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
⌀ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
201 | 4 | standard | A circular coil of radius 10 cm is placed in a magnetic field $\vec{B} = (1.0 \hat{i} + 0.5 \hat{j})$ mT such that the outward unit vector normal to the surface of the coil is $(0.6 \hat{i} + 0.8 \hat{j})$. The magnetic flux linked with the coil is : | 1 | [
"Magnetic Flux",
"Magnetic Field"
] | Moving Charges and Magnetism | null | null | {
"A": "0.314 μWb",
"B": "3.14 μWb",
"C": "31.4 μWb",
"D": "1.256 μWb"
} | null | false | null | null | null | null |
202 | 5 | standard | Which of the following quantity/quantities remains same in primary and secondary coils of an ideal transformer ? Current, Voltage, Power, Magnetic flux | 1 | [
"Transformer",
"Electromagnetic Induction"
] | Electromagnetic Induction | null | null | {
"A": "Current only",
"B": "Voltage only",
"C": "Power only",
"D": "Magnetic flux and Power both"
} | null | false | null | null | null | null |
203 | 6 | standard | In an ac circuit, the instantaneous values of current (in A) and voltage (in V) are I = 5 sin $\omega t$ and E = 200 cos $(\omega t + \frac{\pi}{3})$ respectively. The phase difference between voltage and current at any instant is : | 1 | [
"AC Circuits",
"Phase Difference"
] | Alternating Current | null | null | {
"A": "$\\frac{5\\pi}{6}$",
"B": "$\\frac{5\\pi}{4}$",
"C": "$\\frac{5\\pi}{2}$",
"D": "$\\frac{3\\pi}{2}$"
} | null | false | null | null | null | null |
204 | 7 | standard | In four regions I, II, III and IV, the magnetic field is given by :
I. $B_y = B_0 \sin kz$
II. $B_y = B_0 \cos kz$
III. $B_y = B_0 \sin (kz – \omega t)$
IV. $B_y = B_0 \sin kz + B_0 \cos kz$
The electromagnetic wave will exist in the region : | 1 | [
"Electromagnetic Waves",
"Magnetic Field"
] | Electromagnetic Waves | null | null | {
"A": "IV",
"B": "I",
"C": "III",
"D": "II"
} | null | false | null | null | null | null |
205 | 13 | assertion_reason | null | 1 | [
"Motion in a magnetic field",
"Force on a moving charge"
] | 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 | An electron and a proton enter with the same momentum $\vec{p}$ in a magnetic field $\vec{B}$ such that $\vec{p} \perp \vec{B}$. Then both describe a circular path of the same radius. | The radius of the circular path described by the charged particle (charge q, mass m) moving in the magnetic field $\vec{B}$ is given by $r = \frac{mv}{qB}$. | null | null |
206 | 14 | assertion_reason | null | 1 | [
"Compound microscope",
"Magnification"
] | 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 | The magnifying power of a compound microscope is negative. | The final image formed is erect with respect to the object. | null | null |
207 | 15 | assertion_reason | null | 1 | [
"Lenz's Law",
"Conservation of energy",
"Inductors"
] | 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 | Lenz's law is a consequence of the law of conservation of energy. | There is no power loss in an ideal inductor. | null | null |
208 | 16 | assertion_reason | null | 1 | [
"Photoelectric effect",
"Intensity of light",
"Photoelectric current"
] | 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 | Photoelectric current increases with an increase in intensity of incident radiation, for a given frequency of incident radiation and the accelerating potential. | Increase in the intensity of incident radiation results in an increase in the number of photoelectrons emitted per second and hence an increase in the photocurrent. | null | null |
209 | 17 | standard | An electric field E is maintained in a wire of length 'l' and area of cross-section 'a'. Derive the relation between the current density ‘σ' in the wire and the electric field E. | 2 | [
"Current density",
"Electric field",
"Drift velocity",
"Ohm's law"
] | Current Electricity | null | null | null | null | false | null | null | null | null |
210 | 18 | standard | How does the energy gap of an intrinsic semiconductor effectively change when doped with a (a) trivalent impurity, and (b) pentavalent impurity ? Justify your answer in each case. | 2 | [
"Energy bands in semiconductors",
"Doping",
"Intrinsic semiconductor",
"Extrinsic semiconductor",
"p-type semiconductor",
"n-type semiconductor"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | null | [
{
"part": "a",
"text": "trivalent impurity"
},
{
"part": "b",
"text": "pentavalent impurity"
}
] | null | null | false | null | null | null | null |
211 | 19 | standard | Two waves, each of amplitude 'a' and frequency 'ω' emanating from two coherent sources of light superpose at a point. If the phase difference between the two waves is φ, obtain an expression for the resultant intensity at that point. | 2 | [
"Wave superposition",
"Coherent sources",
"Interference",
"Resultant intensity",
"Phase difference"
] | Wave Optics | null | null | null | {
"figure_paths": null,
"marks": 2,
"options": null,
"or_question": null,
"question_number": "19",
"question_text": "What is the effect on the interference pattern in Young's double-slit experiment when (i) the source slit is moved closer to the plane of the slits, and (ii) the separation between the two slits is increased ? Justify your answers.",
"question_type": "standard",
"related_chapter": "Wave Optics",
"related_topics": [
"Young's double-slit experiment",
"Interference pattern",
"Fringe width",
"Coherent sources"
],
"sub_parts": [
{
"part": "i",
"text": "the source slit is moved closer to the plane of the slits"
},
{
"part": "ii",
"text": "the separation between the two slits is increased"
}
],
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
212 | 20 | standard | In Bohr model of hydrogen atom, find the ratio of period of revolution of the electron in the orbit n = 2 to that in the orbit n = 1. | 2 | [
"Bohr model of hydrogen atom",
"Period of revolution of electron",
"Quantization of angular momentum",
"Energy levels"
] | Atoms | null | null | null | null | false | null | null | null | null |
213 | 21 | standard | A convex lens (n = 1.52) has a focal length of 15.0 cm in air. Find its focal length when it is immersed in liquid of refractive index 1.65. What will be the nature of the lens? | 2 | [
"Refraction at spherical surfaces",
"Lens maker’s formula",
"Refractive index",
"Focal length",
"Nature of lens"
] | Ray Optics and Optical Instruments | null | null | null | null | false | null | null | null | null |
214 | 22 | standard | Two long, straight, parallel conductors carry steady currents in opposite directions. Explain the nature of the force of interaction between them. Obtain an expression for the magnitude of the force between the two conductors. Hence define one ampere. | 3 | [
"Force between two parallel current-carrying conductors",
"Magnetic field due to a current",
"Ampere's law",
"Definition of ampere"
] | Moving Charges and Magnetism | null | null | null | {
"figure_paths": null,
"marks": 3,
"options": null,
"or_question": null,
"question_number": "22",
"question_text": "Obtain an expression for the torque $\\vec{\\tau}$ acting on a current carrying loop in a uniform magnetic field $\\vec{B}$. Draw the necessary diagram.",
"question_type": "standard",
"related_chapter": "Moving Charges and Magnetism",
"related_topics": [
"Torque on a current loop in a magnetic field",
"Magnetic dipole moment",
"Uniform magnetic field"
],
"sub_parts": null,
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
215 | (b) | standard | Two media A and B are separated by a plane boundary. The speed of light in medium A and B is $2 \times 10^8$ ms$^{-1}$ and $2.5 \times 10^8$ ms$^{-1}$ respectively. The critical angle for a ray of light going from medium A to medium B is : | 1 | [
"Total Internal Reflection",
"Refraction"
] | Ray Optics and Optical Instruments | null | null | {
"A": "$\\sin^{-1} \\frac{1}{2}$",
"B": "$\\sin^{-1} \\frac{4}{5}$",
"C": "$\\sin^{-1} \\frac{3}{5}$",
"D": "$\\sin^{-1} \\frac{2}{5}$"
} | null | null | null | null | null | null |
216 | (iv) | standard | The figure shows the path of a light ray through a triangular prism. In this phenomenon, the angle $\theta$ is given by : | 1 | [
"Refraction through a prism"
] | Ray Optics and Optical Instruments | [
"img\\img_51.jpeg"
] | null | {
"A": "$\\sin^{-1} \\left[\\sqrt{n^2-1}\\right]$",
"B": "$\\sin^{-1} \\left(n^2 - 1\\right)$",
"C": "$\\sin^{-1} \\left[\\frac{1}{\\sqrt{n^2-1}}\\right]$",
"D": "$\\sin^{-1} \\left[\\frac{1}{n^2-1}\\right]$"
} | null | null | null | null | null | null |
217 | 30 | standard | When the terminals of a cell are connected to a conductor of resistance R, an electric current flows through the circuit. The electrolyte of the cell also offers some resistance in the path of the current, like the conductor. This resistance offered by the electrolyte is called internal resistance of the cell (r). It depends upon the nature of the electrolyte, the area of the electrodes immersed in the electrolyte and the temperature. Due to internal resistance, a part of the energy supplied by the cell is wasted in the form of heat.
When no current is drawn from the cell, the potential difference between the two electrodes in known as emf of the cell ($\varepsilon$). With a current drawn from the cell, the potential difference between the two electrodes is termed as terminal potential difference (V). | null | [
"Internal resistance",
"EMF",
"Terminal potential difference",
"Ohm's law"
] | Current Electricity | null | [
{
"part": "Conceptual Explanation",
"text": "The electrolyte of a cell offers resistance to the flow of current, termed internal resistance (r)."
},
{
"part": "Factors Affecting Internal Resistance",
"text": "Internal resistance depends on the nature of the electrolyte, the area of the electrodes, and the temperature."
},
{
"part": "Energy Loss",
"text": "Due to internal resistance, some energy supplied by the cell is wasted as heat."
},
{
"part": "EMF Definition",
"text": "The potential difference between the electrodes when no current is drawn is the electromotive force ($\\varepsilon$)."
},
{
"part": "Terminal Potential Difference Definition",
"text": "The potential difference between the electrodes when current is drawn is the terminal potential difference (V)."
}
] | null | null | null | null | null | null | null |
218 | (i) | standard | Choose the incorrect statement :
(A) The potential difference (V) between the two terminals of a cell in a closed circuit is always less than its emf ($\varepsilon$), during discharge of the cell.
(B) The internal resistance of a cell decreases with the decrease in temperature of the electrolyte.
(C) When current is drawn from the cell then V = $\varepsilon$ – Ir.
(D) The graph between potential difference between the two terminals of the cell (V) and the current (I) through it is a straight line with a negative slope. | 1 | [
"Internal resistance",
"EMF",
"Terminal voltage"
] | Current Electricity | null | null | {
"A": "The potential difference (V) between the two terminals of a cell in a closed circuit is always less than its emf ($\\varepsilon$), during discharge of the cell.",
"B": "The internal resistance of a cell decreases with the decrease in temperature of the electrolyte.",
"C": "When current is drawn from the cell then V = $\\varepsilon$ – Ir.",
"D": "The graph between potential difference between the two terminals of the cell (V) and the current (I) through it is a straight line with a negative slope."
} | null | false | null | null | null | null |
219 | (ii) | standard | Two cells of emfs 2.0 V and 6.0 V and internal resistances 0·1 $\Omega$ and 0.4 $\Omega$ respectively, are connected in parallel. The equivalent emf of the combination will be : | 1 | [
"Combination of cells",
"Parallel connection"
] | Current Electricity | null | null | {
"A": "2.0 V",
"B": "2.8 V",
"C": "6.0 V",
"D": "8.0 V"
} | null | false | null | null | null | null |
220 | (iii) | standard | Dipped in the solution, the electrode exchanges charges with the electrolyte. The positive electrode develops a potential V$_{+}$ (V$_{+}$ > 0), and the negative electrode develops a potential – (V$_-$) (V$_-$ $\geq$ 0), relative to the electrolyte adjacent to it. When no current is drawn from the cell then : | 1 | [
"EMF of a cell",
"Electrode potential"
] | Current Electricity | null | null | {
"A": "$\\varepsilon$ = V$_{+}$ + V$_-$ > 0",
"B": "$\\varepsilon$ = V$_{+}$ − V$_-$ > 0",
"C": "$\\varepsilon$ = V$_{+}$ + V$_-$ < 0",
"D": "$\\varepsilon$ = V$_{+}$ + V$_-$ = 0"
} | null | false | null | null | null | null |
221 | (iv) | standard | Five identical cells, each of emf 2 V and internal resistance 0.1 $\Omega$ are connected in parallel. This combination in turn is connected to an external resistor of 9.98 $\Omega$. The current flowing through the resistor is : | 1 | [
"Combination of cells",
"Parallel connection",
"Ohm's law"
] | Current Electricity | null | [
{
"part": "a",
"text": "Five identical cells, each of emf 2 V and internal resistance 0.1 $\\Omega$ are connected in parallel. This combination in turn is connected to an external resistor of 9.98 $\\Omega$. The current flowing through the resistor is :"
}
] | {
"A": "0.05 A",
"B": "0.1 A",
"C": "0.15 A",
"D": "0.2 A"
} | {
"figure_paths": null,
"marks": 1,
"options": {
"A": "1.0 $\\Omega$",
"B": "1.5 $\\Omega$",
"C": "2.0 $\\Omega$",
"D": "2.5 $\\Omega$"
},
"or_question": null,
"question_number": "(iv)",
"question_text": "Potential difference across a cell in the open circuit is 6 V. It becomes 4 V when a current of 2 A is drawn from it. The internal resistance of the cell is :",
"question_type": "standard",
"related_chapter": "Current Electricity",
"related_topics": [
"Internal resistance",
"Terminal voltage",
"Ohm's law"
],
"sub_parts": [
{
"part": "b",
"text": "Potential difference across a cell in the open circuit is 6 V. It becomes 4 V when a current of 2 A is drawn from it. The internal resistance of the cell is :"
}
],
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
222 | 31. | standard | (a) (i) Give any two differences between the interference pattern obtained in Young's double-slit experiment and a diffraction pattern due to a single slit.
(ii) Draw an intensity distribution graph in case of a double-slit interference pattern.
(iii) In Young's double-slit experiment using monochromatic light of wavelength $\lambda$, the intensity of light at a point on the screen, where path difference is $\lambda$, is K units. Find the intensity of light at a point on the screen where the path difference is $\frac{\lambda}{6}$. | 5 | [
"Interference",
"Diffraction",
"Young's double-slit experiment",
"Intensity distribution"
] | Wave Optics | null | [
{
"part": "(i)",
"text": "Give any two differences between the interference pattern obtained in Young's double-slit experiment and a diffraction pattern due to a single slit."
},
{
"part": "(ii)",
"text": "Draw an intensity distribution graph in case of a double-slit interference pattern."
},
{
"part": "(iii)",
"text": "In Young's double-slit experiment using monochromatic light of wavelength $\\lambda$, the intensity of light at a point on the screen, where path difference is $\\lambda$, is K units. Find the intensity of light at a point on the screen where the path difference is $\\frac{\\lambda}{6}$."
}
] | null | {
"figure_paths": null,
"marks": 5,
"options": null,
"or_question": null,
"question_number": "31.",
"question_text": "(b) (i) Draw a labelled ray diagram of a compound microscope showing image formation at least distance of distinct vision. Derive an expression for its magnifying power.\n(ii) A telescope consists of two lenses of focal length 100 cm and 5 cm. Find the magnifying power when the final image is formed at infinity.",
"question_type": "standard",
"related_chapter": "Ray Optics and Optical Instruments",
"related_topics": [
"Compound Microscope",
"Ray Diagram",
"Magnifying Power",
"Telescope"
],
"sub_parts": [
{
"part": "(i)",
"text": "Draw a labelled ray diagram of a compound microscope showing image formation at least distance of distinct vision. Derive an expression for its magnifying power."
},
{
"part": "(ii)",
"text": "A telescope consists of two lenses of focal length 100 cm and 5 cm. Find the magnifying power when the final image is formed at infinity."
}
],
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
223 | 32. | standard | (a) (i) Obtain an expression for the electric potential due to a small dipole of dipole moment $\vec{p}$, at a point $\vec{r}$ from its centre, for much larger distances compared to the size of the dipole.
(ii) Three point charges q, 2q and nq are placed at the vertices of an equilateral triangle. If the potential energy of the system is zero, find the value of n. | 5 | [
"Electric Potential",
"Electric Dipole",
"Potential Energy",
"Point Charges"
] | Electrostatic Potential and Capacitance | null | [
{
"part": "(i)",
"text": "Obtain an expression for the electric potential due to a small dipole of dipole moment $\\vec{p}$, at a point $\\vec{r}$ from its centre, for much larger distances compared to the size of the dipole."
},
{
"part": "(ii)",
"text": "Three point charges q, 2q and nq are placed at the vertices of an equilateral triangle. If the potential energy of the system is zero, find the value of n."
}
] | null | null | false | null | null | null | null |
224 | (b) | standard | 5 | [
"Gauss's Law",
"Electric Field",
"Force on a charge",
"Electric field due to a line charge"
] | Electric Charges and Fields | [
"img\\img_52.jpeg",
"img\\img_53.jpeg"
] | [
{
"part": "(i)",
"text": "State Gauss's Law in electrostatics. Apply this to obtain the electric field E at a point near a uniformly charged infinite plane sheet."
},
{
"part": "(ii)",
"text": "Two long straight wires 1 and 2 are kept as shown in the figure. The linear charge density of the two wires are $\\lambda_1 = 10 \\mu C/m$ and $\\lambda_2 = -20 \\mu C/m$. Find the net force $\\vec{F}$ experienced by an electron held at point P."
}
] | null | null | false | null | null | null | null |
|
225 | 33.(a) | standard | 25 | [
"Motion in Magnetic Field",
"Magnetic Force",
"Frequency of Revolution"
] | Moving Charges and Magnetism | [
"img\\img_54.jpeg"
] | [
{
"part": "(i)",
"text": "A particle of mass m and charge q is moving with a velocity $\\vec{v}$ in a magnetic field $\\vec{B}$ as shown in the figure. Show that it follows a helical path. Hence, obtain its frequency of revolution."
}
] | null | null | false | null | null | null | null |
|
226 | (ii) | standard | In a hydrogen atom, the electron moves in an orbit of radius 2 Å making 8×10¹⁴ revolutions per second. Find the magnetic moment associated with the orbital motion of the electron. | 5 | [
"Bohr model of hydrogen atom",
"Magnetic moment of a revolving electron"
] | Atoms | null | null | null | {
"figure_paths": null,
"marks": 5,
"options": null,
"or_question": null,
"question_number": "(b)",
"question_text": null,
"question_type": "standard",
"related_chapter": "Moving Charges and Magnetism",
"related_topics": [
"Current sensitivity of a galvanometer",
"Voltage sensitivity of a galvanometer",
"Conversion of galvanometer to voltmeter"
],
"sub_parts": [
{
"part": "(i)",
"text": "What is current sensitivity of a galvanometer ? Show how the current sensitivity of a galvanometer may be increased. \"Increasing the current sensitivity of a galvanometer may not necessarily increase its voltage sensitivity.\" Explain."
},
{
"part": "(ii)",
"text": "A moving coil galvanometer has a resistance 15 Ω and takes 20 mA to produce full scale deflection. How can this galvanometer be converted into a voltmeter of range 0 to 100 V ?"
}
],
"text": null,
"vi_candidate": null
} | false | null | null | null | null |
227 | 1 | standard | Consider a group of charges 91, 92, 93 ... such that Σq ≠ 0. Then equipotentials at a large distance, due to this group are approximately : | 1 | [
"Equipotential Surfaces",
"Electric Potential due to a system of charges"
] | Electrostatic Potential and Capacitance | null | null | {
"A": "Plane",
"B": "Spherical surface",
"C": "Paraboloidal surface",
"D": "Ellipsoidal surface"
} | null | false | null | null | null | null |
228 | 2 | standard | A proton is taken from point P₁ to point P₂, both located in an electric field. The potentials at points P₁ and P₂ are – 5 V and + 5 V respectively. Assuming that kinetic energies of the proton at points P₁ and P₂ are zero, the work done on the proton is : | 1 | [
"Electric Potential Difference",
"Work done in moving a charge"
] | Electrostatic Potential and Capacitance | null | null | {
"A": "- 1.6 × 10⁻¹⁸ J",
"B": "1.6 × 10⁻¹⁸ J",
"C": "Zero",
"D": "0.8 × 10⁻¹⁸ J"
} | null | false | null | null | null | null |
229 | 3 | standard | A 2.0 cm segment of wire, carrying 5.0 A current in positive y-direction lies along y-axis, as shown in the figure. The magnetic field at a point (3 m, 4 m, 0) due to this segment (part of a circuit) is : | 1 | [
"Biot-Savart Law",
"Magnetic field due to a current element"
] | Moving Charges and Magnetism | [
"img\\img_55.jpeg"
] | null | {
"A": "(0.12 nT) ĵ",
"B": "– (0.10 nT) ĵ",
"C": "– (0.24 nT) k̂",
"D": "(0.24 nT) k̂"
} | null | false | null | null | null | null |
230 | 4 | standard | A circular loop of wire, carrying a current ‘I’ is lying in xy-plane with its centre coinciding with the origin. It is subjected to a uniform magnetic field pointing along + z-axis. The loop will : | 1 | [
"Torque on a current loop in a magnetic field",
"Force on a current carrying conductor in a magnetic field"
] | Moving Charges and Magnetism | null | null | {
"A": "move along x-axis",
"B": "move along – y-axis",
"C": "move along z-axis",
"D": "remain stationary"
} | null | false | null | null | null | null |
231 | 5. | standard | A current carrying circular loop of magnetic moment $\vec{M}$ is suspended in a vertical plane in an external magnetic field $\vec{B}$ such that its plane is normal to $\vec{B}$. The work done in rotating this loop by $45^\circ$ about an axis perpendicular to $\vec{B}$ is closest to : | 1 | [
"Torque on a current loop in a magnetic field",
"Work done in rotating a magnetic dipole in a magnetic field"
] | Moving Charges and Magnetism | [] | null | {
"A": "- 0.3 MB",
"B": "0.3 MB",
"C": "- 1.7 MB",
"D": "1.7 MB"
} | null | false | null | null | null | null |
232 | 6. | standard | The current in a coil of 15 mH increases uniformly from zero to 4 A in 0.004 s. The emf induced in the coil will be : | 1 | [
"Electromagnetic Induction",
"Induced EMF",
"Self-inductance"
] | Electromagnetic Induction | [] | null | {
"A": "22.5 V",
"B": "17.5 V",
"C": "15.0 V",
"D": "12.5 V"
} | null | false | null | null | null | null |
233 | 7. | standard | Consider a solenoid of length $l$ and area of cross-section A with fixed number of turns. The self-inductance of the solenoid will increase if : | 1 | [
"Self-inductance of a solenoid"
] | Electromagnetic Induction | [] | null | {
"A": "both $l$ and A are increased",
"B": "$l$ is decreased and A is increased",
"C": "$l$ is increased and A is decreased",
"D": "both $l$ and A are decreased"
} | null | false | null | null | null | null |
234 | 8. | standard | Which one of the following has the highest frequency ? | 1 | [
"Electromagnetic Spectrum",
"Frequency of electromagnetic waves"
] | Electromagnetic Waves | [] | null | {
"A": "Infrared rays",
"B": "Gamma rays",
"C": "Radio waves",
"D": "Microwaves"
} | null | false | null | null | null | null |
235 | 9. | standard | A proton and an alpha particle having equal velocities approach a target nucleus. They come momentarily to rest and then reverse their directions. The ratio of the distance of closest approach of the proton to that of the alpha particle will be : | 1 | [
"Distance of closest approach",
"Rutherford's scattering experiment",
"Electrostatic potential energy"
] | Atoms | [] | null | {
"A": "$\\frac{1}{2}$",
"B": "2",
"C": "$\\frac{1}{4}$",
"D": "4"
} | null | false | null | null | null | null |
236 | 10 | standard | Which one of the following is the correct graph between the maximum kinetic energy (Km) of the emitted photoelectrons and the frequency of incident radiation ($\nu$) for a given photosensitive surface ? | 1 | [
"Photoelectric effect",
"Einstein's photoelectric equation"
] | Dual Nature of Radiation and Matter | [
"img\\img_56.jpeg"
] | null | {
"A": null,
"B": null,
"C": null,
"D": null
} | null | false | null | null | null | null |
237 | 11 | standard | An electron makes a transition from n = 2 level to n = 1 level in the Bohr model of a hydrogen atom. Its period of revolution : | 1 | [
"Bohr model of hydrogen atom",
"Energy levels",
"Period of revolution of electron"
] | Atoms | null | null | {
"A": "increases by 87.5%",
"B": "decreases by 87.5%",
"C": "increases by 43.75%",
"D": "decreases by 43.75%"
} | null | false | null | null | null | null |
238 | 12 | standard | Si is doped with a pentavalent element. The energy required to set the additional electron free is about : | 1 | [
"Doping",
"Energy bands in semiconductors",
"Extrinsic semiconductors"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | null | null | {
"A": "0.01 eV",
"B": "0.05 eV",
"C": "0.72 eV",
"D": "1.1 eV"
} | null | false | null | null | null | null |
239 | 13 | assertion_reason | null | 1 | [
"Energy bands in semiconductors",
"Valence band",
"Conduction band",
"Doping"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | 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 a semiconductor, the electrons in the conduction band have lesser energy than those in the valence band. | Donor energy level is just above the valence band in a semiconductor. | null | null |
240 | 14 | assertion_reason | null | 1 | [
"Photoelectric effect",
"Particle nature of light",
"Intensity of light",
"Frequency of light"
] | 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 | Photoelectric effect demonstrates the particle nature of light. | Photoelectric current is proportional to frequency of incident radiation. | null | null |
241 | 15 | assertion_reason | null | 1 | [
"Motion in a magnetic field",
"Force on a moving charge",
"Radius of circular path",
"Momentum"
] | 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 | A proton and an electron enter a uniform magnetic field $\vec{B}$ with the same momentum $\vec{p}$ such that $\vec{p}$ is perpendicular to $\vec{B}$. They describe circular paths of the same radius. | In a magnetic field, orbital radius r is equal to $\frac{p}{qB}$. | null | null |
242 | 16 | assertion_reason | null | 1 | [
"Refraction",
"Lenses",
"Refractive index",
"Lens maker’s formula"
] | 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 | A convex lens, when immersed in a liquid, disappears. | The refractive indices of material of the lens and the liquid are equal. | null | null |
243 | 17 | standard | (a) What is meant by ‘relaxation time' of free electrons in a conductor ? Show that the resistance of a conductor can be expressed by R = $\frac{ml}{ne^2\tau A}$, where symbols have their usual meanings. | 2 | [
"Drift velocity",
"Electrical resistivity",
"Ohm's law"
] | Current Electricity | null | [
{
"part": "a",
"text": "What is meant by ‘relaxation time' of free electrons in a conductor ?"
},
{
"part": "a",
"text": "Show that the resistance of a conductor can be expressed by R = $\\frac{ml}{ne^2\\tau A}$, where symbols have their usual meanings."
}
] | null | {
"figure_paths": null,
"marks": 2,
"options": null,
"or_question": null,
"question_number": "17",
"question_text": "(b) Draw the circuit diagram of a Wheatstone bridge. Obtain the condition when no current flows through the galvanometer in it.",
"question_type": "standard",
"related_chapter": "Current Electricity",
"related_topics": [
"Kirchhoff's rules",
"Wheatstone bridge"
],
"sub_parts": [
{
"part": "b",
"text": "Draw the circuit diagram of a Wheatstone bridge."
},
{
"part": "b",
"text": "Obtain the condition when no current flows through the galvanometer in it."
}
],
"text": null,
"vi_candidate": null
} | false | null | null | null | null |
244 | 18 | standard | The magnifying power of an astronomical telescope is 24. In normal adjustment, distance between its two lenses is 150 cm. Find the focal length of the objective lens. | 2 | [
"Telescope",
"Magnifying power",
"Ray Optics"
] | Ray Optics and Optical Instruments | null | null | null | null | false | null | null | null | null |
245 | 19 | standard | Explain the following : | 2 | [] | null | null | [
{
"part": "a",
"text": "For a simple microscope, the angular size of the object equals the angular size of the image. Yet it offers magnification."
},
{
"part": "b",
"text": "Both plane and convex mirrors produce virtual images of objects. Can they produce real images under some circumstances ?"
}
] | null | null | false | null | null | null | null |
246 | 20 | standard | The minimum intensity of white light that our eyes can perceive is about 0.1 nWm$^{-2}$. Calculate the number of photons of this light entering our pupil (area 0.4 cm$^2$) per second. (Take average wavelength of white light = 500 nm and Planck's constant = 6.6 × 10$^{-34}$ Js) | 2 | [
"Photoelectric effect",
"Dual Nature of Radiation"
] | Dual Nature of Radiation and Matter | null | null | null | null | false | null | null | null | null |
247 | 21 | standard | Suppose a pure Si crystal has 5 × 10$^{28}$ atoms m$^{-3}$. It is doped by 1 ppm concentration of boron. Calculate the concentration of holes and electrons, given that n$_i$ = 1.5 × 10$^{16}$ m$^{-3}$. Is the doped crystal n-type or p-type? | 2 | [
"Semiconductors",
"Doping",
"p-type semiconductor",
"n-type semiconductor"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | null | null | null | null | false | null | null | null | null |
248 | 22 | standard | Determine the current in branches AB, AC and BC of the network shown in figure. | 3 | [
"Kirchhoff's rules",
"Current electricity"
] | Current Electricity | [
"img/img_57.jpeg",
"img/img_38.jpeg"
] | null | null | null | false | null | null | null | null |
249 | 23 | standard | Two long straight parallel conductors carrying currents, exert a force on each other. Why ? Derive an expression for the force per unit length between two long straight parallel conductors carrying currents in opposite directions. Explain the nature of the force between these conductors. | 3 | [
"Force on a current-carrying conductor in a magnetic field",
"Force between two parallel current-carrying conductors"
] | Moving Charges and Magnetism | null | null | null | null | false | null | null | null | null |
250 | 24 | standard | A sinusoidal voltage is applied to an electric circuit containing a circuit element 'X' in which the current leads the voltage by $\frac{\pi}{2}$. | 3 | [
"AC circuits",
"Reactance"
] | Alternating Current | null | [
{
"part": "(a)",
"text": "Identify the circuit element 'X' in the circuit."
},
{
"part": "(b)",
"text": "Write the formula for its reactance."
},
{
"part": "(c)",
"text": "Show graphically the variation of this reactance with frequency of ac voltage."
},
{
"part": "(d)",
"text": "Explain the behaviour of this element when it is used in (i) an ac circuit, and (ii) a dc circuit."
}
] | null | null | false | null | null | null | null |
251 | 25 | standard | The electric field in an electromagnetic wave in vacuum is given by :
$\vec{E} = (6.3 \text{ N/C}) [\cos (1.5 \text{ rad/m}) y + (4.5 \times 10^8 \text{ rad/s}) t] \hat{i}$ | 3 | [
"Electromagnetic Waves",
"Electric Field",
"Wavelength",
"Frequency",
"Amplitude of Magnetic Field"
] | Electromagnetic Waves | null | [
{
"part": "a",
"text": "Find the wavelength and frequency of the wave."
},
{
"part": "b",
"text": "What is the amplitude of the magnetic field of the wave ?"
},
{
"part": "c",
"text": "Write an expression for the magnetic field of this wave."
}
] | null | null | false | null | null | null | null |
252 | 26 | standard | State Bohr's first and second postulates. Use them to derive an expression for the radius of the $n^{th}$ orbit in a hydrogen atom. | 3 | [
"Bohr's Postulates",
"Atomic Model",
"Radius of nth orbit"
] | Atoms | null | null | null | null | false | null | null | null | null |
253 | 27 | standard | 3 | [
"Atomic Mass Unit",
"Nuclear Binding Energy",
"Mass Defect"
] | Nuclei | null | [
{
"part": "a",
"text": "Define atomic mass unit (u)."
},
{
"part": "b",
"text": "Calculate the energy required to separate a deuteron into its constituent parts (a proton and a neutron). Given :\nm(D) = 2.014102 u\nm$_H$ = 1.007825 u\nm$_n$ = 1.008665 u"
}
] | null | null | false | null | null | null | null |
|
254 | 28 | standard | 3 | [
"p-n junction diode",
"V-I characteristics",
"Forward biasing",
"Reverse biasing",
"Energy band diagrams",
"Insulator",
"Semiconductor",
"Conductor"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | null | [
{
"part": "a",
"text": "Draw the circuit diagrams for obtaining the V – I characteristics of a p-n junction diode. Explain briefly the salient features of the V - I characteristics in (i) forward biasing, and (ii) reverse biasing."
}
] | null | {
"figure_paths": null,
"marks": 3,
"options": null,
"or_question": null,
"question_number": "28",
"question_text": "On the basis of energy band diagrams, distinguish between (i) an insulator, (ii) a semiconductor, and (iii) a conductor.",
"question_type": "standard",
"related_chapter": "Semiconductor Electronics: Materials, Devices and Simple Circuits",
"related_topics": [
"Energy band diagrams",
"Insulator",
"Semiconductor",
"Conductor"
],
"sub_parts": null,
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
|
255 | 29 | case_study | null | 3 | [
"Electric Potential",
"Electric Field",
"Motion of Charges in Electric Field"
] | Chapter–2: Electrostatic Potential and Capacitance | [
"pathiimg\\img_59.jpeg",
"path.fmg\\img_60.jpeg"
] | null | null | null | null | null | null | The figure shows four pairs of parallel identical conducting plates, separated by the same distance 2.0 cm and arranged perpendicular to x-axis. The electric potential of each plate is mentioned. The electric field between a pair of plates is uniform and normal to the plates. | [
{
"number": "(i)",
"options": {
"A": "I",
"B": "II",
"C": "III",
"D": "IV"
},
"text": "For which pair of the plates is the electric field $\\vec{E}$ along $\\hat{i}$ ?"
},
{
"number": "(ii)",
"options": {
"A": "move along $\\hat{i}$ at constant speed",
"B": "move along $-\\hat{i}$ at constant speed",
"C": "accelerate along $\\hat{i}$",
"D": "accelerate along $-\\hat{i}$"
},
"text": "An electron is released midway between the plates of pair IV. It will :"
},
{
"number": "(iii)",
"options": {
"A": "V = $V_0 + \\alpha x$",
"B": "V = $V_0 + \\alpha x^2$",
"C": "V = $V_0 + \\alpha x^{1/2}$",
"D": "V = $V_0 + \\alpha x^{3/2}$"
},
"text": "Let $V_0$ be the potential at the left plate of any set, taken to be at x = 0 m. Then potential V at any point ($0 \\le x \\le 2$ cm) between the plates of that set can be expressed as :"
}
] |
256 | (iv) | standard | Let E₁, E₂, E₃ and E₄ be the magnitudes of the electric field between the pairs of plates, I, II, III and IV respectively. Then : | 1 | [
"Electric Field"
] | Electric Charges and Fields | null | null | {
"A": "E₁ > E₂ > E₃ > E₄",
"B": "E₃ > E₄ > E₁ > E₂",
"C": "E₄ > E₃ > E₂ > E₁",
"D": "E₂ > E₃ > E₄ > E₁"
} | {
"figure_paths": null,
"marks": 1,
"options": {
"A": "1.3 × 10⁵ m/s",
"B": "2.6 × 10⁶ m/s",
"C": "6.5 × 10⁵ m/s",
"D": "5.2 × 10⁷ m/s"
},
"or_question": null,
"question_number": "(iv)",
"question_text": "An electron is projected from the right plate of set I directly towards its left plate. It just comes to rest at the plate. The speed with which it was projected is about : (Take (e/m) =1.76 × 10¹¹ C/kg)",
"question_type": "standard",
"related_chapter": "Electric Charges and Fields",
"related_topics": [
"Electric Field",
"Work and Energy"
],
"sub_parts": null,
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
257 | 30 | case_study | null | 1 | [
"Diffraction",
"Interference",
"Wave Optics"
] | Wave Optics | null | null | null | null | null | null | null | Diffraction and interference are closely related phenomena that occur together. Diffraction is the phenomenon of bending of light around the edges of the obstacle, while interference is the combination of waves that results in a new wave pattern. In order to get interference, there must be at least two waves that are diffracting. So while diffraction can occur without interference, interference cannot occur without diffraction.
Two slits of width 2 μm each in an opaque material are separated by a distance of 6 μm. Monochromatic light of wavelength 450 nm is incident normally on the slits. One finds a combined interference and diffraction pattern on the screen. | [
{
"number": "(i)",
"options": {
"A": "2",
"B": "3",
"C": "4",
"D": "6"
},
"text": "The number of peaks of the interference fringes formed within the central peak of the envelope of the diffraction pattern will be :"
},
{
"number": "(ii)",
"options": {
"A": "1",
"B": "2",
"C": "3",
"D": "4"
},
"text": "The number of peaks of the interference formed if the slit width is doubled while keeping the distance between the slits same will be :"
}
] |
258 | (iii)(a) | standard | If instead of 450 nm light, another light of wavelength 680 nm is used, number of peaks of the interference formed in the central peak of the envelope of the diffraction pattern will be : | 1 | [
"Wave Optics",
"Interference",
"Diffraction"
] | Chapter–10 | null | null | {
"A": "2",
"B": "4",
"C": "6",
"D": "9"
} | null | null | null | null | null | null |
259 | (iii)(b) | standard | Consider the diffraction of light by a single slit described in this case study. The first minimum falls at an angle 0 equal to: | 1 | [
"Wave Optics",
"Diffraction"
] | Chapter–10 | null | null | {
"A": "sin-1 (0.12)",
"B": "sin-1 (0.225)",
"C": "sin-1 (0.32)",
"D": "sin-1 (0.45)"
} | {
"figure_paths": null,
"marks": 1,
"options": {
"A": "2",
"B": "4",
"C": "6",
"D": "9"
},
"or_question": null,
"question_number": "(iii)(a)",
"question_text": "If instead of 450 nm light, another light of wavelength 680 nm is used, number of peaks of the interference formed in the central peak of the envelope of the diffraction pattern will be :",
"question_type": "standard",
"related_chapter": "Chapter–10",
"related_topics": [
"Wave Optics",
"Interference",
"Diffraction"
],
"sub_parts": null,
"text": null,
"vi_candidate": null
} | null | null | null | null | null |
260 | (iv) | standard | The number of bright fringes formed due to interference on 1 m of screen placed at $\frac{4}{3}$ m away from the slits is : | 1 | [
"Wave Optics",
"Interference"
] | Chapter–10 | null | null | {
"A": "2",
"B": "3",
"C": "6",
"D": "10"
} | null | null | null | null | null | null |
261 | 31.(a) | standard | Obtain the expression for the capacitance of a parallel plate capacitor with a dielectric medium between its plates. | 5 | [
"Electrostatic Potential and Capacitance",
"Capacitors",
"Dielectrics"
] | Chapter–2 | null | [
{
"part": "(i)",
"text": "Obtain the expression for the capacitance of a parallel plate capacitor with a dielectric medium between its plates."
},
{
"part": "(ii)",
"text": "A charge of 6 $\\mu$C is given to a hollow metallic sphere of radius 0.2 m. Find the potential at (i) the surface and (ii) the centre of the sphere."
}
] | null | null | null | null | null | null | null |
262 | 31.(b) | standard | A charge + Q is placed on a thin conducting spherical shell of radius R. Use Gauss's theorem to derive an expression for the electric field at a point lying (i) inside and (ii) outside the shell. | 5 | [
"Electric Charges and Fields",
"Gauss's theorem",
"Electric field"
] | Chapter–1 | null | [
{
"part": "(i)",
"text": "A charge + Q is placed on a thin conducting spherical shell of radius R. Use Gauss's theorem to derive an expression for the electric field at a point lying (i) inside and (ii) outside the shell."
},
{
"part": "(ii)",
"text": "Show that the electric field for same charge density ($\\sigma$) is twice in case of a conducting plate or surface than in a nonconducting sheet."
}
] | null | {
"figure_paths": null,
"marks": 5,
"options": null,
"or_question": null,
"question_number": "31.(a)",
"question_text": "Obtain the expression for the capacitance of a parallel plate capacitor with a dielectric medium between its plates.",
"question_type": "standard",
"related_chapter": "Chapter–2",
"related_topics": [
"Electrostatic Potential and Capacitance",
"Capacitors",
"Dielectrics"
],
"sub_parts": [
{
"part": "(i)",
"text": "Obtain the expression for the capacitance of a parallel plate capacitor with a dielectric medium between its plates."
},
{
"part": "(ii)",
"text": "A charge of 6 $\\mu$C is given to a hollow metallic sphere of radius 0.2 m. Find the potential at (i) the surface and (ii) the centre of the sphere."
}
],
"text": null,
"vi_candidate": null
} | null | null | null | null | null |
263 | 32 | standard | (a) (i) (1) What is meant by current sensitivity of a galvanometer ?
Mention the factors on which it depends.
(2) A galvanometer of resistance G is converted into a
voltmeter of range (0 – V) by using a resistance R. Find
the resistance, in terms of R and G, required to convert it
into a voltmeter of range $\left(0 - \frac{V}{2}\right)$. | 5 | [
"Current sensitivity of galvanometer",
"Conversion of galvanometer to voltmeter"
] | Moving Charges and Magnetism | null | [
{
"part": "(a) (i) (1)",
"text": "What is meant by current sensitivity of a galvanometer ?\nMention the factors on which it depends."
},
{
"part": "(a) (i) (2)",
"text": "A galvanometer of resistance G is converted into a\nvoltmeter of range (0 – V) by using a resistance R. Find\nthe resistance, in terms of R and G, required to convert it\ninto a voltmeter of range $\\left(0 - \\frac{V}{2}\\right)$."
}
] | null | null | null | null | null | null | null |
264 | 32 | standard | (a) (ii) The magnetic flux through a coil of resistance 5 $\Omega$ increases
with time as :
$\phi = (2.0 t^3 + 5.0 t^2 + 6.0 t)$ mWb
Find the magnitude of induced current through the coil at
t = 2 s. | 5 | [
"Magnetic flux",
"Induced current",
"Faraday's law"
] | Electromagnetic Induction | null | [
{
"part": "(a) (ii)",
"text": "The magnetic flux through a coil of resistance 5 $\\Omega$ increases\nwith time as :\n$\\phi = (2.0 t^3 + 5.0 t^2 + 6.0 t)$ mWb\nFind the magnitude of induced current through the coil at\nt = 2 s."
}
] | null | null | null | null | null | null | null |
265 | 32 | standard | (b) (i) A rectangular coil of N turns and area of cross-section A is
rotated at a steady angular speed $\omega$ in a uniform magnetic
field. Obtain an expression for the emf induced in the coil at
any instant of time. | 5 | [
"EMF induced in a rotating coil",
"Faraday's law"
] | Electromagnetic Induction | null | [
{
"part": "(b) (i)",
"text": "A rectangular coil of N turns and area of cross-section A is\nrotated at a steady angular speed $\\omega$ in a uniform magnetic\nfield. Obtain an expression for the emf induced in the coil at\nany instant of time."
}
] | null | null | null | null | null | null | null |
266 | 32 | standard | (b) (ii) Two coplanar and concentric circular loops $L_1$ and $L_2$ are
placed coaxially with their centres coinciding. The radii of $L_1$
and $L_2$ are 1 cm and 100 cm respectively. Calculate the
mutual inductance of the loops. (Take $\pi^2 = 10$) | 5 | [
"Mutual inductance"
] | Electromagnetic Induction | null | [
{
"part": "(b) (ii)",
"text": "Two coplanar and concentric circular loops $L_1$ and $L_2$ are\nplaced coaxially with their centres coinciding. The radii of $L_1$\nand $L_2$ are 1 cm and 100 cm respectively. Calculate the\nmutual inductance of the loops. (Take $\\pi^2 = 10$)"
}
] | null | null | null | null | null | null | null |
267 | 32 | standard | null | 5 | [
"Current sensitivity of galvanometer",
"Conversion of galvanometer to voltmeter",
"Magnetic flux",
"Induced current",
"Faraday's law"
] | Moving Charges and Magnetism, Electromagnetic Induction | null | [
{
"part": "(a)",
"text": "(i) (1) What is meant by current sensitivity of a galvanometer ?\nMention the factors on which it depends.\n(2) A galvanometer of resistance G is converted into a\nvoltmeter of range (0 – V) by using a resistance R. Find\nthe resistance, in terms of R and G, required to convert it\ninto a voltmeter of range $\\left(0 - \\frac{V}{2}\\right)$.\n(ii) The magnetic flux through a coil of resistance 5 $\\Omega$ increases\nwith time as :\n$\\phi = (2.0 t^3 + 5.0 t^2 + 6.0 t)$ mWb\nFind the magnitude of induced current through the coil at\nt = 2 s."
}
] | null | {
"figure_paths": null,
"marks": 5,
"options": null,
"or_question": null,
"question_number": "32",
"question_text": null,
"question_type": "standard",
"related_chapter": "Electromagnetic Induction",
"related_topics": [
"EMF induced in a rotating coil",
"Faraday's law",
"Mutual inductance"
],
"sub_parts": [
{
"part": "(b)",
"text": "(i) A rectangular coil of N turns and area of cross-section A is\nrotated at a steady angular speed $\\omega$ in a uniform magnetic\nfield. Obtain an expression for the emf induced in the coil at\nany instant of time.\n(ii) Two coplanar and concentric circular loops $L_1$ and $L_2$ are\nplaced coaxially with their centres coinciding. The radii of $L_1$\nand $L_2$ are 1 cm and 100 cm respectively. Calculate the\nmutual inductance of the loops. (Take $\\pi^2 = 10$)"
}
],
"text": null,
"vi_candidate": null
} | null | null | null | null | null |
268 | 33 | standard | (a) (i) Trace the path of a ray of light showing refraction through a
triangular prism and hence obtain an expression for angle of
deviation ($\delta$) in terms of A, i and e, where symbols have their
usual meanings. Draw a graph showing the variation of angle
of deviation with the angle of incidence. | 5 | [
"Refraction through a prism",
"Angle of deviation"
] | Ray Optics and Optical Instruments | null | [
{
"part": "(a) (i)",
"text": "Trace the path of a ray of light showing refraction through a\ntriangular prism and hence obtain an expression for angle of\ndeviation ($\\delta$) in terms of A, i and e, where symbols have their\nusual meanings. Draw a graph showing the variation of angle\nof deviation with the angle of incidence."
}
] | null | null | null | null | null | null | null |
269 | 1 | standard | An isolated conductor, with a cavity, has a net charge +Q. A point charge +q is inside the cavity. The charges on the cavity wall and the outer surface are respectively : | 1 | [
"Electrostatic Induction",
"Gauss's Law"
] | Chapter–1: Electric Charges and Fields | null | null | {
"A": "0 and Q",
"B": "- q and Q - q",
"C": "- q and Q + q",
"D": "0 and Q - q"
} | null | null | null | null | null | null |
270 | 2 | standard | A proton is taken from point P₁ to point P₂, both located in an electric field. The potentials at points P₁ and P₂ are – 5 V and + 5 V respectively. Assuming that kinetic energies of the proton at points P₁ and P₂ are zero, the work done on the proton is : | 1 | [
"Electric Potential",
"Work Done by Electric Field"
] | Chapter–2: Electrostatic Potential and Capacitance | null | null | {
"A": "$– 1.6 × 10^{-18}$ J",
"B": "$1.6 × 10^{-18}$ J",
"C": "Zero",
"D": "$0.8 × 10^{-18}$ J"
} | null | null | null | null | null | null |
271 | 3 | standard | A 2.0 cm segment of wire, carrying 5.0 A current in positive y-direction lies along y-axis, as shown in the figure. The magnetic field at a point (3 m, 4 m, 0) due to this segment (part of a circuit) is : | 1 | [
"Biot-Savart Law",
"Magnetic Field due to a Current Element"
] | Chapter–4: Moving Charges and Magnetism | [
"img\\img_62.jpeg"
] | null | {
"A": "(0.12 nT) $\\hat{j}$",
"B": "– (0.10 nT) $\\hat{j}$",
"C": "– (0.24 nT) $\\hat{k}$",
"D": "(0.24 nT) $\\hat{k}$"
} | null | null | null | null | null | null |
272 | 4 | standard | Two thin long parallel wires separated by a distance 'a' carry current 'I' in opposite directions. The wires will : | 1 | [
"Force between two parallel current-carrying conductors"
] | Moving Charges and Magnetism | null | null | {
"A": "Repel each other with a force $\\frac{\\mu_0 I^2}{2\\pi a}$, per unit length.",
"B": "Attract each other with a force $\\frac{\\mu_0 I^2}{2\\pi a}$, per unit length.",
"C": "Attract each other with a force $\\frac{\\mu_0 I^2}{2\\pi a^2}$, per unit length.",
"D": "Repel each other with a force $\\frac{\\mu_0 I^2}{2\\pi a^2}$, per unit length."
} | null | false | null | null | null | null |
273 | 5 | standard | A current carrying circular loop of magnetic moment $\vec{M}$ is suspended in a vertical plane in an external magnetic field $\vec{B}$ such that its plane is normal to $\vec{B}$. The work done in rotating this loop by $45^\circ$ about an axis perpendicular to $\vec{B}$ is closest to : | 1 | [
"Torque on a current loop in uniform magnetic field",
"Work done in rotating a magnetic dipole in a magnetic field"
] | Moving Charges and Magnetism | null | null | {
"A": "- 0.3 MB",
"B": "0.3 MB",
"C": "- 1.7 MB",
"D": "1.7 MB"
} | null | false | null | null | null | null |
274 | 6 | standard | The mutual inductance of two coils $C_1$ and $C_2$ is 20 mH. In coil $C_1$, the current changes from 4 A to zero in 0.2 s. If the resistance of coil $C_2$ is 4 $\Omega$, then the charge that flows through it per second will be : | 1 | [
"Mutual induction",
"Induced EMF",
"Induced current"
] | Electromagnetic Induction | null | null | {
"A": "4.0 C",
"B": "1.5 C",
"C": "0.05 C",
"D": "0.1 C"
} | null | false | null | null | null | null |
275 | 7 | standard | Consider a solenoid of length $l$ and area of cross-section A with fixed number of turns. The self-inductance of the solenoid will increase if : | 1 | [
"Self induction",
"Inductance of a solenoid"
] | Electromagnetic Induction | null | null | {
"A": "both $l$ and A are increased",
"B": "$l$ is decreased and A is increased",
"C": "$l$ is increased and A is decreased",
"D": "both $l$ and A are decreased"
} | null | false | null | null | null | null |
276 | 8 | standard | Electromagnetic waves with frequency $1.0 imes 10^{18}$ Hz are known as : | 1 | [
"Electromagnetic Waves",
"Electromagnetic Spectrum"
] | Electromagnetic Waves | null | null | {
"A": "Infrared rays",
"B": "Ultraviolet rays",
"C": "X-rays",
"D": "Gamma rays"
} | null | false | null | null | null | null |
277 | 9 | standard | A proton and an alpha particle having equal velocities approach a target nucleus. They come momentarily to rest and then reverse their directions. The ratio of the distance of closest approach of the proton to that of the alpha particle will be : | 1 | [
"Electrostatic Potential Energy",
"Nuclear Physics"
] | Electrostatic Potential and Capacitance | null | null | {
"A": "$\\frac{1}{2}$",
"B": "2",
"C": "$\\frac{1}{4}$",
"D": "4"
} | null | false | null | null | null | null |
278 | 10 | standard | The figure shows the variation of stopping potential $V_0$ with frequency $\nu$ of incident radiation, for three materials $M_1$, $M_2$ and $M_3$ with work functions $\phi_1$, $\phi_2$ and $\phi_3$ respectively. Then : | 1 | [
"Photoelectric Effect",
"Work Function",
"Stopping Potential"
] | Dual Nature of Radiation and Matter | [
"img\\img_63.jpeg"
] | null | {
"A": "$\\phi_1 > \\phi_2 > \\phi_3$",
"B": "$\\phi_2 > \\phi_3 > \\phi_1$",
"C": "$\\phi_3 > \\phi_2 > \\phi_1$",
"D": "$\\phi_2 > \\phi_1 > \\phi_3$"
} | null | false | null | null | null | null |
279 | 11 | standard | An electron makes a transition from n = 2 level to n = 1 level in the Bohr model of a hydrogen atom. Its period of revolution : | 1 | [
"Bohr Model",
"Atomic Spectra"
] | Atoms | null | null | {
"A": "increases by 87.5%",
"B": "decreases by 87.5%",
"C": "increases by 43.75%",
"D": "decreases by 43.75%"
} | null | false | null | null | null | null |
280 | 12 | standard | Si is doped with a pentavalent element. The energy required to set the additional electron free is about : | 1 | [
"Doping",
"Energy bands in semiconductors"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | null | null | {
"A": "0.01 eV",
"B": "0.05 eV",
"C": "0.72 eV",
"D": "1.1 eV"
} | null | false | null | null | null | null |
281 | 13 | assertion_reason | null | 1 | [
"Energy bands in semiconductors",
"Intrinsic and extrinsic semiconductors"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | 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 a semiconductor, the electrons in the conduction band have lesser energy than those in the valence band. | Donor energy level is just above the valence band in a semiconductor. | null | null |
282 | 14 | assertion_reason | null | 1 | [
"Photoelectric effect",
"Dual nature of radiation"
] | 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 | Photoelectric effect demonstrates the particle nature of light. | Photoelectric current is proportional to frequency of incident radiation. | null | null |
283 | 15 | assertion_reason | null | 1 | [
"Motion in a magnetic field",
"Force on a moving charge in magnetic field"
] | 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 | A proton and an electron enter a uniform magnetic field $\vec{B}$ with the same momentum $\vec{p}$ such that $\vec{p}$ is perpendicular to $\vec{B}$. They describe circular paths of the same radius. | In a magnetic field, orbital radius r is equal to $\frac{p}{qB}$. | null | null |
284 | 16 | assertion_reason | null | 2 | [
"Refraction of light",
"Lenses"
] | 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 | Assertion (A) : A convex lens, when immersed in a liquid, disappears. | Reason (R) : The refractive indices of material of the lens and the liquid are equal. | null | null |
285 | 17 | standard | (a) What is meant by 'relaxation time' of free electrons in a conductor ? Show that the resistance of a conductor can be expressed by R = $\frac{ml}{ne^2\tau A}$, where symbols have their usual meanings. | 2 | [
"Drift velocity",
"Electrical resistivity",
"Ohm's law"
] | Current Electricity | null | [
{
"part": "(a)",
"text": "What is meant by 'relaxation time' of free electrons in a conductor ? Show that the resistance of a conductor can be expressed by R = $\\frac{ml}{ne^2\\tau A}$, where symbols have their usual meanings."
}
] | null | {
"figure_paths": null,
"marks": 2,
"options": null,
"or_question": null,
"question_number": "17",
"question_text": "(b) Draw the circuit diagram of a Wheatstone bridge. Obtain the condition when no current flows through the galvanometer in it.",
"question_type": "standard",
"related_chapter": "Current Electricity",
"related_topics": [
"Kirchhoff's rules",
"Wheatstone bridge"
],
"sub_parts": [
{
"part": "(b)",
"text": "Draw the circuit diagram of a Wheatstone bridge. Obtain the condition when no current flows through the galvanometer in it."
}
],
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
286 | 18 | standard | The magnifying power of an astronomical telescope is 24. In normal adjustment, distance between its two lenses is 150 cm. Find the focal length of the objective lens. | 2 | [
"Telescope",
"Magnifying power"
] | Ray Optics and Optical Instruments | null | null | null | null | false | null | null | null | null |
287 | 19 | standard | Write two points of difference between interference and diffraction of light. | 2 | [
"Interference",
"Diffraction"
] | Wave Optics | null | null | null | null | false | null | null | null | null |
288 | 20 | standard | Light of wavelength 500 nm is incident on caesium metal (work function 2.14 eV) and photoemission of electrons occurs. Calculate the (i) kinetic energy (in eV) of the fastest electrons and (ii) stopping potential for this situation. (Take hc = 1240 eV. nm) | 2 | [
"Photoelectric effect",
"Work function",
"Stopping potential"
] | Dual Nature of Radiation and Matter | null | [
{
"part": "(i)",
"text": "kinetic energy (in eV) of the fastest electrons"
},
{
"part": "(ii)",
"text": "stopping potential for this situation."
}
] | null | null | false | null | null | null | null |
289 | 21 | standard | Suppose a pure Si crystal has 5 × 10$^{28}$ atoms m$^{-3}$. It is doped by 1 ppm concentration of boron. Calculate the concentration of holes and electrons, given that nᵢ = 1.5 × 10$^{16}$ m$^{-3}$. Is the doped crystal n-type or p-type? | 2 | [
"Doping",
"Semiconductors",
"p-type semiconductor",
"n-type semiconductor"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | null | null | null | null | false | null | null | null | null |
290 | 22 | standard | A battery of unknown emf E and internal resistance r is connected in a circuit as shown in the figure. When the key (K) is open, the voltmeter reads 10.0 V and ammeter reads 0 A. In the closed circuit, the voltmeter reads 6.0 V and ammeter reads 2·0 A. Calculate : | 3 | [
"emf",
"internal resistance",
"Ohm's law",
"circuit analysis"
] | Current Electricity | [
"img\\img_64.jpeg",
"img\\img_65.jpeg"
] | [
{
"part": "(a)",
"text": "emf of the battery,"
},
{
"part": "(b)",
"text": "internal resistance of the battery (r), and"
},
{
"part": "(c)",
"text": "external resistance (R)."
}
] | null | null | false | null | null | null | null |
291 | 23 | standard | A rectangular loop of area $\vec{A}$, carrying current I, is placed in a uniform magnetic field $\vec{B}$. With the help of a suitable diagram, derive an expression, in vector form, for the torque acting on the loop. | 3 | [
"torque on a current loop",
"magnetic field",
"magnetic dipole moment"
] | Moving Charges and Magnetism | null | null | null | null | false | null | null | null | null |
292 | 24 | standard | Distinguish between reactance and impedance of an ac circuit. Show that an ideal inductor in an ac circuit does not dissipate any power. | 3 | [
"reactance",
"impedance",
"AC circuits",
"power in AC circuits",
"inductor"
] | Alternating Current | null | null | null | null | false | null | null | null | null |
293 | 25 | standard | The electric field in an electromagnetic wave in vacuum is given by :
$\vec{E} = (6.3 \text{ N/C}) [\cos (1.5 \text{ rad/m}) y + (4.5 \times 10^8 \text{ rad/s}) t] \hat{i}$ | 3 | [
"Electromagnetic waves",
"Wave properties",
"Electric and magnetic fields"
] | Electromagnetic Waves | null | [
{
"part": "(a)",
"text": "Find the wavelength and frequency of the wave."
},
{
"part": "(b)",
"text": "What is the amplitude of the magnetic field of the wave ?"
},
{
"part": "(c)",
"text": "Write an expression for the magnetic field of this wave."
}
] | null | null | false | null | null | null | null |
294 | 26 | standard | Explain the origin of the spectral lines of hydrogen atom using Bohr's theory. Draw the energy level diagram of hydrogen atom showing its various spectral series. | 3 | [
"Bohr model of atom",
"Hydrogen spectrum",
"Energy levels"
] | Atoms | null | null | null | null | false | null | null | null | null |
295 | 27 | standard | 3 | [
"Atomic mass unit",
"Nuclear binding energy",
"Mass defect"
] | Nuclei | null | [
{
"part": "(a)",
"text": "Define atomic mass unit (u)."
},
{
"part": "(b)",
"text": "Calculate the energy required to separate a deuteron into its constituent parts (a proton and a neutron). Given :\nm(D) = 2.014102 u\nm<0xE2><0x82><0x91> = 1.007825 u\nmn = 1.008665 u"
}
] | null | null | false | null | null | null | null |
|
296 | 28 | standard | Draw the circuit diagrams for obtaining the V – I characteristics of a p-n junction diode. Explain briefly the salient features of the V – I characteristics in (i) forward biasing, and (ii) reverse biasing. | 3 | [
"p-n junction diode",
"V-I characteristics",
"Forward biasing",
"Reverse biasing",
"Circuit diagrams"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | null | [
{
"part": "(a)",
"text": "Draw the circuit diagrams for obtaining the V – I characteristics of a p-n junction diode. Explain briefly the salient features of the V – I characteristics in (i) forward biasing, and (ii) reverse biasing."
}
] | null | {
"figure_paths": null,
"marks": 3,
"options": null,
"or_question": null,
"question_number": null,
"question_text": "On the basis of energy band diagrams, distinguish between (i) an insulator, (ii) a semiconductor, and (iii) a conductor.",
"question_type": "standard",
"related_chapter": "Semiconductor Electronics: Materials, Devices and Simple Circuits",
"related_topics": [
"Energy bands",
"Insulator",
"Semiconductor",
"Conductor"
],
"sub_parts": [
{
"part": "(b)",
"text": "On the basis of energy band diagrams, distinguish between (i) an insulator, (ii) a semiconductor, and (iii) a conductor."
}
],
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
297 | 29 | case_study | null | 3 | [
"Electric field",
"Electric potential",
"Parallel plate capacitor"
] | Chapter–2: Electrostatic Potential and Capacitance | [
"pathiimg\\img_66.jpeg",
"path:Img\\img_67.jpeg"
] | null | null | null | null | null | null | The figure shows four pairs of parallel identical conducting plates, separated by the same distance 2.0 cm and arranged perpendicular to x-axis. The electric potential of each plate is mentioned. The electric field between a pair of plates is uniform and normal to the plates. | [
{
"number": "(i)",
"options": {
"A": "I",
"B": "II",
"C": "III",
"D": "IV"
},
"text": "For which pair of the plates is the electric field $\\vec{E}$ along $\\hat{i}$ ?"
},
{
"number": "(ii)",
"options": {
"A": "move along $\\hat{i}$ at constant speed",
"B": "move along $-\\hat{i}$ at constant speed",
"C": "accelerate along $\\hat{i}$",
"D": "accelerate along $-\\hat{i}$"
},
"text": "An electron is released midway between the plates of pair IV. It will :"
},
{
"number": "(iii)",
"options": {
"A": "$V = V_0 + \\alpha x$",
"B": "$V = V_0 + \\alpha x^2$",
"C": "$V = V_0 + \\alpha x^{1/2}$",
"D": "$V = V_0 + \\alpha x^{3/2}$"
},
"text": "Let $V_0$ be the potential at the left plate of any set, taken to be at $x = 0$ m. Then potential $V$ at any point ($0 \\le x \\le 2$ cm) between the plates of that set can be expressed as :"
}
] |
298 | (iv) | standard | Let E₁, E₂, E₃ and E₄ be the magnitudes of the electric field between the pairs of plates, I, II, III and IV respectively. Then : | 1 | [
"Electric field"
] | Chapter–1: Electric Charges and Fields | null | null | {
"A": "E₁ > E₂ > E₃ > E₄",
"B": "E₃ > E₄ > E₁ > E₂",
"C": "E₄ > E₃ > E₂ > E₁",
"D": "E₂ > E₃ > E₄ > E₁"
} | {
"figure_paths": null,
"marks": 1,
"options": {
"A": "1.3 × 10⁵ m/s",
"B": "2.6 × 10⁶ m/s",
"C": "6.5 × 10⁵ m/s",
"D": "5.2 × 10⁷ m/s"
},
"or_question": null,
"question_number": "(iv)",
"question_text": "An electron is projected from the right plate of set I directly towards its left plate. It just comes to rest at the plate. The speed with which it was projected is about : (Take (e/m) =1.76 × 10¹¹ C/kg)",
"question_type": "standard",
"related_chapter": "Chapter–1: Electric Charges and Fields",
"related_topics": [
"Electric field",
"Work and energy"
],
"sub_parts": null,
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
299 | 30 | case_study | null | 1 | [
"Diffraction",
"Interference",
"Wave Optics"
] | Chapter–10: Wave Optics | null | null | null | null | null | null | null | Diffraction and interference are closely related phenomena that occur together. Diffraction is the phenomenon of bending of light around the edges of the obstacle, while interference is the combination of waves that results in a new wave pattern. In order to get interference, there must be at least two waves that are diffracting. So while diffraction can occur without interference, interference cannot occur without diffraction. Two slits of width 2 \(\mu\)m each in an opaque material are separated by a distance of 6 \(\mu\)m. Monochromatic light of wavelength 450 nm is incident normally on the slits. One finds a combined interference and diffraction pattern on the screen. | [
{
"number": "(i)",
"options": {
"A": "2",
"B": "3",
"C": "4",
"D": "6"
},
"text": "The number of peaks of the interference fringes formed within the central peak of the envelope of the diffraction pattern will be :"
},
{
"number": "(ii)",
"options": {
"A": "1",
"B": "2",
"C": "3",
"D": "4"
},
"text": "The number of peaks of the interference formed if the slit width is doubled while keeping the distance between the slits same will be :"
}
] |
300 | (iii)(a) | standard | If instead of 450 nm light, another light of wavelength 680 nm is used, number of peaks of the interference formed in the central peak of the envelope of the diffraction pattern will be : | 1 | [
"Wave Optics",
"Interference",
"Diffraction"
] | Chapter–10 | null | null | {
"A": "2",
"B": "4",
"C": "6",
"D": "9"
} | {
"figure_paths": null,
"marks": 1,
"options": {
"A": "sin-1 (0.12)",
"B": "sin-1 (0.225)",
"C": "sin-1 (0.32)",
"D": "sin−1 (0.45)"
},
"or_question": null,
"question_number": "(iii)(b)",
"question_text": "Consider the diffraction of light by a single slit described in this case study. The first minimum falls at an angle 0 equal to:",
"question_type": "standard",
"related_chapter": "Chapter–10",
"related_topics": [
"Wave Optics",
"Diffraction"
],
"sub_parts": null,
"text": null,
"vi_candidate": null
} | false | null | null | null | null |
Subsets and Splits