CBSE Class 12 Physics 2026 question paper (55/3)
Maximum marks 70 · Time 3 hours · 3 sets
Try each question first, then open its model answer. Where the paper offers a choice, both questions are shown with OR between them.
Section A
1 mark each
- Q.11 markA particle of mass m and charge q starts from rest and moves in an electric field . After travelling a distance x in the field along x-axis, the kinetic energy of the particle will be :
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- Q.21 markA square loop of side 50 cm is placed in a uniform magnetic field of T acting perpendicular to the plane of the loop. If the loop is rotated through an angle of in s, the value of emf induced in the loop would be :
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- Q.31 markA plane electromagnetic wave travels through a medium and the magnetic field associated with it is given by T where x is in metres and t is in seconds. The velocity of the wave is :
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- Q.41 markA thin plano-convex lens and a thin equi-concave lens are kept coaxially in contact as shown in the figure. Assuming both the lenses are made of glass of refractive index , and R is the radius of curvature of each curved surface, the focal length of the combination is :
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- Q.51 markThe phase difference between the two superimposing waves that give rise to a bright spot in a Young's double-slit experiment is (n is an integer) :
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- Q.61 markA telescope has an objective lens of focal length 144 cm and an eyepiece of focal length cm. The magnifying power and the length of telescope tube will be respectively :
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- Q.71 markIn which of the following, total internal reflection does not occur ?
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- Q.81 markRadiation of wavelength 200 nm is incident on a photosensitive surface of work function eV. The kinetic energy of fastest photoelectrons emitted from this surface will be close to :
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- Q.91 markA proton and an alpha particle have equal momentum. The ratio of their kinetic energies and de Broglie wavelengths associated with them respectively are :
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- Q.101 markIf and are the radii of atomic nuclei of mass numbers 64 and 27 respectively, then the value of is :
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- Q.111 markWhen the forward bias voltage in a semiconductor diode is changed from V to V, the forward current changes by mA. The forward bias resistance of the diode will be :
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- Q.121 markThe process named 'minority carrier injection' in a p-n junction diode occurs during :
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- Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.Q.131 markAssertion (A) : In a Wheatstone bridge circuit, if we interchange the position of the cell and the galvanometer, the balance condition remains unchanged. Reason (R) : so balance condition remains same.
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- Q.141 markAssertion (A) : The cylindrical soft iron core in a moving coil galvanometer only makes the magnetic field radial and does not affect the strength of the magnetic field. Reason (R) : In a moving coil galvanometer, the plane of the coil is always perpendicular to the magnetic field.
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- Q.151 markAssertion (A) : Photoelectric current depends upon the intensity of the incident radiation. Reason (R) : Stopping potential is independent of the intensity of the incident radiation.
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- Q.161 markAssertion (A) : Nuclear forces are always attractive. Reason (R) : The nuclear force between protons and neutrons in a nucleus is a weak force.
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Section B
2 marks each
- Q.17 (a)2 marksIn the given figure, a steady current I flows through the circuit when points A and C are connected by a wire of negligible resistance. Find the potential difference between points B and C.
OR
Q.17 (b)2 marksA battery of emf 21 V and internal resistance is connected to a resistor. If the current in the circuit is 3 A, find : (i) the resistance of the resistor. (ii) the terminal voltage of the battery.- Q.182 marksExplain why diffraction of sound is more common in daily experience than that of light.
- Q.192 marksExplain the terms mass defect and binding energy. How are they related ?
- Q.202 marksA particle of mass M at rest splits up into two particles of masses and having non-zero velocities. Calculate the ratio of the de Broglie wavelengths associated with the two particles.
- Q.212 marksHow are charge carriers created in an intrinsic semiconductor ? Explain.
Section C
3 marks each
- Q.223 marks(a) Establish the relation between drift velocity of electrons and electric current (I) in a conductor. (b) How is affected when the length of the conductor is doubled, keeping the voltage applied across the conductor constant ?
- Q.23 (a)3 marksA circular coil of 30 turns and radius cm carrying a current of 6 A is suspended vertically in a uniform horizontal magnetic field of T. The field lines make an angle of with the plane of the coil. Calculate the magnitude of the external torque that must be applied to prevent the coil from turning. What would happen if the circular coil is replaced by a planar coil of irregular shape that encloses the same area, keeping other parameters unchanged ?
OR
Q.23 (b)3 marksAn alpha particle (mass kg and charge C) having MeV energy, enters a region of a uniform magnetic field of T. If the field is directed perpendicular to the velocity of the particle, find the radius of the circular path described by the particle. Mention the condition under which the particle in this region (i) describes a helical path, and (ii) goes straight undeviated.- Q.243 marks(a) Discuss the behaviour of an inductor connected to (i) a dc source, and (ii) a high frequency ac source. (b) What is the phase relation between current and voltage in an ideal inductor connected to an ac source ? Draw a phasor diagram for the circuit.
- Q.253 marks(a) Depict the variation of electric field and magnetic field with respect to the direction of propagation of an electromagnetic wave. Write their two important characteristics. (b) Show that gives the velocity of an electromagnetic wave in free space.
- Q.263 marksA ray of light is travelling through a rectangular glass slab (refractive index ) and is incident on the horizontal glass-air surface at the critical angle for the two media. The slab is then brought in contact with water (refractive index ) such that a thin horizontal layer of water is formed on the surface of the slab. Find the angle at which the ray will emerge into air from the water-air surface.
- Q.273 marksDifferentiate between nuclear fission and nuclear fusion. Give one example for each with nuclear reaction.
- Q.283 marksWith the help of circuit diagrams, briefly explain the forward biasing and the reverse biasing of a p-n junction diode.
Section D
1 mark each
- Capacitors are manufactured with certain standard capacitances and working voltages. However, these standard values may not be the ones that are actually needed in a particular application. Two or more capacitors can be grouped in series or in parallel to achieve desired capacitance and voltage. When connected in series, the total capacitance decreases while the voltage rating increases, whereas in parallel connections, the total capacitance increases and maintains the same voltage rating. A capacitor stores energy in the electric field between its plates and stored energy is proportional to the square of the voltage and capacitance , where symbols have their usual meanings. Two capacitors, one of and the other of , are connected in series in the circuit as shown in the figure, for a long time.Q.29 (i)1 markThe total capacitance of the circuit is :
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- Q.29 (ii)1 markThe current in the resistor is :
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- Q.29 (iii)1 markThe potential difference between point A and B is :
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- Q.29 (iv) (a)1 markThe value of charge on the plates of the capacitor is :
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OR
Q.29 (iv) (b)1 markThe wire between two capacitors is cut at point P. The current in the circuit will :Tap an option to check your answer.
- A charged particle +q in an electric field experiences a force in the direction of the electric field. As a result, its kinetic energy changes. Similarly, the charged particle also experiences a force when it moves in a magnetic field . But this magnetic force is perpendicular to both velocity of the charged particle and the magnetic field , so it cannot change the kinetic energy of the charged particle. Consider two charged particles 1 and 2 of masses m and having charges and respectively. They are accelerated from rest through the same potential difference V and acquire kinetic energy and . Then they enter in a region of uniform magnetic field perpendicular to their velocities.Q.30 (i)1 markThe ratio of their kinetic energies is :
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- Q.30 (ii)1 markThe ratio of the radii of the circular paths described by them is :
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- Q.30 (iii)1 markSuppose particles 1 and 2 enter the magnetic field with velocities and . Then :
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- Q.30 (iv) (a)1 markIf period of revolution for particle 1 is 4 s, then for particle 2, the period will be :
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OR
Q.30 (iv) (b)1 markIf the value of momentum for particles 1 and 2 are and , then :Tap an option to check your answer.
Section E
5 marks each
- Q.31 (a)5 marks(i) In the figure, OA and OB show the variation of electric potential V at a point due to two point charges and with respectively. Here r represents the distance of the point from the two point charges. (I) Identify the nature of the two charges and . (II) What is the value of ? Justify your answer. (ii) Two point charges and are placed at and respectively in an external electric field , where . Find the electrostatic potential energy of this configuration.
OR
Q.31 (b)5 marks(i) Two infinitely long straight wires having linear charge densities and are held vertically parallel to each other, distance r apart in free space. Find the nature and magnitude of the force/length exerted by one wire on the other. (ii) A small hollow conducting sphere of radius is given a charge Q. It is surrounded by a concentric conducting spherical shell of inner radius and outer radius , having charge . If a point charge 2q were kept at the centre, find : (I) the electric flux through a concentric spherical Gaussian surface of radius x for (1) , and (2) . (II) electric field at a point distant x from the centre for (1) , and (2) . (III) surface charge density on the inner surface of (1) sphere, and (2) shell.- Q.32 (a)5 marks(i) A light bulb and an open coil inductor are connected in series across an ac source of variable frequency. How will the glow of the bulb be affected when : (I) an iron bar is inserted inside the coil, and (II) the frequency of the source is decreased ? Justify your answers. Assume that in each above case other factors remain unchanged. (ii) An ac voltage volt is connected across a series LCR circuit in which , H and . Taking , calculate : (I) impedance of the circuit. (II) rms value of current that flows in the circuit. (III) power factor of the circuit.
OR
Q.32 (b)5 marks(i) State Lenz's law and explain that it follows the law of conservation of energy. (ii) Write the dimensional formula for self-inductance. The current in a coil changes from A to A in s. If an average emf induced in the coil is 50 V, calculate the self-inductance of the coil.- Q.33 (a)5 marks(i) A point object is kept in front of a convex spherical surface of radius of curvature R. Draw the ray diagram to show the formation of image and derive the relation between the object and image distance (u and v) in terms of refractive index n of the medium and R. (ii) A convex lens of focal length of 20 cm is used to form the image of an object placed 30 cm away from the lens. Find the position and nature of the image formed.
OR
Q.33 (b)5 marks(i) Two thin converging lenses of focal length and are placed coaxially in contact. Derive expression for the focal length of the combination. (ii) A beam of coherent light of wavelength 550 nm is incident normal to the plane of a pair of two slits and each of width m separated by mm. Dark and bright fringes are observed on a screen m away from the plane of the slits. Calculate : (I) fringe width. (II) distance of the second dark fringe from the central maximum. (III) what will happen when the entire apparatus is immersed in water.
Section A
1 mark each
- Q.11 markThe phase difference between the two superimposing waves that give rise to a bright spot in a Young's double-slit experiment is (n is an integer) :
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- Q.21 markIf and are the radii of atomic nuclei of mass numbers 64 and 27 respectively, then the value of is :
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- Q.31 markAn equiconvex lens of focal length 15 cm is cut into two equal plano-convex halves. The focal length of each half will be :
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- Q.41 markAn electric dipole is placed in x-y plane, centred at the origin. Let and be the magnitudes of electric field at a point distant r (>> a) from its centre, along its axis and on its equatorial plane, respectively. Then the value of is :
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- Q.51 markA plano-convex lens, made of glass (n = ) has a curved surface whose radius is 40 cm. The image formed of an object is of the same size as that of the object. The distance of the object from the lens is :
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- Q.61 markRadiation of wavelength 200 nm is incident on a photosensitive surface of work function eV. The kinetic energy of fastest photoelectrons emitted from this surface will be close to :
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- Q.71 markA metallic rod of 1 m length is rotated with a frequency of 40 rev/s, with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius 1 m, about an axis passing through the centre and perpendicular to the plane of the ring. A constant and uniform magnetic field of T parallel to the axis is present in the region. The value of emf induced between the centre and the metallic ring is close to :
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- Q.81 markWhich of the following p-n junction diodes is forward biased ?
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- Q.91 markWhen the forward bias voltage in a semiconductor diode is changed from V to V, the forward current changes by mA. The forward bias resistance of the diode will be :
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- Q.101 markA plane electromagnetic wave travels through a medium and the magnetic field associated with it is given by T where x is in metres and t is in seconds. The velocity of the wave is :
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- Q.111 markThe velocity of the photoelectrons emitted from a surface depends upon the :
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- Q.121 markA thin plano-convex lens and a thin equi-concave lens are kept coaxially in contact as shown in the figure. Assuming both the lenses are made of glass of refractive index , and R is the radius of curvature of each curved surface, the focal length of the combination is :
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- Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.Q.131 markAssertion (A) : Photoelectric current depends upon the intensity of the incident radiation. Reason (R) : Stopping potential is independent of the intensity of the incident radiation.
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- Q.141 markAssertion (A) : Nuclear forces are always attractive. Reason (R) : The nuclear force between protons and neutrons in a nucleus is a weak force.
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- Q.151 markAssertion (A) : The cylindrical soft iron core in a moving coil galvanometer only makes the magnetic field radial and does not affect the strength of the magnetic field. Reason (R) : In a moving coil galvanometer, the plane of the coil is always perpendicular to the magnetic field.
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- Q.161 markAssertion (A) : In a Wheatstone bridge circuit, if we interchange the position of the cell and the galvanometer, the balance condition remains unchanged. Reason (R) : so balance condition remains same.
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Section B
2 marks each
- Q.172 marksCalculate the de Broglie wavelength of a neutron having kinetic energy of 150 eV.
- Q.182 marksExplain, with the help of suitable diagram, the two important processes that occur during the formation of a p-n junction.
- Q.19 (a)2 marksIn the given figure, a steady current I flows through the circuit when points A and C are connected by a wire of negligible resistance. Find the potential difference between points B and C.
OR
Q.19 (b)2 marksA battery of emf 21 V and internal resistance is connected to a resistor. If the current in the circuit is 3 A, find : (i) the resistance of the resistor. (ii) the terminal voltage of the battery.- Q.202 marksDraw a labelled ray diagram of an astronomical telescope when final image is formed at infinity. Write the expression for its magnifying power.
- Q.212 marksExplain the terms mass defect and binding energy. How are they related ?
Section C
3 marks each
- Q.223 marksWith the help of circuit diagrams, briefly explain the forward biasing and the reverse biasing of a p-n junction diode.
- Q.233 marksDefine the term 'critical angle'. A small bulb is placed at the bottom of a tank containing a liquid of refractive index at a depth H. It is observed that the light emerges from a circular area of radius r of the surface. Obtain the expression for r in terms of H and .
- Q.24 (a)3 marksA circular coil of 30 turns and radius cm carrying a current of 6 A is suspended vertically in a uniform horizontal magnetic field of T. The field lines make an angle of with the plane of the coil. Calculate the magnitude of the external torque that must be applied to prevent the coil from turning. What would happen if the circular coil is replaced by a planar coil of irregular shape that encloses the same area, keeping other parameters unchanged ?
OR
Q.24 (b)3 marksAn alpha particle (mass kg and charge C) having MeV energy, enters a region of a uniform magnetic field of T. If the field is directed perpendicular to the velocity of the particle, find the radius of the circular path described by the particle. Mention the condition under which the particle in this region (i) describes a helical path, and (ii) goes straight undeviated.- Q.253 marksA series combination of circuit elements X and Y is connected across an ac source. It is found that the voltage is ahead of current in phase by radian. When element Y is replaced by element Z, the current leads the voltage by radian. (a) Identify the elements X, Y and Z. (b) What will the phase angle and power factor for the circuit be if X, Y and Z were connected in series across the same ac source ? What can you say about the current that flows in the circuit in this case ?
- Q.263 marks(a) Depict the variation of electric field and magnetic field with respect to the direction of propagation of an electromagnetic wave. Write their two important characteristics. (b) Show that gives the velocity of an electromagnetic wave in free space.
- Q.273 marksDifferentiate between nuclear fission and nuclear fusion. Give one example for each with nuclear reaction.
- Q.283 marksDraw a plot showing the variation of potential energy of a pair of nucleons as a function of their separation (r). Using this plot, show that the nuclear force is (i) attractive for , and (ii) repulsive for .
Section D
1 mark each
- A charged particle +q in an electric field experiences a force in the direction of the electric field. As a result, its kinetic energy changes. Similarly, the charged particle also experiences a force when it moves in a magnetic field . But this magnetic force is perpendicular to both velocity of the charged particle and the magnetic field , so it cannot change the kinetic energy of the charged particle. Consider two charged particles 1 and 2 of masses m and having charges and respectively. They are accelerated from rest through the same potential difference V and acquire kinetic energy and . Then they enter in a region of uniform magnetic field perpendicular to their velocities.Q.29 (i)1 markThe ratio of their kinetic energies is :
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- Q.29 (ii)1 markThe ratio of the radii of the circular paths described by them is :
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- Q.29 (iii)1 markSuppose particles 1 and 2 enter the magnetic field with velocities and . Then :
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- Q.29 (iv) (a)1 markIf period of revolution for particle 1 is 4 s, then for particle 2, the period will be :
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OR
Q.29 (iv) (b)1 markIf the value of momentum for particles 1 and 2 are and , then :Tap an option to check your answer.
- Capacitors are manufactured with certain standard capacitances and working voltages. However, these standard values may not be the ones that are actually needed in a particular application. Two or more capacitors can be grouped in series or in parallel to achieve desired capacitance and voltage. When connected in series, the total capacitance decreases while the voltage rating increases, whereas in parallel connections, the total capacitance increases and maintains the same voltage rating. A capacitor stores energy in the electric field between its plates and stored energy is proportional to the square of the voltage and capacitance , where symbols have their usual meanings. Two capacitors, one of and the other of , are connected in series in the circuit as shown in the figure, for a long time.Q.30 (i)1 markThe total capacitance of the circuit is :
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- Q.30 (ii)1 markThe current in the resistor is :
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- Q.30 (iii)1 markThe potential difference between point A and B is :
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- Q.30 (iv) (a)1 markThe value of charge on the plates of the capacitor is :
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OR
Q.30 (iv) (b)1 markThe wire between two capacitors is cut at point P. The current in the circuit will :Tap an option to check your answer.
Section E
5 marks each
- Q.31 (a)5 marks(i) A light bulb and an open coil inductor are connected in series across an ac source of variable frequency. How will the glow of the bulb be affected when : (I) an iron bar is inserted inside the coil, and (II) the frequency of the source is decreased ? Justify your answers. Assume that in each above case other factors remain unchanged. (ii) An ac voltage volt is connected across a series LCR circuit in which , H and . Taking , calculate : (I) impedance of the circuit. (II) rms value of current that flows in the circuit. (III) power factor of the circuit.
OR
Q.31 (b)5 marks(i) State Lenz's law and explain that it follows the law of conservation of energy. (ii) Write the dimensional formula for self-inductance. The current in a coil changes from A to A in s. If an average emf induced in the coil is 50 V, calculate the self-inductance of the coil.- Q.32 (a)5 marks(i) A point object is kept in front of a convex spherical surface of radius of curvature R. Draw the ray diagram to show the formation of image and derive the relation between the object and image distance (u and v) in terms of refractive index n of the medium and R. (ii) A convex lens of focal length of 20 cm is used to form the image of an object placed 30 cm away from the lens. Find the position and nature of the image formed.
OR
Q.32 (b)5 marks(i) Two thin converging lenses of focal length and are placed coaxially in contact. Derive expression for the focal length of the combination. (ii) A beam of coherent light of wavelength 550 nm is incident normal to the plane of a pair of two slits and each of width m separated by mm. Dark and bright fringes are observed on a screen m away from the plane of the slits. Calculate : (I) fringe width. (II) distance of the second dark fringe from the central maximum. (III) what will happen when the entire apparatus is immersed in water.- Q.33 (a)5 marks(i) In the figure, OA and OB show the variation of electric potential V at a point due to two point charges and with respectively. Here r represents the distance of the point from the two point charges. (I) Identify the nature of the two charges and . (II) What is the value of ? Justify your answer. (ii) Two point charges and are placed at and respectively in an external electric field , where . Find the electrostatic potential energy of this configuration.
OR
Q.33 (b)5 marks(i) Two infinitely long straight wires having linear charge densities and are held vertically parallel to each other, distance r apart in free space. Find the nature and magnitude of the force/length exerted by one wire on the other. (ii) A small hollow conducting sphere of radius is given a charge Q. It is surrounded by a concentric conducting spherical shell of inner radius and outer radius , having charge . If a point charge 2q were kept at the centre, find : (I) the electric flux through a concentric spherical Gaussian surface of radius x for (1) , and (2) . (II) electric field at a point distant x from the centre for (1) , and (2) . (III) surface charge density on the inner surface of (1) sphere, and (2) shell.
Section A
1 mark each
- Q.11 markA plane electromagnetic wave travels through a medium and the magnetic field associated with it is given by T where x is in metres and t is in seconds. The velocity of the wave is :
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- Q.21 markA ray of monochromatic light travelling in air is incident on a glass slab and is partly reflected and partly refracted. Both the reflected and refracted lights will have :
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- Q.31 markWhen the forward bias voltage in a semiconductor diode is changed from V to V, the forward current changes by mA. The forward bias resistance of the diode will be :
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- Q.41 markA square loop of side L lies in the x-y plane in a magnetic field , where is a constant. The magnetic flux through the loop is :
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- Q.51 markAn electric dipole with dipole moment is placed in an electric field . An external agent turns the dipole until its electric dipole moment is . The work done by the agent is :
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- Q.61 markA thin plano-convex lens and a thin equi-concave lens are kept coaxially in contact as shown in the figure. Assuming both the lenses are made of glass of refractive index , and R is the radius of curvature of each curved surface, the focal length of the combination is :
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- Q.71 markIf the given figure, is the potential barrier across a p-n junction in an unbiased condition. Which of the following statements is correct ?
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- Q.81 markIf and are the radii of atomic nuclei of mass numbers 64 and 27 respectively, then the value of is :
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- Q.91 markA ray of yellow light undergoes total internal reflection when it is incident at the interface of two media. This ray is successively replaced by the ray of blue, green and red lights. Which of the following statements is true if the angle of incidence is same in all cases ?
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- Q.101 markThe ratio of the de Broglie wavelengths associated with the electron revolving in the first and third orbits in hydrogen atom is :
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- Q.111 markRadiation of wavelength 200 nm is incident on a photosensitive surface of work function eV. The kinetic energy of fastest photoelectrons emitted from this surface will be close to :
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- Q.121 markThe phase difference between the two superimposing waves that give rise to a bright spot in a Young's double-slit experiment is (n is an integer) :
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- Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.Q.131 markAssertion (A) : Nuclear forces are always attractive. Reason (R) : The nuclear force between protons and neutrons in a nucleus is a weak force.
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- Q.141 markAssertion (A) : Photoelectric current depends upon the intensity of the incident radiation. Reason (R) : Stopping potential is independent of the intensity of the incident radiation.
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- Q.151 markAssertion (A) : In a Wheatstone bridge circuit, if we interchange the position of the cell and the galvanometer, the balance condition remains unchanged. Reason (R) : so balance condition remains same.
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- Q.161 markAssertion (A) : The cylindrical soft iron core in a moving coil galvanometer only makes the magnetic field radial and does not affect the strength of the magnetic field. Reason (R) : In a moving coil galvanometer, the plane of the coil is always perpendicular to the magnetic field.
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Section B
2 marks each
- Q.172 marksWrite any two points of difference between intrinsic and extrinsic semiconductors.
- Q.182 marksExplain the terms mass defect and binding energy. How are they related ?
- Q.192 marksLight of frequency Hz is incident on a metal surface. If the maximum speed of photoelectrons emitted is , calculate the threshold frequency for the surface.
- Q.20 (a)2 marksIn the given figure, a steady current I flows through the circuit when points A and C are connected by a wire of negligible resistance. Find the potential difference between points B and C.
OR
Q.20 (b)2 marksA battery of emf 21 V and internal resistance is connected to a resistor. If the current in the circuit is 3 A, find : (i) the resistance of the resistor. (ii) the terminal voltage of the battery.- Q.212 marksIn Young's double slit experiment, the central maximum is bright in the interference pattern obtained on a screen. What will happen when : (a) light waves emitted out of slits and have an initial phase difference of radian ? (b) one of the slits is closed ? Justify your answers.
Section C
3 marks each
- Q.223 marks(a) Depict the variation of electric field and magnetic field with respect to the direction of propagation of an electromagnetic wave. Write their two important characteristics. (b) Show that gives the velocity of an electromagnetic wave in free space.
- Q.233 marksA ray of light is incident at angle of on one face of a prism with an equilateral triangular base. If it passes symmetrically through the prism, find the : (a) angle of minimum deviation for the prism, and (b) refractive index of the material of the prism.
- Q.243 marksWith the help of circuit diagrams, briefly explain the forward biasing and the reverse biasing of a p-n junction diode.
- Q.253 marks(a) Establish the relation between drift velocity of electrons and electric current (I) in a conductor. (b) How is affected when the length of the conductor is doubled, keeping the voltage applied across the conductor constant ?
- Q.26 (a)3 marksA circular coil of 30 turns and radius cm carrying a current of 6 A is suspended vertically in a uniform horizontal magnetic field of T. The field lines make an angle of with the plane of the coil. Calculate the magnitude of the external torque that must be applied to prevent the coil from turning. What would happen if the circular coil is replaced by a planar coil of irregular shape that encloses the same area, keeping other parameters unchanged ?
OR
Q.26 (b)3 marksAn alpha particle (mass kg and charge C) having MeV energy, enters a region of a uniform magnetic field of T. If the field is directed perpendicular to the velocity of the particle, find the radius of the circular path described by the particle. Mention the condition under which the particle in this region (i) describes a helical path, and (ii) goes straight undeviated.- Q.273 marksState Faraday's law of electromagnetic induction. Briefly describe two methods for producing induced emf.
- Q.283 marksA deuterium nucleus and an alpha particle approach a target nucleus separately in head-on position. Find the ratio of their distance of closest approach to the nucleus, when both have : (a) the same velocity, and (b) the same momentum.
Section D
1 mark each
- Capacitors are manufactured with certain standard capacitances and working voltages. However, these standard values may not be the ones that are actually needed in a particular application. Two or more capacitors can be grouped in series or in parallel to achieve desired capacitance and voltage. When connected in series, the total capacitance decreases while the voltage rating increases, whereas in parallel connections, the total capacitance increases and maintains the same voltage rating. A capacitor stores energy in the electric field between its plates and stored energy is proportional to the square of the voltage and capacitance , where symbols have their usual meanings. Two capacitors, one of and the other of , are connected in series in the circuit as shown in the figure, for a long time.Q.29 (i)1 markThe total capacitance of the circuit is :
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- Q.29 (ii)1 markThe current in the resistor is :
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- Q.29 (iii)1 markThe potential difference between point A and B is :
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- Q.29 (iv) (a)1 markThe value of charge on the plates of the capacitor is :
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OR
Q.29 (iv) (b)1 markThe wire between two capacitors is cut at point P. The current in the circuit will :Tap an option to check your answer.
- A charged particle +q in an electric field experiences a force in the direction of the electric field. As a result, its kinetic energy changes. Similarly, the charged particle also experiences a force when it moves in a magnetic field . But this magnetic force is perpendicular to both velocity of the charged particle and the magnetic field , so it cannot change the kinetic energy of the charged particle. Consider two charged particles 1 and 2 of masses m and having charges and respectively. They are accelerated from rest through the same potential difference V and acquire kinetic energy and . Then they enter in a region of uniform magnetic field perpendicular to their velocities.Q.30 (i)1 markThe ratio of their kinetic energies is :
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- Q.30 (ii)1 markThe ratio of the radii of the circular paths described by them is :
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- Q.30 (iii)1 markSuppose particles 1 and 2 enter the magnetic field with velocities and . Then :
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- Q.30 (iv) (a)1 markIf period of revolution for particle 1 is 4 s, then for particle 2, the period will be :
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OR
Q.30 (iv) (b)1 markIf the value of momentum for particles 1 and 2 are and , then :Tap an option to check your answer.
Section E
5 marks each
- Q.31 (a)5 marks(i) A point object is kept in front of a convex spherical surface of radius of curvature R. Draw the ray diagram to show the formation of image and derive the relation between the object and image distance (u and v) in terms of refractive index n of the medium and R. (ii) A convex lens of focal length of 20 cm is used to form the image of an object placed 30 cm away from the lens. Find the position and nature of the image formed.
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Q.31 (b)5 marks(i) Two thin converging lenses of focal length and are placed coaxially in contact. Derive expression for the focal length of the combination. (ii) A beam of coherent light of wavelength 550 nm is incident normal to the plane of a pair of two slits and each of width m separated by mm. Dark and bright fringes are observed on a screen m away from the plane of the slits. Calculate : (I) fringe width. (II) distance of the second dark fringe from the central maximum. (III) what will happen when the entire apparatus is immersed in water.- Q.32 (a)5 marks(i) In the figure, OA and OB show the variation of electric potential V at a point due to two point charges and with respectively. Here r represents the distance of the point from the two point charges. (I) Identify the nature of the two charges and . (II) What is the value of ? Justify your answer. (ii) Two point charges and are placed at and respectively in an external electric field , where . Find the electrostatic potential energy of this configuration.
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Q.32 (b)5 marks(i) Two infinitely long straight wires having linear charge densities and are held vertically parallel to each other, distance r apart in free space. Find the nature and magnitude of the force/length exerted by one wire on the other. (ii) A small hollow conducting sphere of radius is given a charge Q. It is surrounded by a concentric conducting spherical shell of inner radius and outer radius , having charge . If a point charge 2q were kept at the centre, find : (I) the electric flux through a concentric spherical Gaussian surface of radius x for (1) , and (2) . (II) electric field at a point distant x from the centre for (1) , and (2) . (III) surface charge density on the inner surface of (1) sphere, and (2) shell.- Q.33 (a)5 marks(i) A light bulb and an open coil inductor are connected in series across an ac source of variable frequency. How will the glow of the bulb be affected when : (I) an iron bar is inserted inside the coil, and (II) the frequency of the source is decreased ? Justify your answers. Assume that in each above case other factors remain unchanged. (ii) An ac voltage volt is connected across a series LCR circuit in which , H and . Taking , calculate : (I) impedance of the circuit. (II) rms value of current that flows in the circuit. (III) power factor of the circuit.
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Q.33 (b)5 marks(i) State Lenz's law and explain that it follows the law of conservation of energy. (ii) Write the dimensional formula for self-inductance. The current in a coil changes from A to A in s. If an average emf induced in the coil is 50 V, calculate the self-inductance of the coil.