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values | question_text
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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
101 | 10 | 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 |
102 | 11 | 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 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 |
103 | 12 | standard | Ge is doped with As. Due to doping, | 1 | [
"Doping",
"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 |
104 | 13 | 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 |
105 | 14 | assertion_reason | null | 1 | [
"Reflection of light",
"Real and virtual images",
"Mirrors"
] | 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 |
106 | 15 | assertion_reason | null | 2 | [
"Mutual Inductance",
"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 |
107 | 16 | assertion_reason | null | 2 | [
"Photoelectric Effect",
"Kinetic Energy of Photoelectrons",
"Intensity of Light",
"Photoelectric Current",
"Wavelength 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 | 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 |
108 | 17 | standard | A uniform wire of length L and area of cross-section A has resistance R. The wire is uniformly stretched so that its length increases by 25%. Calculate the percentage increase in the resistance of the wire. | 2 | [
"Resistance",
"Resistivity",
"Length of Conductor",
"Area of Cross-section"
] | Current Electricity | null | null | null | null | false | null | null | null | null |
109 | 18 | 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 | [
"Concave Mirror",
"Radius of Curvature",
"Object Distance",
"Image Distance",
"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 |
110 | 19 | 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",
"Kinetic Energy",
"Wavelength of Photon",
"Dual Nature of Matter and Radiation"
] | Dual Nature of Radiation and Matter | null | null | null | null | false | null | null | null | null |
111 | 20 | 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 | [
"Refraction",
"Reflection",
"Refractive Index",
"Frequency",
"Wavelength"
] | Wave Optics | 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": 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",
"Focal Length",
"Refractive Index",
"Radius of Curvature"
],
"sub_parts": null,
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
112 | 21 | standard | Differentiate between ‘diffusion current’ and ‘drift current’. Explain their role in the formation of p-n junction. | 2 | [
"Diffusion Current",
"Drift Current",
"p-n Junction",
"Semiconductor Diode"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | null | null | null | null | false | null | null | null | null |
113 | 22. | standard | An air-filled parallel plate capacitor with plate separation 1 mm has a capacitance of 20 pF. It is charged to 4.0 µC. Calculate the amount of work done to pull its plates to a separation of 5 mm. Assume the charge on the plates remains the same. | 3 | [
"Capacitance",
"Parallel Plate Capacitor",
"Work done in changing capacitor separation"
] | Electrostatic Potential and Capacitance | null | null | null | null | false | null | null | null | null |
114 | 23. | standard | (a) 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",
"Relaxation Time",
"Ohm's Law"
] | Current Electricity | null | [
{
"part": "a",
"text": "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 $\\alpha = \\left( \\frac{ne^2}{m} \\right) \\tau$."
}
] | null | {
"figure_paths": null,
"marks": 3,
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"question_number": "23.",
"question_text": "(b) 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 Laws"
],
"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 |
115 | 24. | standard | A circular coil with cross-sectional area 0.2 cm² carries a current of 4 A. It is kept in a uniform magnetic field of magnitude 0.5 T normal to the plane of the coil. Calculate : | 3 | [
"Force on a current-carrying conductor in a magnetic field",
"Torque on a current loop in a magnetic field"
] | Moving Charges and Magnetism | null | [
{
"part": "a",
"text": "the net force on the coil."
},
{
"part": "b",
"text": "the torque on the coil."
},
{
"part": "c",
"text": "the average force on each electron in the coil due to the magnetic field. The free electron density in the material of the coil is $10^{28}$ m$^{-3}$."
}
] | null | null | false | null | null | null | null |
116 | 25. | standard | (a) Draw the graphs showing the variation of the following with the frequency of ac source in a circuit : | 3 | [
"AC Circuits",
"Resistance",
"Capacitive Reactance",
"Inductive Reactance"
] | Alternating Current | null | [
{
"part": "a",
"text": "Draw the graphs showing the variation of the following with the frequency of ac source in a circuit :"
},
{
"part": "i",
"text": "Resistance"
},
{
"part": "ii",
"text": "Capacitive reactance"
},
{
"part": "iii",
"text": "Inductive reactance"
},
{
"part": "b",
"text": "Can the voltage drop across the inductor or the capacitor in a series LCR circuit be greater than the applied voltage of the ac source ? Justify your answer."
}
] | null | null | false | null | null | null | null |
117 | (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 | null | null | null | null | null |
118 | (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 | null | null | null | null | null |
119 | (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_20.jpeg"
] | null | {
"A": "$\\frac{P}{2}$",
"B": "P",
"C": "2P",
"D": "$\\frac{P}{4}$"
} | null | null | null | null | null | null |
120 | (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 not in contact"
] | Ray Optics and Optical Instruments | [
"ing\\img_21.jpeg"
] | [
{
"part": "(a)",
"text": "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 :"
}
] | {
"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": null,
"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": null
} | null | null | null | null | null |
121 | 30 | case_study | null | 3 | [
"Semiconductor diode",
"p-n junction",
"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 :"
}
] |
122 | (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 | null | {
"A": "100 Hz",
"B": "50 Hz",
"C": "25 Hz",
"D": "150 Hz"
} | {
"figure_paths": [
"img\\img_22.jpeg"
],
"marks": 1,
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"A": "path: img\\img_23.jpeg",
"B": "-path: Img\\img_24.jpeg",
"C": "-path: Img\\img_25.jpeg",
"D": "path. img\\img_26.jpeg"
},
"or_question": null,
"question_number": "(iv)",
"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",
"Rectifier",
"Input and Output waveforms"
],
"sub_parts": null,
"text": null,
"vi_candidate": null
} | false | null | null | null | null |
123 | 31 | standard | (a) (i) A resistor and a capacitor are connected in series to an ac source v = $V_m$ sin ωt. Derive an expression for the impedance of the circuit. | 5 | [
"AC Circuits",
"Impedance",
"Series R-C Circuit"
] | Alternating Current | null | [
{
"part": "(i)",
"text": "A resistor and a capacitor are connected in series to an ac source v = $V_m$ sin ωt. Derive an expression for the impedance of the circuit."
}
] | null | {
"figure_paths": null,
"marks": 5,
"options": null,
"or_question": null,
"question_number": "31",
"question_text": "(b) (i) 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": "(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": null
} | false | null | null | null | null |
124 | 31 | standard | (a) (ii) When does an inductor act as a conductor in a circuit ? Give reason for it. | 5 | [
"Inductors",
"DC Circuits",
"Reactance"
] | Electromagnetic Induction | null | [
{
"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 |
125 | 31 | standard | (a) (iii) 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",
"Series L-R Circuit"
] | Alternating Current | null | [
{
"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 | null | false | null | null | null | null |
126 | 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 Dipole",
"Potential Energy",
"Torque",
"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": "32.",
"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 $\\left( \\frac{2 \\times 10^{-9}}{\\pi} \\right) \\text{C/m}^2$. 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",
"Charge Density",
"Capacitance"
],
"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 $\\left( \\frac{2 \\times 10^{-9}}{\\pi} \\right) \\text{C/m}^2$. 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 |
127 | 33. | 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.
(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 $n = \frac{\sin \left( \frac{A + \delta}{2} \right)}{\sin \left( \frac{A}{2} \right)}$. | 5 | [
"Refraction",
"Triangular Prism",
"Angle of Deviation",
"Angle of Incidence",
"Minimum Deviation",
"Refractive Index"
] | 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."
},
{
"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 $n = \\frac{\\sin \\left( \\frac{A + \\delta}{2} \\right)}{\\sin \\left( \\frac{A}{2} \\right)}$."
}
] | null | null | false | null | null | null | null |
128 | (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
(1) Angle of minimum deviation, and
(2) Angle of incidence. | 5 | [
"Refraction of light through a prism",
"Angle of minimum deviation"
] | Ray Optics and Optical Instruments | null | [
{
"part": "(1)",
"text": "Angle of minimum deviation"
},
{
"part": "(2)",
"text": "Angle of incidence."
}
] | null | {
"figure_paths": null,
"marks": 5,
"options": null,
"or_question": null,
"question_number": "(b)",
"question_text": "(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.\n(ii) What are the coherent sources of light ? Can two independent sodium lamps act like coherent sources ? Explain.\n(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 $\\lambda$.",
"question_type": "standard",
"related_chapter": "Wave Optics",
"related_topics": [
"Huygens' principle",
"Reflection of light",
"Wavefront",
"Coherent sources",
"Interference",
"Young's double slit experiment"
],
"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": false
} | false | null | null | null | null |
129 | 9 | standard | Energy levels A, B and C of an atom correspond to increasing values of energy i.e. $E_A < E_B < E_C$. Let $\lambda_1$, $\lambda_2$ and $\lambda_3$ be the wavelengths of radiation corresponding to the transitions C to B, B to A and C to A, respectively. The correct relation between $\lambda_1$, $\lambda_2$ and $\lambda_3$ is : | 1 | [
"Energy levels",
"Atomic transitions",
"Wavelength of radiation"
] | Chapter–12: Atoms | null | null | {
"A": "$\\lambda_1^2 + \\lambda_2^2 = \\lambda_3^2$",
"B": "$\\frac{1}{\\lambda_1} + \\frac{1}{\\lambda_2} = \\frac{1}{\\lambda_3}$",
"C": "$\\lambda_1 + \\lambda_2 + \\lambda_3 = 0$",
"D": "$\\lambda_1 + \\lambda_2 = \\lambda_3$"
} | null | null | null | null | null | null |
130 | 10 | standard | An alpha particle approaches a gold nucleus in Geiger-Marsden experiment with kinetic energy K. It momentarily stops at a distance d from the nucleus and reverses its direction. Then d is proportional to : | 1 | [
"Alpha particle scattering",
"Kinetic energy",
"Electrostatic potential energy"
] | Chapter–12: Atoms | null | null | {
"A": "$\\frac{1}{\\sqrt{K}}$",
"B": "$\\sqrt{K}$",
"C": "$\\frac{1}{K}$",
"D": "$K$"
} | null | null | null | null | null | null |
131 | 11 | standard | An n-type semiconducting Si is obtained by doping intrinsic Si with : | 1 | [
"n-type semiconductor",
"Doping",
"Extrinsic semiconductor"
] | Chapter–14: Semiconductor Electronics: Materials, Devices and Simple Circuits | null | null | {
"A": "Al",
"B": "B",
"C": "P",
"D": "In"
} | null | null | null | null | null | null |
132 | 12 | standard | When a p-n junction diode is subjected to reverse biasing : | 1 | [
"p-n junction diode",
"Reverse biasing",
"Barrier height",
"Depletion region"
] | Chapter–14: Semiconductor Electronics: Materials, Devices and Simple Circuits | null | null | {
"A": "the barrier height decreases and the depletion region widens.",
"B": "the barrier height increases and the depletion region widens.",
"C": "the barrier height decreases and the depletion region shrinks.",
"D": "the barrier height increases and the depletion region shrinks."
} | null | null | null | null | null | null |
133 | 13. | assertion_reason | null | null | [
"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 |
134 | 14. | assertion_reason | null | null | [
"Lenz's Law",
"Law of conservation of energy",
"Inductor"
] | 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 |
135 | 15. | assertion_reason | null | null | [
"Motion in magnetic field",
"Momentum",
"Radius of circular path"
] | 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 |
136 | 16. | assertion_reason | null | null | [
"Magnifying power",
"Compound microscope",
"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 | The magnifying power of a compound microscope is negative. | The final image formed is erect with respect to the object. | null | null |
137 | 17. | standard | Define resistivity of a conductor. How does the resistivity of a conductor depend upon the following : | 2 | [
"Resistivity",
"Number density of free electrons",
"Relaxation time"
] | Current Electricity | null | [
{
"part": "(a)",
"text": "Number density of free electrons in the conductor (n)"
},
{
"part": "(b)",
"text": "Their relaxation time ($\\tau$)"
}
] | null | null | null | null | null | null | null |
138 | 18 | standard | null | 2 | [
"Superposition of waves",
"Interference"
] | Wave Optics | null | [
{
"part": "a",
"text": "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."
}
] | null | {
"figure_paths": null,
"marks": 2,
"options": null,
"or_question": null,
"question_number": null,
"question_text": null,
"question_type": "standard",
"related_chapter": "Wave Optics",
"related_topics": [
"Interference",
"Young's double-slit experiment"
],
"sub_parts": [
{
"part": "b",
"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."
}
],
"text": null,
"vi_candidate": null
} | false | null | null | null | null |
139 | 19 | 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",
"Lenses",
"Lens maker’s formula"
] | Ray Optics and Optical Instruments | null | null | null | null | false | null | null | null | null |
140 | 20 | standard | The carbon isotope $_{6}^{12}C$ has a nuclear mass of 12.000000 u. Calculate the binding energy of its nucleus.
Given $m_p$ = 1.007825 u; $m_n$ = 1·008665 u. | 2 | [
"Composition and size of nucleus",
"Mass-energy relation",
"Mass defect",
"Binding energy per nucleon"
] | Nuclei | null | null | null | null | false | null | null | null | null |
141 | 21 | 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",
"Intrinsic and extrinsic semiconductors",
"p and n type semiconductors"
] | 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 |
142 | 22 | standard | The figure shows a circuit with three ideal batteries. Find the magnitude and direction of currents in the branches AG, BF and CD. | 3 | [
"Kirchhoff's rules",
"Electric current"
] | Current Electricity | [
"img\\img_27.jpeg",
"img\\img_28.jpeg"
] | null | null | null | false | null | null | null | null |
143 | 23. | standard | (a) On what factors does the speed of an electromagnetic wave in a medium depend?
(b) How is an electromagnetic wave produced ?
(c) Sketch a schematic diagram depicting the electric and magnetic fields for an electromagnetic wave propagating along z-axis. | 3 | [
"Electromagnetic Waves",
"Production of Electromagnetic Waves",
"Properties of Electromagnetic Waves"
] | Electromagnetic Waves | null | [
{
"part": "(a)",
"text": "On what factors does the speed of an electromagnetic wave in a medium depend?"
},
{
"part": "(b)",
"text": "How is an electromagnetic wave produced ?"
},
{
"part": "(c)",
"text": "Sketch a schematic diagram depicting the electric and magnetic fields for an electromagnetic wave propagating along z-axis."
}
] | null | null | false | null | null | null | null |
144 | 24. | standard | A 100-turn coil of radius 1.6 cm and resistance 5.0 Ω is co-axial with a solenoid of 250 turns/cm and radius 1.8 cm. The solenoid current drops from 1.5 A to zero in 25 ms. Calculate the current induced in the coil in this duration. (Take π² = 10) | 3 | [
"Electromagnetic Induction",
"Mutual Induction",
"Induced EMF",
"Induced Current"
] | Electromagnetic Induction | null | null | null | null | false | null | null | null | null |
145 | 25. | standard | (a) 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 | [
"Magnetic Force",
"Force between parallel currents",
"Ampere's Law"
] | Moving Charges and Magnetism | null | [
{
"part": "(a)",
"text": "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."
}
] | null | {
"figure_paths": null,
"marks": 3,
"options": null,
"or_question": null,
"question_number": "25.",
"question_text": "(b) 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",
"Magnetic field"
],
"sub_parts": [
{
"part": "(b)",
"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."
}
],
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
146 | 26. | standard | Using Bohr's postulates, derive the expression for the radius of the n$^{th}$ orbit of an electron in a hydrogen atom. Also find the numerical value of Bohr's radius a₀. | 3 | [
"Bohr's Model",
"Atomic Spectra",
"Radius of Bohr Orbit"
] | Atoms | null | null | null | null | false | null | null | null | null |
147 | 27. | standard | de Broglie wavelength λ as a function of $\frac{1}{\sqrt{K}}$, for two particles of masses m₁ and m₂ are shown in the figure. Here, K is the energy of the moving particles. | 3 | [
"Dual Nature of Radiation and Matter",
"de Broglie Wavelength",
"Kinetic Energy"
] | Dual Nature of Radiation and Matter | [
"img\\img_29.jpeg"
] | [
{
"part": "(a)",
"text": "What does the slope of a line represent ?"
},
{
"part": "(b)",
"text": "Which of the two particles is heavier ?"
},
{
"part": "(c)",
"text": "Is this graph also valid for a photon ? Justify your answer in each case."
}
] | null | null | false | null | null | null | null |
148 | 28 | standard | With the help of a circuit diagram, explain the working of a p-n junction diode as a full wave rectifier. Draw its input and output waveforms. | 3 | [
"p-n junction diode",
"full wave rectifier",
"circuit diagram",
"input waveform",
"output waveform"
] | Semiconductor Electronics: Materials, Devices and Simple Circuits | [] | null | null | null | false | null | null | null | null |
149 | 29 | case_study | null | 1 | [
"Internal resistance",
"EMF",
"Terminal potential difference",
"Cells in parallel"
] | Current Electricity | [] | null | null | null | null | null | null | 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). | [
{
"number": "(i)",
"options": {
"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."
},
"text": "Choose the incorrect statement :"
},
{
"number": "(ii)",
"options": {
"A": "2.0 V",
"B": "2.8 V",
"C": "6.0 V",
"D": "8.0 V"
},
"text": "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 :"
}
] |
150 | (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₋ ≥ 0), relative to the electrolyte adjacent to it. When no current is drawn from the cell then : | 1 | [
"Electrode potential",
"EMF of a cell"
] | 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 |
151 | (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",
"Ohm's law",
"Current electricity"
] | 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": null,
"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",
"EMF and potential difference"
],
"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 |
152 | 30. | standard | When a ray of light propagates from a denser medium to a rarer medium, it bends away from the normal. When the incident angle is increased, the refracted ray deviates more from the normal. For a particular angle of incidence in the denser medium, the refracted ray just grazes the interface of the two surfaces. This angle of incidence is called the critical angle for the pair of media involved. | 1 | [
"Total internal reflection",
"Refraction"
] | Ray Optics and Optical Instruments | null | [
{
"part": "(i)",
"text": "For a ray incident at the critical angle, the angle of reflection is :"
}
] | {
"A": "0°",
"B": "< 90°",
"C": "> 90°",
"D": "90°"
} | null | false | null | null | null | null |
153 | 30. | standard | A ray of light of wavelength 600 nm is incident in water $\left(n=\frac{4}{3}\right)$ on the water-air interface at an angle less than the critical angle. The wavelength associated with the refracted ray is : | 1 | [
"Refraction",
"Wavelength and refractive index"
] | Ray Optics and Optical Instruments | null | [
{
"part": "(ii)",
"text": "A ray of light of wavelength 600 nm is incident in water $\\left(n=\\frac{4}{3}\\right)$ on the water-air interface at an angle less than the critical angle. The wavelength associated with the refracted ray is :"
}
] | {
"A": "400 nm",
"B": "450 nm",
"C": "600 nm",
"D": "800 nm"
} | null | false | null | null | null | null |
154 | iii(a) | standard | The interface AB between the two media A and B is shown in the figure. In the denser medium A, the incident ray PQ makes an angle of 30° with the horizontal. The refracted ray is parallel to the interface. The refractive index of medium B w.r.t. medium A is : | 1 | [
"Refraction",
"Snell's Law",
"Refractive Index"
] | Ray Optics and Optical Instruments | [
"img\\img_30.jpeg"
] | null | {
"A": "\\frac{\\sqrt{3}}{2}",
"B": "\\frac{\\sqrt{5}}{2}",
"C": "\\frac{4}{\\sqrt{3}}",
"D": "\\frac{2}{\\sqrt{3}}"
} | {
"figure_paths": null,
"marks": 1,
"options": {
"A": "sin$^{-1} \\frac{1}{2}$",
"B": "sin$^{-1} \\frac{4}{5}$",
"C": "sin$^{-1} \\frac{3}{5}$",
"D": "sin$^{-1} \\frac{2}{5}$"
},
"or_question": null,
"question_number": "iii(b)",
"question_text": "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 :",
"question_type": "standard",
"related_chapter": "Ray Optics and Optical Instruments",
"related_topics": [
"Total Internal Reflection",
"Critical Angle",
"Refractive Index"
],
"sub_parts": null,
"text": null,
"vi_candidate": null
} | null | null | null | null | null |
155 | 31 | 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 due to a dipole",
"Potential energy of a system of 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 | {
"figure_paths": [
"img\\img_32.jpeg",
"img\\img_33.jpeg"
],
"marks": 5,
"options": null,
"or_question": null,
"question_number": "31",
"question_text": "(b) (i) State Gauss's Law in electrostatics. Apply this to obtain the electric field $\\vec{E}$ at a point near a uniformly charged infinite plane sheet.\n(ii) 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.",
"question_type": "standard",
"related_chapter": "Electric Charges and Fields",
"related_topics": [
"Gauss's Law",
"Electric field due to an infinite plane sheet",
"Electric field due to a line charge",
"Force on a charge in an electric field"
],
"sub_parts": [
{
"part": "(i)",
"text": "State Gauss's Law in electrostatics. Apply this to obtain the electric field $\\vec{E}$ 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."
}
],
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
156 | 32 | standard | (a) (i) 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. | 5 | [
"Force on a moving charge in uniform magnetic field",
"Motion of a charged particle in a magnetic field",
"Frequency of revolution"
] | Moving Charges and Magnetism | [
"img\\img_34.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 | null | null | null | null | null |
157 | 32 | standard | (a) (ii) In a hydrogen atom, the electron moves in an orbit of radius 2 Å making 8×10$^{14}$ revolutions per second. Find the magnetic moment associated with the orbital motion of the electron. | 5 | [
"Magnetic moment of a current loop",
"Magnetic moment of an orbiting electron"
] | Moving Charges and Magnetism | null | [
{
"part": "(ii)",
"text": "In a hydrogen atom, the electron moves in an orbit of radius 2 Å making 8×10$^{14}$ revolutions per second. Find the magnetic moment associated with the orbital motion of the electron."
}
] | null | null | null | null | null | null | null |
158 | 32 | standard | (b) (i) 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. | 5 | [
"Current sensitivity of a galvanometer",
"Voltage sensitivity of a galvanometer",
"Moving coil galvanometer"
] | Moving Charges and Magnetism | null | [
{
"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."
}
] | null | null | null | null | null | null | null |
159 | 32 | standard | (b) (ii) A moving coil galvanometer has a resistance 15 $\Omega$ and takes 20 mA to produce full scale deflection. How can this galvanometer be converted into a voltmeter of range 0 to 100 V ? | 5 | [
"Conversion of galvanometer into voltmeter",
"Moving coil galvanometer"
] | Moving Charges and Magnetism | null | [
{
"part": "(ii)",
"text": "A moving coil galvanometer has a resistance 15 $\\Omega$ and takes 20 mA to produce full scale deflection. How can this galvanometer be converted into a voltmeter of range 0 to 100 V ?"
}
] | null | null | null | null | null | null | null |
160 | 32 | or_question | null | null | null | null | null | null | null | {
"figure_paths": null,
"marks": 5,
"options": null,
"or_question": null,
"question_number": null,
"question_text": null,
"question_type": "standard",
"related_chapter": "Moving Charges and Magnetism",
"related_topics": [
"Current sensitivity of a galvanometer",
"Voltage sensitivity of a galvanometer",
"Moving coil galvanometer",
"Conversion of galvanometer into 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 $\\Omega$ 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 |
161 | 33 | 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 of light"
] | Wave Optics | [] | [
{
"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": [],
"marks": 5,
"options": null,
"or_question": null,
"question_number": null,
"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",
"Magnifying power",
"Ray diagram",
"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": null
} | false | null | null | null | null |
162 | 1 | standard | The capacitance of a parallel plate capacitor having a medium of dielectric constant K = 4 in between the plates is C. If this medium is removed, then the capacitance of the capacitor becomes : | 1 | [
"Capacitance",
"Parallel Plate Capacitor",
"Dielectric Constant"
] | Electrostatic Potential and Capacitance | null | null | {
"A": "4C",
"B": "C",
"C": "C/4",
"D": "2C"
} | null | false | null | null | null | null |
163 | 2 | standard | Electrons drift with speed $v_d$ in a conductor with potential difference V across its ends. If V is reduced to $\frac{V}{2}$, their drift speed will become : | 1 | [
"Drift Velocity",
"Electric Current",
"Potential Difference"
] | Current Electricity | null | null | {
"A": "$\\frac{v_d}{2}$",
"B": "$v_d$",
"C": "$2 v_d$",
"D": "$4 v_d$"
} | null | false | null | null | null | null |
164 | 3 | standard | A conducting loop is placed in a magnetic field, normal to its plane. The magnitude of the magnetic field varies with time as shown in the figure. If $\varepsilon_1$, $\varepsilon_2$ and $\varepsilon_3$ are magnitudes of induced emfs during periods $0 \le t \le T$, $T \le t \le 2T$ and $2T < t \le 3T$, then : | 1 | [
"Electromagnetic Induction",
"Faraday's Laws",
"Induced EMF"
] | Electromagnetic Induction | [
"Img\\Img_36.jpeg"
] | null | {
"A": "$\\varepsilon_1 > \\varepsilon_2 > \\varepsilon_3$",
"B": "$\\varepsilon_2 > \\varepsilon_3 > \\varepsilon_1$",
"C": "$\\varepsilon_3 > \\varepsilon_1 > \\varepsilon_2$",
"D": "$\\varepsilon_1 > \\varepsilon_3 > \\varepsilon_2$"
} | null | false | null | null | null | null |
165 | 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 |
166 | 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"
] | Alternating Current | null | null | {
"A": "Current only",
"B": "Voltage only",
"C": "Power only",
"D": "Magnetic flux and Power both"
} | null | false | null | null | null | null |
167 | 6 | standard | A series LCR circuit (L = 2 mH, C = 0.2 µF and R = 30 Ω) is connected to an ac source of variable frequency. The impedance of this circuit will be minimum at a frequency of : | 1 | [
"LCR series circuit",
"Resonance",
"Impedance"
] | Alternating Current | null | null | {
"A": "$\\frac{10^5}{4\\pi}$ Hz",
"B": "$\\frac{10^5}{2\\pi}$ Hz",
"C": "$\\frac{10^4}{4\\pi}$ Hz",
"D": "$\\frac{10^4}{2\\pi}$ Hz"
} | null | false | null | null | null | null |
168 | 7 | standard | Welders wear special glass goggles or face masks with glass windows to protect their eyes from radiations produced by welding arcs. These radiations are : | 1 | [
"Electromagnetic spectrum",
"Ultraviolet radiation"
] | Electromagnetic Waves | null | null | {
"A": "X-rays",
"B": "Ultraviolet rays",
"C": "Infrared waves",
"D": "Gamma rays"
} | null | false | null | null | null | null |
169 | 8 | standard | A photosensitive surface has a work function of 2.00 eV. The maximum kinetic energy of electrons ejected from this surface by radiation of wavelength 300 nm is : | 1 | [
"Photoelectric effect",
"Work function",
"Kinetic energy",
"Einstein's photoelectric equation"
] | Dual Nature of Radiation and Matter | null | null | {
"A": "0.54 eV",
"B": "1.07 eV",
"C": "1.61 eV",
"D": "2.14 eV"
} | null | false | null | null | null | null |
170 | 9 | standard | Energy levels A, B and C of an atom correspond to increasing values of energy i.e. E<sub>A</sub> < E<sub>B</sub> < E<sub>C</sub>. Let λ<sub>1</sub>, λ<sub>2</sub> and λ<sub>3</sub> be the wavelengths of radiation corresponding to the transitions C to B, B to A and C to A, respectively. The correct relation between λ<sub>1</sub>, λ<sub>2</sub> and λ<sub>3</sub> is : | 1 | [
"Energy levels",
"Atomic spectra",
"Bohr model"
] | Atoms | null | null | {
"A": "$\\lambda_1^2 + \\lambda_2^2 = \\lambda_3^2$",
"B": "$\\frac{1}{\\lambda_1} + \\frac{1}{\\lambda_2} = \\frac{1}{\\lambda_3}$",
"C": "$\\lambda_1 + \\lambda_2 + \\lambda_3 = 0$",
"D": "$\\lambda_1 + \\lambda_2 = \\lambda_3$"
} | null | false | null | null | null | null |
171 | 10 | standard | An alpha particle approaches a gold nucleus in Geiger-Marsden experiment with kinetic energy K. It momentarily stops at a distance d from the nucleus and reverses its direction. Then d is proportional to : | 1 | [
"Rutherford's model of atom",
"Electrostatic potential energy"
] | Chapter–12: Atoms | null | null | {
"A": "$\\frac{1}{\\sqrt{K}}$",
"B": "$\\sqrt{K}$",
"C": "$\\frac{1}{K}$",
"D": "K"
} | null | null | null | null | null | null |
172 | 11 | standard | An n-type semiconducting Si is obtained by doping intrinsic Si with : | 1 | [
"n-type semiconductor",
"Doping"
] | Chapter–14: Semiconductor Electronics: Materials, Devices and Simple Circuits | null | null | {
"A": "Al",
"B": "B",
"C": "P",
"D": "In"
} | null | null | null | null | null | null |
173 | 12 | standard | When a p-n junction diode is subjected to reverse biasing : | 1 | [
"p-n junction diode",
"Reverse biasing",
"Barrier height",
"Depletion region"
] | Chapter–14: Semiconductor Electronics: Materials, Devices and Simple Circuits | null | null | {
"A": "the barrier height decreases and the depletion region widens.",
"B": "the barrier height increases and the depletion region widens.",
"C": "the barrier height decreases and the depletion region shrinks.",
"D": "the barrier height increases and the depletion region shrinks."
} | null | null | null | null | null | null |
174 | 13 | assertion_reason | null | 1 | [
"Compound microscope",
"Magnifying power",
"Image formation"
] | Chapter–9: 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": "Both Assertion (A) and Reason (R) are false"
} | null | null | Assertion (A): The magnifying power of a compound microscope is negative. | Reason (R) : The final image formed is erect with respect to the object. | null | null |
175 | 14 | assertion_reason | null | 1 | [
"Motion in a magnetic field",
"Radius of circular path"
] | 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 |
176 | 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 |
177 | 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 |
178 | 17 | standard | null | 2 | [
"Drift velocity",
"Electric current",
"Ohm's Law"
] | Current Electricity | null | [
{
"part": "a",
"text": "“The electron drift speed is only a few mm/s for currents in the range of a few amperes for a given conductor.” How then is current established almost the instant a circuit is closed ? Explain."
},
{
"part": "b",
"text": "'V = IR is a statement of Ohm's Law' is not true. Explain."
}
] | null | null | false | null | null | null | null |
179 | 18 | 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"
] | Ray Optics and Optical Instruments | null | null | null | null | false | null | null | null | null |
180 | 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 optics",
"Interference",
"Superposition of waves",
"Resultant intensity"
] | Wave Optics | null | [
{
"part": "a",
"text": "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."
}
] | null | {
"figure_paths": null,
"marks": 2,
"options": null,
"or_question": null,
"question_number": null,
"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"
],
"sub_parts": [
{
"part": "b",
"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."
}
],
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
181 | 20 | standard | Calculate the energy released/absorbed in the following nuclear reaction :
$_{6}^{12}C$ + $_{6}^{12}C$ $\longrightarrow$ $_{10}^{20}Ne$ + $_{2}^{4}He$
Given : m($_{6}^{12}C$) = 12.000000 u
m($_{10}^{20}Ne$) = 19.992439 u
m($_{2}^{4}He$) = 4.002603 u
1 u = 931 MeV/c$^2$ | 2 | [
"Nuclear Reactions",
"Mass Defect",
"Binding Energy"
] | Chapter–13: Nuclei | null | null | null | null | false | null | null | null | null |
182 | 21 | 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",
"p-type Semiconductor",
"n-type Semiconductor"
] | Chapter–14: 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 |
183 | 22 | standard | (a) On what factors does the speed of an electromagnetic wave in a medium depend ?
(b) How is an electromagnetic wave produced ?
(c) Sketch a schematic diagram depicting the electric and magnetic fields for an electromagnetic wave propagating along z-axis. | 3 | [
"Electromagnetic Waves",
"Production of Electromagnetic Waves",
"Properties of Electromagnetic Waves"
] | Chapter–8: Electromagnetic Waves | null | [
{
"part": "(a)",
"text": "On what factors does the speed of an electromagnetic wave in a medium depend ?"
},
{
"part": "(b)",
"text": "How is an electromagnetic wave produced ?"
},
{
"part": "(c)",
"text": "Sketch a schematic diagram depicting the electric and magnetic fields for an electromagnetic wave propagating along z-axis."
}
] | null | null | false | null | null | null | null |
184 | 23 | standard | The figure shows a circuit with three ideal batteries. Find the magnitude and direction of currents in the branches AG, BF and CD. | 3 | [
"Kirchhoff's Laws",
"Electric Circuits",
"Current",
"Voltage"
] | Chapter–3: Current Electricity | [
"img\\img_37.jpeg",
"img\\img_38.jpeg"
] | null | null | null | false | null | null | null | null |
185 | 24 | standard | A rectangular loop of sides 10 cm × 20 cm is kept outside a region of uniform magnetic field | $\vec{B}$ | = 5 mT as shown in the figure. The loop is moved with the velocity of 5 cm/s till it goes completely out of the magnetic field. | 3 | [
"Magnetic flux",
"Electromagnetic induction",
"Work done by magnetic forces"
] | Electromagnetic Induction | [
"img\\img_39.jpeg",
"img\\img_40.jpeg",
"img\\img_41.jpeg"
] | [
{
"part": "a",
"text": "Plot a graph showing variation of the magnetic flux $\\phi$ with x (0 ≤ x ≤ 100 cm)."
},
{
"part": "b",
"text": "Find the maximum value of magnetic flux linked with the loop."
},
{
"part": "c",
"text": "Will an external work be required to be done to move the loop through the magnetic field ?"
}
] | null | null | false | null | null | null | null |
186 | 25 | 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 parallel currents",
"Ampere's law"
] | Moving Charges and Magnetism | null | null | null | {
"figure_paths": null,
"marks": 3,
"options": null,
"or_question": null,
"question_number": null,
"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",
"Magnetic dipole moment"
],
"sub_parts": null,
"text": null,
"vi_candidate": null
} | false | null | null | null | null |
187 | (iii)(a) | standard | The interface AB between the two media A and B is shown in the figure. In the denser medium A, the incident ray PQ makes an angle of 30° with the horizontal. The refracted ray is parallel to the interface. The refractive index of medium B w.r.t. medium A is : | 1 | [
"Refraction",
"Snell's Law",
"Refractive Index"
] | Ray Optics and Optical Instruments | [
"img\\img_42.jpeg"
] | null | {
"A": "\\frac{\\sqrt{3}}{2}",
"B": "\\frac{\\sqrt{5}}{2}",
"C": "\\frac{4}{\\sqrt{3}}",
"D": "\\frac{2}{\\sqrt{3}}"
} | {
"figure_paths": null,
"marks": 1,
"options": {
"A": "sin$^{-1} \\frac{1}{2}$",
"B": "sin$^{-1} \\frac{4}{5}$",
"C": "sin$^{-1} \\frac{3}{5}$",
"D": "sin$^{-1} \\frac{2}{5}$"
},
"or_question": null,
"question_number": "(iii)(b)",
"question_text": "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 :",
"question_type": "standard",
"related_chapter": "Ray Optics and Optical Instruments",
"related_topics": [
"Total Internal Reflection",
"Critical Angle",
"Refractive Index"
],
"sub_parts": null,
"text": null,
"vi_candidate": false
} | false | null | null | null | null |
188 | (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",
"Angle of Minimum Deviation"
] | Ray Optics and Optical Instruments | [
"img\\img_43.jpeg"
] | null | {
"A": "sin$^{-1} \\sqrt{n^2-1}$",
"B": "sin$^{-1} (n^2 – 1)$",
"C": "sin$^{-1} \\left[ \\frac{1}{\\sqrt{n^2-1}} \\right]$",
"D": "sin$^{-1} \\left[ \\frac{1}{(n^2-1)} \\right]$"
} | null | false | null | null | null | null |
189 | 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 (ɛ). With a current drawn from the cell, the potential difference between the two electrodes is termed as terminal potential difference (V). | 3 | [
"Internal resistance",
"EMF",
"Terminal potential difference",
"Combination of cells"
] | Current Electricity | null | [
{
"part": "(i)",
"text": "Choose the incorrect statement :"
},
{
"part": "(ii)",
"text": "Two cells of emfs 2.0 V and 6.0 V and internal resistances 0·1 Ω and 0.4 Ω respectively, are connected in parallel. The equivalent emf of the combination will be :"
},
{
"part": "(iii)",
"text": "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_ ≥ 0), relative to the electrolyte adjacent to it. When no current is drawn from the cell then :"
}
] | null | null | null | null | null | null | null |
190 | 30 (i) | standard | Choose the incorrect statement : | 1 | [
"Internal resistance",
"EMF",
"Terminal potential difference"
] | 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 (ɛ), 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 = ɛ – 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 |
191 | 30 (ii) | standard | Two cells of emfs 2.0 V and 6.0 V and internal resistances 0·1 Ω and 0.4 Ω 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 |
192 | 30 (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_ ≥ 0), relative to the electrolyte adjacent to it. When no current is drawn from the cell then : | 1 | [
"EMF",
"Electrode potential"
] | Current Electricity | null | null | {
"A": "£ = V+ + V_ > 0",
"B": "ε = V+ − V_ > 0",
"C": "ɛ = V+ + V_ < 0",
"D": "ε = V+ + V_ = 0"
} | null | false | null | null | null | null |
193 | (iv)(a) | 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",
"Internal resistance",
"Ohm's law"
] | Current Electricity | null | null | {
"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)(b)",
"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",
"Potential difference",
"EMF"
],
"sub_parts": null,
"text": null,
"vi_candidate": null
} | null | null | null | null | null |
194 | 31.(a) | standard | null | 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.(b)",
"question_text": null,
"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": null
} | null | null | null | null | null |
195 | 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 due to a dipole",
"Potential energy of a system of 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 | {
"figure_paths": [
"img\\img_44.jpeg",
"img\\img_45.jpeg"
],
"marks": 5,
"options": null,
"or_question": null,
"question_number": null,
"question_text": "(b) (i) State Gauss's Law in electrostatics. Apply this to obtain the electric field $\\vec{E}$ at a point near a uniformly charged infinite plane sheet.\n(ii) 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.",
"question_type": "standard",
"related_chapter": "Electric Charges and Fields",
"related_topics": [
"Gauss's Law",
"Electric field due to an infinite plane sheet",
"Electric field due to a long straight wire",
"Force on a charge in an electric field"
],
"sub_parts": [
{
"part": "(i)",
"text": "State Gauss's Law in electrostatics. Apply this to obtain the electric field $\\vec{E}$ 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."
}
],
"text": null,
"vi_candidate": null
} | false | null | null | null | null |
196 | 33 | standard | (a) (i) 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. | 5 | [
"Motion in Magnetic Field",
"Helical Path",
"Frequency of Revolution"
] | Moving Charges and Magnetism | [
"img\\img_46.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 | {
"figure_paths": null,
"marks": 5,
"options": null,
"or_question": null,
"question_number": null,
"question_text": "(b) (i) What is current sensitivity of a galvanometer ? Show how the current sensitivity of a galvanometer may be increased.\n“Increasing the current sensitivity of a galvanometer may not necessarily increase its voltage sensitivity.” Explain.",
"question_type": "standard",
"related_chapter": "Moving Charges and Magnetism",
"related_topics": [
"Current Sensitivity",
"Galvanometer",
"Voltage Sensitivity"
],
"sub_parts": [
{
"part": "(i)",
"text": "What is current sensitivity of a galvanometer ? Show how the current sensitivity of a galvanometer may be increased.\n“Increasing the current sensitivity of a galvanometer may not necessarily increase its voltage sensitivity.” Explain."
}
],
"text": null,
"vi_candidate": null
} | false | null | null | null | null |
197 | 33 | standard | (a) (ii) 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 | [
"Magnetic Moment",
"Orbital Motion of Electron",
"Hydrogen Atom"
] | Moving Charges and Magnetism | null | [
{
"part": "(ii)",
"text": "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."
}
] | null | {
"figure_paths": null,
"marks": 5,
"options": null,
"or_question": null,
"question_number": null,
"question_text": "(b) (ii) 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 ?",
"question_type": "standard",
"related_chapter": "Moving Charges and Magnetism",
"related_topics": [
"Moving Coil Galvanometer",
"Conversion to Voltmeter",
"Series Resistance"
],
"sub_parts": [
{
"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 |
198 | 1 | standard | Coulomb force F versus $\left(\frac{1}{r^2}\right)$ graphs for two pairs of point charges (q₁ and q₂) and (q₂ and q₃) are shown in the figure. The ratio of charges $\left(\frac{q_1}{q_3}\right)$ is : | 1 | [
"Coulomb's law",
"Force between two-point charges"
] | Electric Charges and Fields | [
"img\\img_47.jpeg"
] | null | {
"A": "$\\sqrt{3}$",
"B": "$\\frac{1}{\\sqrt{3}}$",
"C": "3",
"D": "$\\frac{1}{3}$"
} | null | false | null | null | null | null |
199 | 2 | standard | Electrons drift with speed $v_d$ in a conductor with potential difference V across its ends. If V is reduced to $\left(\frac{V}{2}\right)$, their drift speed will become : | 1 | [
"Drift velocity",
"Relation between drift velocity and potential difference"
] | Current Electricity | null | null | {
"A": "$\\frac{v_d}{2}$",
"B": "$v_d$",
"C": "$2 v_d$",
"D": "$4 v_d$"
} | null | false | null | null | null | null |
200 | 3 | standard | The emf induced in a coil rotating in a magnetic field does not depend upon the following : | 1 | [
"Electromagnetic induction",
"Induced EMF"
] | Electromagnetic Induction | null | null | {
"A": "Area of the coil",
"B": "Resistance of the coil",
"C": "Number of turns in the coil",
"D": "Angular speed of rotation of the coil"
} | null | false | null | null | null | null |
Subsets and Splits