a p-n junction diode makes it suitable for its use as a rectifier.
Thus, when an ac voltage is applied across a p-n junction, it conducts only during those alternate half cycles for which it is forward biased. A rectifier which rectifies only half cycle of an ac voltage is called a half-wave rectifier and one that rectifies both the half cycles is known as a full-wave rectifier. | [
{
"number": "(i)",
"options": {
"A": "$\\frac{V_0}{\\sqrt{2}}$",
"B": "$\\frac{V_0^2}{2}$",
"C": "$\\frac{2V_0}{\\sqrt{2}}$",
"D": "$\\frac{V_0}{2\\sqrt{2}}$"
},
"text": "The root mean square value of an alternating voltage applied to a full-wave rectifier is $\\frac{V_0}{\\sqrt{2}}$. Then the root mean square value of the rectified output voltage is :"
},
{
"number": "(ii)",
"options": {
"A": "Complete cycle of the input signal",
"B": "Half cycle of the input signal",
"C": "Less than half cycle of the input signal",
"D": "Only for the positive half cycle of the input signal"
},
"text": "In a full-wave rectifier, the current in each of the diodes flows for :"
},
{
"number": "(iii)",
"options": {
"A": "Both diodes are forward biased at the same time.",
"B": "Both diodes are reverse biased at the same time.",
"C": "One is forward biased and the other is reverse biased at the same time.",
"D": "Both are forward biased in the first half of the cycle and reverse biased in the second half of the cycle."
},
"text": "In a full-wave rectifier :"
}
] |
35 | (iv)(a) | standard | An alternating voltage of frequency of 50 Hz is applied to a half-wave rectifier. Then the ripple frequency of the output will be : | 1 | [
"Rectifiers",
"Ripple frequency"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | null | null | {
"A": "100 Hz",
"B": "50 Hz",
"C": "25 Hz",
"D": "150 Hz"
} | {
"figure_paths": [
"img\\img_5.jpeg",
"img\\img_6.jpeg",
"img\\img_7.jpeg",
"img\\img_8.jpeg",
"img\\img_9.jpeg"
],
"marks": 1,
"options": {
"A": "10 V\npath: img\\img_6.jpeg",
"B": "- 10 V\npath: img\\img_7.jpeg",
"C": "-path: Img\\img_8.jpeg",
"D": "+ 5 V\npath. img img_9.jpeg"
},
"or_question": null,
"question_number": "(iv)(b)",
"question_text": "A signal, as shown in the figure, is applied to a p-n junction diode. Identify the output across resistance R<sub>L</sub> :",
"question_type": "standard",
"related_chapter": "Semiconductor Electronics: Materials, Devices and Simple Circuits",
"related_topics": [
"p-n junction diode",
"Rectifiers",
"Input and Output waveforms"
],
"sub_parts": null,
"text": null,
"vi_candidate": null
} | false | null | null | null | null |
36 | 31. | standard | (a) (i) Derive an expression for potential energy of an electric dipole $\vec{p}$ in an external uniform electric field $\vec{E}$. When is the potential energy of the dipole (1) maximum, and (2) minimum ?
(ii) An electric dipole consists of point charges – 1.0 pC and + 1.0 pC located at (0, 0) and (3 mm, 4 mm) respectively in x – y plane. An electric field $\vec{E} = \left(\frac{1000 \text{ V}}{\text{m}}\right) \hat{i}$ is switched on in the region. Find the torque $\vec{\tau}$ acting on the dipole. | 5 | [
"Electric Dipole",
"Potential Energy",
"Torque"
] | Electrostatic Potential and Capacitance | null | [
{
"part": "(i)",
"text": "Derive an expression for potential energy of an electric dipole $\\vec{p}$ in an external uniform electric field $\\vec{E}$. When is the potential energy of the dipole (1) maximum, and (2) minimum ?"
},
{
"part": "(ii)",
"text": "An electric dipole consists of point charges – 1.0 pC and + 1.0 pC located at (0, 0) and (3 mm, 4 mm) respectively in x – y plane. An electric field $\\vec{E} = \\left(\\frac{1000 \\text{ V}}{\\text{m}}\\right) \\hat{i}$ is switched on in the region. Find the torque $\\vec{\\tau}$ acting on the dipole."
}
] | null | {
"figure_paths": null,
"marks": 5,
"options": null,
"or_question": null,
"question_number": null,
"question_text": "(b) (i) An electric dipole (dipole moment $\\vec{p} = p\\hat{i}$), consisting of charges - q and q, separated by distance 2a, is placed along the x-axis, with its centre at the origin. Show that the potential V, due to this dipole, at a point x, (x >> a) is equal to $\\frac{1}{4\\pi\\varepsilon_0} \\cdot \\frac{\\vec{p}\\cdot\\hat{i}}{x^2}$.\n(ii) Two isolated metallic spheres $S_1$ and $S_2$ of radii 1 cm and 3 cm respectively are charged such that both have the same charge density $\\left(\\frac{2}{\\pi} \\times 10^{-9}\\right) \\text{C/m}^2$. They are placed far away from each other and connected by a thin wire. Calculate the new charge on sphere $S_1$.",
"question_type": "standard",
"related_chapter": "Electrostatic Potential and Capacitance",
"related_topics": [
"Electric Dipole",
"Electric Potential",
"Capacitance",
"Charge Distribution"
],
"sub_parts": [
{
"part": "(i)",
"text": "An electric dipole (dipole moment $\\vec{p} = p\\hat{i}$), consisting of charges - q and q, separated by distance 2a, is placed along the x-axis, with its centre at the origin. Show that the potential V, due to this dipole, at a point x, (x >> a) is equal to $\\frac{1}{4\\pi\\varepsilon_0} \\cdot \\frac{\\vec{p}\\cdot\\hat{i}}{x^2}$."
},
{
"part": "(ii)",
"text": "Two isolated metallic spheres $S_1$ and $S_2$ of radii 1 cm and 3 cm respectively are charged such that both have the same charge density $\\left(\\frac{2}{\\pi} \\times 10^{-9}\\right) \\text{C/m}^2$. They are placed far away from each other and connected by a thin wire. Calculate the new charge on sphere $S_1$."
}
],
"text": null,
"vi_candidate": null
} | false | null | null | null | null |
37 | 32. | standard | (a) (i) A resistor and a capacitor are connected in series to an ac source $v = v_m \sin \omega t$. Derive an expression for the impedance of the circuit.
(ii) When does an inductor act as a conductor in a circuit ? Give reason for it. | 5 | [
"AC Circuits",
"Impedance",
"Inductors"
] | Alternating Current | null | [
{
"part": "(i)",
"text": "A resistor and a capacitor are connected in series to an ac source $v = v_m \\sin \\omega t$. Derive an expression for the impedance of the circuit."
},
{
"part": "(ii)",
"text": "When does an inductor act as a conductor in a circuit ? Give reason for it."
}
] | null | null | false | null | null | null | null |
38 | 33. (a) | standard | null | 5 | [
"Refraction of light through a prism",
"Angle of deviation",
"Angle of minimum deviation",
"Refractive index"
] | Ray Optics and Optical Instruments | [] | [
{
"part": "(i)",
"text": "A ray of light passes through a triangular prism. Show graphically, how the angle of deviation varies with the angle of incidence ? Hence define the angle of minimum deviation."
},
{
"part": "(ii)",
"text": "A ray of light is incident normally on a refracting face of a prism of prism angle A and suffers a deviation of angle δ. Prove that the refractive index n of the material of the prism is given by n=\\(\\frac{sin (A + \\delta)}{sin A}\\)."
}
] | null | null | false | null | null | null | null |
39 | 33. (b) | standard | null | 5 | [
"AC Circuits",
"Inductance",
"Impedance"
] | Alternating Current | [] | [
{
"part": "(iii)",
"text": "An electric lamp is designed to operate at 110 V dc and 11 A current. If the lamp is operated on 220 V, 50 Hz ac source with a coil in series, then find the inductance of the coil."
}
] | null | {
"figure_paths": [],
"marks": 5,
"options": null,
"or_question": null,
"question_number": "33. (b)",
"question_text": null,
"question_type": "standard",
"related_chapter": "Electromagnetic Induction",
"related_topics": [
"Transformers",
"Working principle of transformer",
"Energy losses in transformer",
"Conservation of energy"
],
"sub_parts": [
{
"part": "(i)",
"text": "Draw a labelled diagram of a step-up transformer and describe its working principle. Explain any three causes for energy losses in a real transformer."
},
{
"part": "(ii)",
"text": "A step-up transformer converts a low voltage into high voltage. Does it violate the principle of conservation of energy ? Explain."
},
{
"part": "(iii)",
"text": "A step-up transformer has 200 and 3000 turns in its primary and secondary coils respectively. The input voltage given to the primary coil is 90 V. Calculate :"
},
{
"part": "(iii) (1)",
"text": "The output voltage across the secondary coil"
},
{
"part": "(iii) (2)",
"text": "The current in the primary coil if the current in the secondary coil is 2.0 A."
}
],
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
40 | (iii) | standard | The refractive index of the material of a prism is $\sqrt{2}$. If the refracting angle of the prism is $60^\circ$, find the | 5 | [
"Refraction of light through a prism",
"Angle of minimum deviation"
] | Ray Optics and Optical Instruments | null | [
{
"part": "(1)",
"text": "Angle of minimum deviation, and"
},
{
"part": "(2)",
"text": "Angle of incidence."
}
] | null | {
"figure_paths": null,
"marks": 5,
"options": null,
"or_question": null,
"question_number": "(b)",
"question_text": "",
"question_type": "standard",
"related_chapter": "Wave Optics",
"related_topics": [
"Huygens' principle",
"Reflection of light",
"Coherent sources",
"Young's double slit experiment",
"Interference"
],
"sub_parts": [
{
"part": "(i)",
"text": "State Huygens' principle. A plane wave is incident at an angle i on a reflecting surface. Construct the corresponding reflected wavefront. Using this diagram, prove that the angle of reflection is equal to the angle of incidence."
},
{
"part": "(ii)",
"text": "What are the coherent sources of light ? Can two independent sodium lamps act like coherent sources ? Explain."
},
{
"part": "(iii)",
"text": "A beam of light consisting of a known wavelength 520 nm and an unknown wavelength $\\lambda$, used in Young's double slit experiment produces two interference patterns such that the fourth bright fringe of unknown wavelength coincides with the fifth bright fringe of known wavelength. Find the value of $\\lambda$."
}
],
"text": null,
"vi_candidate": null
} | false | null | null | null | null |
41 | 1 | standard | A thin plastic rod is bent into a circular ring of radius R. It is uniformly charged with charge density \(\lambda\). The magnitude of the electric field at its centre is : | 1 | [
"Electric Charges",
"Electric Fields",
"Electric field due to continuous charge distribution"
] | Chapter–1 | null | null | {
"A": "\\(\\frac{\\lambda}{2\\varepsilon_0 R}\\)",
"B": "Zero",
"C": "\\(\\frac{\\lambda}{4\\pi\\varepsilon_0 R}\\)",
"D": "\\(\\frac{\\lambda}{4\\varepsilon_0 R}\\)"
} | null | null | null | null | null | null |
42 | 2 | standard | A charged sphere of radius r has surface charge density \(\sigma\). The electric field on its surface is E. If the radius of the sphere is doubled, keeping charge density the same, the ratio of the electric field on the old sphere to that on the new sphere will be : | 1 | [
"Electric Charges",
"Electric Fields",
"Electric field due to a charged sphere"
] | Chapter–1 | null | null | {
"A": "1",
"B": "\\(\\frac{1}{2}\\)",
"C": "\\(\\frac{1}{4}\\)",
"D": "4"
} | null | null | null | null | null | null |
43 | 3 | standard | A student is asked to connect four cells, each of emf E and internal resistance r, in series. But she/he connects one cell wrongly in series with the other cells. The equivalent emf and the equivalent internal resistance of the combination will be : | 1 | [
"Current Electricity",
"Cells in series"
] | Chapter–3 | null | null | {
"A": "4E and 2r",
"B": "4E and 3r",
"C": "3E and 4r",
"D": "2E and 4r"
} | null | null | null | null | null | null |
44 | 4 | standard | A piece of wire bent in the form of a circular loop A carries a current I. The wire is then bent into a circular loop B of two turns and carries the same current. The ratio of magnetic fields at the centre of loop A to that of loop B will be : | 1 | [
"Moving Charges and Magnetism",
"Magnetic field due to a current carrying loop"
] | Chapter–4 | null | null | {
"A": "\\(\\frac{1}{16}\\)",
"B": "16",
"C": "4",
"D": "\\(\\frac{1}{4}\\)"
} | null | null | null | null | null | null |
45 | 5 | standard | A 10 cm long wire lies along y-axis. It carries a current of 1.0 A in positive y-direction. A magnetic field \(\vec{B} = (5 \text{mT}) \hat{j} - (8 \text{mT})\hat{k}\) exists in the region. The force on the wire is : | 1 | [
"Moving Charges and Magnetism",
"Force on a current-carrying conductor in a uniform magnetic field"
] | Chapter–4 | null | null | {
"A": "\\((0.8 \\text{mN}) \\hat{i}\\)",
"B": "\\((-0.8 \\text{mN}) \\hat{i}\\)",
"C": "\\((80 \\text{mN}) \\hat{i}\\)",
"D": "\\((-80 \\text{mN}) \\hat{i}\\)"
} | null | null | null | null | null | null |
46 | 6. | standard | A galvanometer of resistance G Ω is converted into an ammeter of range 0 to I A. If the current through the galvanometer is 0.1% of I A, the resistance of the ammeter is : | 1 | [
"Moving Coil Galvanometer",
"Ammeter Conversion",
"Shunt Resistance"
] | Moving Charges and Magnetism | null | null | {
"A": "$\\frac{G}{999} \\Omega$",
"B": "$\\frac{G}{1000} \\Omega$",
"C": "$\\frac{G}{1001} \\Omega$",
"D": "$\\frac{G}{100-1} \\Omega$"
} | null | false | null | null | null | null |
47 | 7. | standard | A conducting circular loop is placed in a uniform magnetic field B = 50 mT with its plane perpendicular to the magnetic field. The radius of the loop is made to shrink at a constant rate of 1 mm s⁻¹. At the instant the radius of the loop is 4 cm, the induced emf in the loop is : | 1 | [
"Electromagnetic Induction",
"Faraday's Law",
"Induced EMF"
] | Electromagnetic Induction | null | null | {
"A": "$\\pi \\mu V$",
"B": "$2\\pi \\mu V$",
"C": "$4\\pi \\mu V$",
"D": "$8\\pi \\mu V$"
} | null | false | null | null | null | null |
48 | 8. | standard | The electric and magnetic fields of electromagnetic waves are : | 1 | [
"Electromagnetic Waves",
"Properties of EM Waves"
] | Electromagnetic Waves | null | null | {
"A": "In the same phase and perpendicular to each other.",
"B": "In the same phase and not perpendicular to each other.",
"C": "Not in the same phase but are perpendicular to each other.",
"D": "Neither in the same phase nor perpendicular to each other."
} | null | false | null | null | null | null |
49 | 9. | standard | Two beams, A and B whose photon energies are 3.3 eV and 11.3 eV respectively, illuminate a metallic surface (work function 2.3 eV) successively. The ratio of maximum speed of electrons emitted due to beam A to that due to beam B is : | 1 | [
"Dual Nature of Radiation and Matter",
"Photoelectric Effect",
"Einstein's Photoelectric Equation"
] | Dual Nature of Radiation and Matter | null | null | {
"A": "3",
"B": "9",
"C": "$\\frac{1}{3}$",
"D": "$\\frac{1}{9}$"
} | null | false | null | null | null | null |
50 | 10. | standard | The waves associated with a moving electron and a moving proton have the same wavelength $\lambda$. It implies that they have the same : | 1 | [
"Dual Nature of Radiation and Matter",
"Matter Waves",
"de-Broglie relation"
] | Dual Nature of Radiation and Matter | null | null | {
"A": "momentum",
"B": "angular momentum",
"C": "speed",
"D": "energy"
} | null | false | null | null | null | null |
51 | 11. | standard | Ge is doped with As. Due to doping, | 1 | [
"Semiconductor Electronics",
"Doping",
"Extrinsic Semiconductors"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | null | null | {
"A": "the structure of Ge lattice is distorted.",
"B": "the number of conduction electrons increases.",
"C": "the number of holes increases.",
"D": "the number of conduction electrons decreases."
} | null | false | null | null | null | null |
52 | 12 | standard | The transition of electron that gives rise to the formation of the second spectral line of the Balmer series in the spectrum of hydrogen atom corresponds to : | 1 | [
"Balmer series",
"Hydrogen spectrum",
"Atomic spectra"
] | Atoms | null | null | {
"A": "nf = 2 and n₁ = 3",
"B": "nf = 3 and n₁ = 4",
"C": "nf = 2 and n₁ = 4",
"D": "nf = 2 and n₁ = ∞"
} | null | false | null | null | null | null |
53 | 13 | assertion_reason | null | 1 | [
"Reflection of light",
"Mirrors",
"Real and virtual images"
] | Ray Optics and Optical Instruments | null | null | {
"A": "Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).",
"B": "Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of the Assertion (A).",
"C": "Assertion (A) is true, but Reason (R) is false.",
"D": "Assertion (A) is false and Reason (R) is also false."
} | null | null | Plane and convex mirrors cannot produce real images under any circumstance. | A virtual image cannot serve as an object to produce a real image. | null | null |
54 | 14 | assertion_reason | null | 1 | [
"Force between parallel currents",
"Magnetic force on a current-carrying conductor"
] | Moving Charges and Magnetism | null | null | {
"A": "Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).",
"B": "Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of the Assertion (A).",
"C": "Assertion (A) is true, but Reason (R) is false.",
"D": "Assertion (A) is false and Reason (R) is also false."
} | null | null | Two long parallel wires, freely suspended and connected in series to a battery, move apart. | Two wires carrying current in opposite directions repel each other. | null | null |
55 | 15 | assertion_reason | null | 1 | [
"Photoelectric effect",
"Kinetic energy of photoelectrons",
"Intensity of light",
"Wavelength of light"
] | Dual Nature of Radiation and Matter | null | null | {
"A": "Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).",
"B": "Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of the Assertion (A).",
"C": "Assertion (A) is true, but Reason (R) is false.",
"D": "Assertion (A) is false and Reason (R) is also false."
} | null | null | In photoelectric effect, the kinetic energy of the emitted photoelectrons increases with increase in the intensity of the incident light. | Photoelectric current depends on the wavelength of the incident light. | null | null |
56 | 16 | assertion_reason | null | 1 | [
"Mutual inductance",
"Magnetic flux linkage"
] | Electromagnetic Induction | null | null | {
"A": "Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).",
"B": "Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of the Assertion (A).",
"C": "Assertion (A) is true, but Reason (R) is false.",
"D": "Assertion (A) is false and Reason (R) is also false."
} | null | null | The mutual inductance between two coils is maximum when the coils are wound on each other. | The flux linkage between two coils is maximum when they are wound on each other. | null | null |
57 | 17 | standard | Two batteries of emfs 6 V and 3 V and internal resistances 0.8 Ω and 0.2 Ω respectively are connected in series to an external resistance R, as shown in figure. Find the value of R so that the potential difference across the 6 V battery be zero. | 2 | [
"Internal resistance",
"Series combination of cells",
"Ohm's law"
] | Current Electricity | [
"img\\img_10.jpeg"
] | null | null | null | false | null | null | null | null |
58 | 18 | standard | Consider a neutron (mass m) of kinetic energy E and a photon of the same energy. Let $\lambda_n$ and $\lambda_p$ be the de Broglie wavelength of neutron and the wavelength of photon respectively. Obtain an expression for $\frac{\lambda_n}{\lambda_p}$. | 2 | [
"de Broglie wavelength",
"Wave nature of particles",
"Energy of a photon"
] | Dual Nature of Radiation and Matter | null | null | null | null | false | null | null | null | null |
59 | 19 | standard | Monochromatic light of frequency $5.0 \times 10^{14}$ Hz passes from air into a medium of refractive index 1.5. Find the wavelength of the light (i) reflected, and (ii) refracted at the interface of the two media. | 2 | [
"Reflection of light",
"Refraction of light",
"Wavelength and refractive index"
] | Ray Optics and Optical Instruments | null | [
{
"part": "(a)",
"text": "Monochromatic light of frequency $5.0 \\times 10^{14}$ Hz passes from air into a medium of refractive index 1.5. Find the wavelength of the light (i) reflected, and (ii) refracted at the interface of the two media."
}
] | null | {
"figure_paths": null,
"marks": 2,
"options": null,
"or_question": null,
"question_number": null,
"question_text": "A plano-convex lens of focal length 16 cm is made of a material of refractive index 1.4. Calculate the radius of the curved surface of the lens.",
"question_type": "standard",
"related_chapter": "Ray Optics and Optical Instruments",
"related_topics": [
"Lens maker’s formula"
],
"sub_parts": [
{
"part": "(b)",
"text": "A plano-convex lens of focal length 16 cm is made of a material of refractive index 1.4. Calculate the radius of the curved surface of the lens."
}
],
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
60 | 20 | standard | An object is placed 30 cm in front of a concave mirror of radius of curvature 40 cm. Find the (i) position of the image formed and (ii) magnification of the image. | 2 | [
"Mirror formula",
"Magnification"
] | Ray Optics and Optical Instruments | null | [
{
"part": "(i)",
"text": "position of the image formed"
},
{
"part": "(ii)",
"text": "magnification of the image"
}
] | null | null | false | null | null | null | null |
61 | 21 | standard | How does the conductivity of an intrinsic semiconductor vary with temperature ? Explain. Show the variation in a plot. | 2 | [
"Conductivity of semiconductors",
"Temperature dependence of conductivity",
"Intrinsic semiconductors"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | null | null | null | null | false | null | null | null | null |
62 | 22. | standard | Three point charges Q₁, Q₂ and Q₃ are located in x – y plane at points (− d, 0), (0, 0) and (d, 0) respectively. Q₁ and Q₃ are identical and Q₂ is positive. What will be the nature and value of Q₁ so that the potential energy of the system is zero ? | 3 | [
"Electric Charges",
"Potential Energy of a System of Charges"
] | Electric Charges and Fields | null | null | null | null | false | null | null | null | null |
63 | 23. | standard | Define 'current density'. Is it a scalar or a vector ? An electric field → E is maintained in a metallic conductor. If n be the number of electrons (mass m, charge – e) per unit volume in the conductor and τ its relaxation time, show that the current density → j = α → E, where α = ( ne²/m ) τ. | 3 | [
"Current Density",
"Drift Velocity",
"Ohm's Law"
] | Current Electricity | null | [
{
"part": "a",
"text": "Define 'current density'. Is it a scalar or a vector ? An electric field → E is maintained in a metallic conductor. If n be the number of electrons (mass m, charge – e) per unit volume in the conductor and τ its relaxation time, show that the current density → j = α → E, where α = ( ne²/m ) τ."
}
] | null | {
"figure_paths": null,
"marks": 3,
"options": null,
"or_question": null,
"question_number": "23.",
"question_text": "What is a Wheatstone bridge ? Obtain the necessary conditions under which the Wheatstone bridge is balanced.",
"question_type": "standard",
"related_chapter": "Current Electricity",
"related_topics": [
"Wheatstone Bridge",
"Kirchhoff's Rules"
],
"sub_parts": [
{
"part": "b",
"text": "What is a Wheatstone bridge ? Obtain the necessary conditions under which the Wheatstone bridge is balanced."
}
],
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
64 | 24. | standard | A bar magnet of magnetic moment 2.5 JT⁻¹ lies aligned with the direction of a uniform magnetic field of 0.32 T. | 3 | [
"Torque on a Magnetic Dipole",
"Work Done on a Magnetic Dipole"
] | Magnetism and Matter | null | [
{
"part": "a",
"text": "Find the amount of work done to turn the magnet so as to align its magnetic moment (i) normal to the field direction, and (ii) opposite to the field direction."
},
{
"part": "b",
"text": "What is the torque on the magnet in above cases (i) and (ii) ?"
}
] | null | null | false | null | null | null | null |
65 | 25. | standard | Consider the arrangement of two coils P and Q shown in the figure. When current in coil P is switched on or switched off, a current flows in coil Q. | 3 | [
"Electromagnetic Induction",
"Faraday's Laws",
"Lenz's Law"
] | Electromagnetic Induction | [
"img\\img_11.jpeg"
] | [
{
"part": "a",
"text": "Explain the phenomenon involved in it."
},
{
"part": "b",
"text": "Mention two factors on which the current produced in coil Q depends."
},
{
"part": "c",
"text": "Give the direction of current in coil Q when there is a current in the coil P and (i) R is increased, and (ii) R is decreased."
}
] | null | null | false | null | null | null | null |
66 | 26 | standard | Write the drawbacks of Rutherford's atomic model. How did Bohr remove them? Show that different orbits in Bohr's atom are not equally spaced. | 3 | [
"Rutherford's model of atom",
"Bohr model of hydrogen atom",
"Atomic spectra"
] | Atoms | null | null | null | null | false | null | null | null | null |
67 | 27 | standard | "The wavelength of the electromagnetic wave is often correlated with the characteristic size of the system that radiates." Give two examples to justify this statement. | 3 | [
"Electromagnetic waves",
"Electromagnetic spectrum"
] | Electromagnetic Waves | null | [
{
"part": "a",
"text": "\"The wavelength of the electromagnetic wave is often correlated with the characteristic size of the system that radiates.\" Give two examples to justify this statement."
},
{
"part": "b",
"text": "(i) Long distance radio broadcasts use short-wave bands. Why?\n(ii) Optical and radio telescopes are built on the ground, but X-ray astronomy is possible only from satellites orbiting the Earth. Why?"
}
] | null | null | false | null | null | null | null |
68 | 27 | standard | Long distance radio broadcasts use short-wave bands. Why? | null | [
"Electromagnetic waves",
"Radio waves"
] | Electromagnetic Waves | null | null | null | null | false | null | null | null | null |
69 | 27 | standard | Optical and radio telescopes are built on the ground, but X-ray astronomy is possible only from satellites orbiting the Earth. Why? | null | [
"Electromagnetic waves",
"Optical instruments",
"Radio waves",
"X-rays"
] | Electromagnetic Waves | null | null | null | null | false | null | null | null | null |
70 | 28 | standard | Write two characteristic properties of nuclear force. | null | [
"Nuclear force"
] | Nuclei | null | [
{
"part": "a",
"text": "Write two characteristic properties of nuclear force."
},
{
"part": "b",
"text": "Draw a plot of potential energy of a pair of nucleons as a function of their separation. Write two important conclusions that can be drawn from the plot."
}
] | null | null | false | null | null | null | null |
71 | 28 | standard | Draw a plot of potential energy of a pair of nucleons as a function of their separation. Write two important conclusions that can be drawn from the plot. | 3 | [
"Nuclear force",
"Potential energy"
] | Nuclei | null | null | null | null | false | null | null | null | null |
72 | 29 | case_study | null | 15 | [
"p-n junction",
"Semiconductor diode",
"Rectifier",
"Forward bias",
"Reverse bias",
"Half-wave rectifier",
"Full-wave rectifier"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | null | null | null | null | null | null | null | Junction Diode as a Rectifier :
The process of conversion of an ac voltage into a dc voltage is called rectification and the device which performs this conversion is called a rectifier. The characteristics of a p-n junction diode reveal that when a p-n junction diode is forward biased, it offers a low resistance and when it is reverse biased, it offers a high resistance. Hence, a p-n junction diode conducts only when it is forward biased. This property of a p-n junction diode makes it suitable for its use as a rectifier.
Thus, when an ac voltage is applied across a p-n junction, it conducts only during those alternate half cycles for which it is forward biased. A rectifier which rectifies only half cycle of an ac voltage is called a half-wave rectifier and one that rectifies both the half cycles is known as a full-wave rectifier. | [] |
73 | (i) | standard | The root mean square value of an alternating voltage applied to a full-wave rectifier is $\frac{V_0}{\sqrt{2}}$. Then the root mean square value of the rectified output voltage is : | 1 | [
"Full-wave rectifier",
"RMS value of alternating voltage",
"RMS value of rectified output voltage"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | null | null | {
"A": "$\\frac{V_0}{\\sqrt{2}}$",
"B": "$\\frac{V_0^2}{\\sqrt{2}}$",
"C": "$\\frac{2V_0}{\\sqrt{2}}$",
"D": "$\\frac{V_0}{2\\sqrt{2}}$"
} | null | false | null | null | null | null |
74 | (ii) | standard | In a full-wave rectifier, the current in each of the diodes flows for : | 1 | [
"Full-wave rectifier",
"Diode operation"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | null | null | {
"A": "Complete cycle of the input signal",
"B": "Half cycle of the input signal",
"C": "Less than half cycle of the input signal",
"D": "Only for the positive half cycle of the input signal"
} | null | false | null | null | null | null |
75 | (iii) | standard | In a full-wave rectifier : | 1 | [
"Full-wave rectifier",
"Diode biasing"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | null | null | {
"A": "Both diodes are forward biased at the same time.",
"B": "Both diodes are reverse biased at the same time.",
"C": "One is forward biased and the other is reverse biased at the same time.",
"D": "Both are forward biased in the first half of the cycle and reverse biased in the second half of the cycle."
} | null | false | null | null | null | null |
76 | (iv) | standard | An alternating voltage of frequency of 50 Hz is applied to a half-wave rectifier. Then the ripple frequency of the output will be : | 1 | [
"Half-wave rectifier",
"Ripple frequency"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | null | [
{
"part": "a",
"text": "An alternating voltage of frequency of 50 Hz is applied to a half-wave rectifier. Then the ripple frequency of the output will be :"
}
] | {
"A": "100 Hz",
"B": "50 Hz",
"C": "25 Hz",
"D": "150 Hz"
} | null | false | null | null | null | null |
77 | b | standard | A signal, as shown in the figure, is applied to a p-n junction diode. Identify the output across resistance R₁: | 1 | [
"Semiconductor diode",
"Rectifier"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | [
"img\\img_12.jpeg"
] | null | {
"A": "waveform with 10 V peak path: img\\img_13.jpeg",
"B": "waveform with - 10 V peak path: Img\\img_14.jpeg",
"C": "waveform with -path: Img\\img_15.jpeg",
"D": "waveform with + 5 V peak path. img\\img_16.jpeg"
} | null | false | null | null | null | null |
78 | 30 | standard | A lens is a transparent medium bounded by two surfaces, with one or both surfaces being spherical. The focal length of a lens is determined by the radii of curvature of its two surfaces and the refractive index of its medium with respect to that of the surrounding medium. The power of a lens is reciprocal of its focal length. If a number of lenses are kept in contact, the power of the combination is the algebraic sum of the powers of the individual lenses. | 1 | [
"Refraction of light",
"Lenses",
"Focal length",
"Power of a lens",
"Combination of lenses"
] | Ray Optics and Optical Instruments | null | null | null | null | false | null | null | null | null |
79 | (i) | standard | A double-convex lens, with each face having same radius of curvature R, is made of glass of refractive index n. Its power is : | 1 | [
"Refraction of light",
"Lenses",
"Power of a lens",
"Lens maker’s formula"
] | Ray Optics and Optical Instruments | null | null | {
"A": "$\\frac{2 (n - 1)}{R}$",
"B": "$\\frac{(2n - 1)}{R}$",
"C": "$\\frac{(n - 1)}{2R}$",
"D": "$\\frac{(2n - 1)}{2R}$"
} | null | false | null | null | null | null |
80 | (ii) | standard | A double-convex lens of power P, with each face having same radius of curvature, is cut into two equal parts perpendicular to its principal axis. The power of one part of the lens will be : | 1 | [
"Refraction of light",
"Lenses",
"Power of a lens",
"Combination of thin lenses in contact"
] | Ray Optics and Optical Instruments | null | null | {
"A": "2P",
"B": "P",
"C": "4P",
"D": "$\\frac{P}{2}$"
} | null | false | null | null | null | null |
81 | (iii) | standard | The above two parts are kept in contact with each other as shown in the figure. The power of the combination will be : | 1 | [
"Refraction of light",
"Lenses",
"Power of a lens",
"Combination of thin lenses in contact"
] | Ray Optics and Optical Instruments | [
"img\\img_17.jpeg"
] | null | {
"A": "$\\frac{P}{2}$",
"B": "P",
"C": "2P",
"D": "$\\frac{P}{4}$"
} | null | false | null | null | null | null |
82 | (iv) | standard | A double-convex lens of power P, with each face having same radius of curvature, is cut along its principal axis. The two parts are arranged as shown in the figure. The power of the combination will be : | 1 | [
"Refraction of light",
"Lenses",
"Power of a lens",
"Combination of thin lenses in contact"
] | Ray Optics and Optical Instruments | [
"ing\\img_18.jpeg"
] | null | {
"A": "Zero",
"B": "P",
"C": "2P",
"D": "$\\frac{P}{2}$"
} | {
"figure_paths": null,
"marks": 1,
"options": {
"A": "6.6 D",
"B": "15 D",
"C": "$\\frac{1}{15}$ D",
"D": "$\\frac{1}{80}$ D"
},
"or_question": null,
"question_number": "(b)",
"question_text": "Two convex lenses of focal lengths 60 cm and 20 cm are held coaxially in contact with each other. The power of the combination is :",
"question_type": "standard",
"related_chapter": "Ray Optics and Optical Instruments",
"related_topics": [
"Refraction of light",
"Lenses",
"Power of a lens",
"Combination of thin lenses in contact"
],
"sub_parts": null,
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
83 | 31. | standard | (a) (i) A ray of light passes through a triangular prism. Show graphically, how the angle of deviation varies with the angle of incidence ? Hence define the angle of minimum deviation. | 5 | [
"Refraction of light through a prism",
"Angle of deviation",
"Angle of minimum deviation"
] | Ray Optics and Optical Instruments | null | [
{
"part": "(i)",
"text": "A ray of light passes through a triangular prism. Show graphically, how the angle of deviation varies with the angle of incidence ? Hence define the angle of minimum deviation."
}
] | null | null | null | null | null | null | null |
84 | 31. | standard | (a) (ii) A ray of light is incident normally on a refracting face of a prism of prism angle A and suffers a deviation of angle $\delta$. Prove that the refractive index n of the material of the prism is given by n=$ rac{\sin (A + \delta)}{\sin A}$. | 5 | [
"Refraction at plane surfaces",
"Refractive index",
"Prism formula"
] | Ray Optics and Optical Instruments | null | [
{
"part": "(ii)",
"text": "A ray of light is incident normally on a refracting face of a prism of prism angle A and suffers a deviation of angle $\\delta$. Prove that the refractive index n of the material of the prism is given by n=$\frac{\\sin (A + \\delta)}{\\sin A}$."
}
] | null | null | null | null | null | null | null |
85 | 31. | standard | (a) (iii) The refractive index of the material of a prism is $\sqrt{2}$. If the refracting angle of the prism is $60^\circ$, find the | 5 | [
"Refraction of light through a prism",
"Refractive index",
"Angle of minimum deviation"
] | Ray Optics and Optical Instruments | null | [
{
"part": "(iii)",
"text": "The refractive index of the material of a prism is $\\sqrt{2}$. If the refracting angle of the prism is $60^\\circ$, find the"
},
{
"part": "(1)",
"text": "Angle of minimum deviation, and"
},
{
"part": "(2)",
"text": "Angle of incidence."
}
] | null | null | null | null | null | null | null |
86 | 31. | standard | (b) (i) State Huygens’ principle. A plane wave is incident at an angle i on a reflecting surface. Construct the corresponding reflected wavefront. Using this diagram, prove that the angle of reflection is equal to the angle of incidence. | 5 | [
"Huygens' principle",
"Reflection of light",
"Wavefront"
] | Wave Optics | null | [
{
"part": "(i)",
"text": "State Huygens’ principle. A plane wave is incident at an angle i on a reflecting surface. Construct the corresponding reflected wavefront. Using this diagram, prove that the angle of reflection is equal to the angle of incidence."
}
] | null | {
"figure_paths": null,
"marks": 5,
"options": null,
"or_question": null,
"question_number": "31.",
"question_text": "(a) (i) A ray of light passes through a triangular prism. Show graphically, how the angle of deviation varies with the angle of incidence ? Hence define the angle of minimum deviation.",
"question_type": "standard",
"related_chapter": "Ray Optics and Optical Instruments",
"related_topics": [
"Refraction of light through a prism",
"Angle of deviation",
"Angle of minimum deviation"
],
"sub_parts": [
{
"part": "(i)",
"text": "A ray of light passes through a triangular prism. Show graphically, how the angle of deviation varies with the angle of incidence ? Hence define the angle of minimum deviation."
}
],
"text": null,
"vi_candidate": null
} | null | null | null | null | null |
87 | 31. | standard | (b) (ii) What are the coherent sources of light ? Can two independent sodium lamps act like coherent sources ? Explain. | 5 | [
"Coherent sources",
"Interference"
] | Wave Optics | null | [
{
"part": "(ii)",
"text": "What are the coherent sources of light ? Can two independent sodium lamps act like coherent sources ? Explain."
}
] | null | null | null | null | null | null | null |
88 | 31. | standard | (b) (iii) A beam of light consisting of a known wavelength 520 nm and an unknown wavelength $\lambda$, used in Young's double slit experiment produces two interference patterns such that the fourth bright fringe of unknown wavelength coincides with the fifth bright fringe of known wavelength. Find the value of $\lambda$. | 5 | [
"Young's double slit experiment",
"Interference",
"Fringe width"
] | Wave Optics | null | [
{
"part": "(iii)",
"text": "A beam of light consisting of a known wavelength 520 nm and an unknown wavelength $\\lambda$, used in Young's double slit experiment produces two interference patterns such that the fourth bright fringe of unknown wavelength coincides with the fifth bright fringe of known wavelength. Find the value of $\\lambda$."
}
] | null | null | null | null | null | null | null |
89 | 32. | standard | (a) (i) Derive an expression for potential energy of an electric dipole $\vec{p}$ in an external uniform electric field $\vec{E}$. When is the potential energy of the dipole (1) maximum, and (2) minimum ?
(ii) An electric dipole consists of point charges $-1.0$ pC and $+1.0$ pC located at (0, 0) and (3 mm, 4 mm) respectively in x – y plane. An electric field $\vec{E} = \left(\frac{1000 \text{V}}{\text{m}}\right) \hat{i}$ is switched on in the region. Find the torque $\vec{\tau}$ acting on the dipole. | 5 | [
"Electric potential energy of a dipole in an electrostatic field",
"Torque on a dipole in uniform electric field"
] | Electrostatic Potential and Capacitance | null | [
{
"part": "(i)",
"text": "Derive an expression for potential energy of an electric dipole $\\vec{p}$ in an external uniform electric field $\\vec{E}$. When is the potential energy of the dipole (1) maximum, and (2) minimum ?"
},
{
"part": "(ii)",
"text": "An electric dipole consists of point charges $-1.0$ pC and $+1.0$ pC located at (0, 0) and (3 mm, 4 mm) respectively in x – y plane. An electric field $\\vec{E} = \\left(\\frac{1000 \\text{V}}{\\text{m}}\\right) \\hat{i}$ is switched on in the region. Find the torque $\\vec{\\tau}$ acting on the dipole."
}
] | null | {
"figure_paths": null,
"marks": 5,
"options": null,
"or_question": null,
"question_number": null,
"question_text": "(b) (i) An electric dipole (dipole moment $\\vec{p} = p\\hat{i}$), consisting of charges – q and q separated by distance 2a, is placed along the x-axis, with its centre at the origin. Show that the potential V, due to this dipole, at a point x, (x >> a) is equal to $\\frac{1}{4\\pi\\epsilon_0} \\cdot \\frac{\\vec{p}\\cdot\\hat{i}}{x^2}$.\n(ii) Two isolated metallic spheres $S_1$ and $S_2$ of radii 1 cm and 3 cm respectively are charged such that both have the same charge density $\\left(\\frac{2}{\\pi} \\times 10^{-9}\\right) C/m^2$. They are placed far away from each other and connected by a thin wire. Calculate the new charge on sphere $S_1$.",
"question_type": "standard",
"related_chapter": "Electrostatic Potential and Capacitance",
"related_topics": [
"Electric potential due to a dipole",
"Capacitance",
"Charge distribution"
],
"sub_parts": [
{
"part": "(i)",
"text": "An electric dipole (dipole moment $\\vec{p} = p\\hat{i}$), consisting of charges – q and q separated by distance 2a, is placed along the x-axis, with its centre at the origin. Show that the potential V, due to this dipole, at a point x, (x >> a) is equal to $\\frac{1}{4\\pi\\epsilon_0} \\cdot \\frac{\\vec{p}\\cdot\\hat{i}}{x^2}$."
},
{
"part": "(ii)",
"text": "Two isolated metallic spheres $S_1$ and $S_2$ of radii 1 cm and 3 cm respectively are charged such that both have the same charge density $\\left(\\frac{2}{\\pi} \\times 10^{-9}\\right) C/m^2$. They are placed far away from each other and connected by a thin wire. Calculate the new charge on sphere $S_1$."
}
],
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
90 | 33. | standard | (a) (i) A resistor and a capacitor are connected in series to an ac source $v = v_m \sin \omega t$. Derive an expression for the impedance of the circuit.
(ii) When does an inductor act as a conductor in a circuit ? Give reason for it. | 5 | [
"Impedance of LCR series circuit",
"Inductors in AC circuits"
] | Alternating Current | null | [
{
"part": "(i)",
"text": "A resistor and a capacitor are connected in series to an ac source $v = v_m \\sin \\omega t$. Derive an expression for the impedance of the circuit."
},
{
"part": "(ii)",
"text": "When does an inductor act as a conductor in a circuit ? Give reason for it."
}
] | null | null | false | null | null | null | null |
91 | (iii) | standard | An electric lamp is designed to operate at 110 V dc and 11 A current. If the lamp is operated on 220 V, 50 Hz ac source with a coil in series, then find the inductance of the coil. | 5 | [
"Inductance",
"AC Circuits",
"Impedance"
] | Alternating Current | null | null | null | {
"figure_paths": null,
"marks": 5,
"options": null,
"or_question": null,
"question_number": "(b)",
"question_text": "Draw a labelled diagram of a step-up transformer and describe its working principle. Explain any three causes for energy losses in a real transformer.",
"question_type": "standard",
"related_chapter": "Electromagnetic Induction",
"related_topics": [
"Transformers",
"Electromagnetic Induction",
"Energy Losses"
],
"sub_parts": [
{
"part": "(i)",
"text": "Draw a labelled diagram of a step-up transformer and describe its working principle. Explain any three causes for energy losses in a real transformer."
},
{
"part": "(ii)",
"text": "A step-up transformer converts a low voltage into high voltage. Does it violate the principle of conservation of energy ? Explain."
},
{
"part": "(iii)",
"text": "A step-up transformer has 200 and 3000 turns in its primary and secondary coils respectively. The input voltage given to the primary coil is 90 V. Calculate :"
},
{
"part": "(1)",
"text": "The output voltage across the secondary coil"
},
{
"part": "(2)",
"text": "The current in the primary coil if the current in the secondary coil is 2.0 A."
}
],
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
92 | 1 | standard | A thin plastic rod is bent into a circular ring of radius R. It is uniformly charged with charge density λ. The magnitude of the electric field at its centre is : | 0 | [
"Electric field due to continuous charge distribution"
] | Electric Charges and Fields | null | null | {
"A": "$\\frac{\\lambda}{2\\varepsilon_0 R}$",
"B": "Zero",
"C": "$\\frac{\\lambda}{4\\pi\\varepsilon_0 R}$",
"D": "$\\frac{\\lambda}{4\\varepsilon_0 R}$"
} | null | false | null | null | null | null |
93 | 2 | standard | Three small charged spheres X, Y and Z carrying charges + q, − q and + q respectively are placed equidistant from each other, as shown in the figure. The spheres Y and Z are held in place. Initially X is also held in place, but is otherwise free to move. When X is released, the path followed by it will be : | 0 | [
"Coulomb's law",
"Force between multiple charges"
] | Electric Charges and Fields | [
"img\\img_19.jpeg"
] | null | {
"A": "A",
"B": "B",
"C": "C",
"D": "D"
} | null | false | null | null | null | null |
94 | 3 | standard | In a uniform straight wire, conduction electrons move along + x direction.
Let $\vec{E}$ and $\vec{j}$ be the electric field and current density in the wire, respectively. Then : | 0 | [
"Drift velocity",
"Electric current",
"Current density"
] | Current Electricity | null | null | {
"A": "$\\vec{E}$ and $\\vec{j}$ both are along + x direction.",
"B": "$\\vec{E}$ and $\\vec{j}$ both are along – x direction.",
"C": "$\\vec{E}$ is along + x direction, but $\\vec{j}$ is along - x direction.",
"D": "$\\vec{E}$ is along - x direction, but $\\vec{j}$ is along + x direction."
} | null | false | null | null | null | null |
95 | 4 | standard | Two charged particles, P and Q, each having charge q but of masses $m_1$ and $m_2$, are accelerated through the same potential difference V. They enter a region of magnetic field $\vec{B}$ ($\vec{v} \perp \vec{B}$) and describe the circular paths of radii a and b respectively. Then $\left(\frac{m_1}{m_2}\right)$ is equal to : | 0 | [
"Motion in a magnetic field",
"Kinetic energy and potential difference"
] | Moving Charges and Magnetism | null | null | {
"A": "$\\frac{a}{b}$",
"B": "$\\frac{b}{a}$",
"C": "$\\left(\\frac{a}{b}\\right)^2$",
"D": "$\\left(\\frac{b}{a}\\right)^2$"
} | null | false | null | null | null | null |
96 | 5 | standard | A galvanometer of resistance G Ω is converted into an ammeter of range 0 to I A. If the current through the galvanometer is 0.1% of I A, the resistance of the ammeter is : | 1 | [
"Moving Coil Galvanometer",
"Conversion to Ammeter",
"Shunt Resistance"
] | Moving Charges and Magnetism | null | null | {
"A": "$\\frac{G}{999} \\Omega$",
"B": "$\\frac{G}{1000} \\Omega$",
"C": "$\\frac{G}{1001} \\Omega$",
"D": "$\\frac{G}{100-1} \\Omega$"
} | null | false | null | null | null | null |
97 | 6 | standard | A 10 cm long wire lies along y-axis. It carries a current of 1.0 A in positive y-direction. A magnetic field $\vec{B} = (5 \text{ mT}) \hat{j} - (8 \text{ mT})\hat{k}$ exists in the region. The force on the wire is : | 1 | [
"Force on a current-carrying conductor in a magnetic field"
] | Moving Charges and Magnetism | null | null | {
"A": "$(0.8 \\text{ mN}) \\hat{i}$",
"B": "$-(0.8 \\text{ mN}) \\hat{i}$",
"C": "$(80 \\text{ mN}) \\hat{i}$",
"D": "$-(80 \\text{ mN}) \\hat{i}$"
} | null | false | null | null | null | null |
98 | 7 | standard | The primary and secondary coils of a transformer have 500 turns and 5000 turns respectively. The primary coil is connected to an ac source of 220 V – 50 Hz. The output across the secondary coil is : | 1 | [
"Transformer",
"Turns Ratio",
"Voltage Transformation"
] | Alternating Current | null | null | {
"A": "220 V – 50 Hz",
"B": "1100 V – 50 Hz",
"C": "2200 V – 5 Hz",
"D": "2200 V – 50 Hz"
} | null | false | null | null | null | null |
99 | 8 | standard | The first scientist who produced and observed electromagnetic waves of wavelengths in the range 25 mm – 5 mm was : | 1 | [
"Electromagnetic Waves",
"Hertz's Experiment"
] | Electromagnetic Waves | null | null | {
"A": "J.C. Maxwell",
"B": "H.R. Hertz",
"C": "J.C. Bose",
"D": "G. Marconi"
} | null | false | null | null | null | null |
100 | 9 | standard | The waves associated with a moving electron and a moving proton have the same wavelength $\lambda$. It implies that they have the same : | 1 | [
"de-Broglie Wavelength",
"Momentum and Wavelength"
] | Dual Nature of Radiation and Matter | null | null | {
"A": "momentum",
"B": "angular momentum",
"C": "speed",
"D": "energy"
} | null | false | null | null | null | null |
Subsets and Splits