CBSE Class 12 Physics 2023 question paper (55/4)
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 markTwo charges and are placed at the centres of two spherical conducting shells of radius and respectively. The shells are arranged such that their centres are distance apart. The force on due to is :
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- Q.21 markAn electron enters a uniform magnetic field with speed . It describes a semicircular path and comes out of the field. The final speed of the electron is :
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- Q.31 markThe magnetic field lines near a substance are as shown in the figure. The substance is :
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- Q.41 markThe figure shows variation of current (I) with time (t) in four devices P, Q, R and S. The device in which an alternating current flows is :
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- Q.51 markThe electromagnetic waves used in radar systems are :
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- Q.61 markIn a Young's double-slit experiment, the fringe width is found to be . If the entire apparatus is immersed in a liquid of refractive index , the new fringe width will be :
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- Q.71 markPhotons of energy eV are incident on a photosensitive surface. If the stopping potential for the emitted electrons is V, the work function for the surface is :
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- Q.81 markWhich of the following statements is not true for nuclear forces ?
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- Q.91 markThe direction of induced current in the loop abc is :
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- Q.101 markAn ac voltage is applied to a series combination of a resistor R and an element X. The instantaneous current in the circuit is . Then which of the following is correct ?
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- Q.111 markA plane wavefront is incident on a concave mirror of radius of curvature R. The radius of the refracted wavefront will be :
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- Q.121 markA proton and an alpha particle have the same kinetic energy. The ratio of de Broglie wavelengths associated with the proton to that with the alpha particle is :
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- Q.131 markThe potential energy of an electron in the second excited state in hydrogen atom is :
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- Q.141 markThe difference in mass of nucleus and total mass of its constituent nucleons is u. The binding energy per nucleon for this nucleus is equal to the energy equivalent of :
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- Q.151 markThe threshold voltage for a p-n junction diode used in the circuit is V. The type of biasing and current in the circuit are :
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- Questions number 16 to 18 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.161 markAssertion (A) : When three electric bulbs of power 200 W, 100 W and 50 W are connected in series to a source, the power consumed by the 50 W bulb is maximum. Reason (R) : In a series circuit, current is the same through each bulb, but the potential difference across each bulb is different.
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- Q.171 markAssertion (A) : A current carrying square loop made of a wire of length L is placed in a magnetic field. It experiences a torque which is greater than the torque on a circular loop made of the same wire carrying the same current in the same magnetic field. Reason (R) : A square loop occupies more area than a circular loop, both made of wire of the same length.
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- Q.181 markAssertion (A) : In 'n' type semiconductor, number density of electrons is greater than the number density of holes but the crystal maintains an overall charge neutrality. Reason (R) : The charge of electrons donated by donor atoms is just equal and opposite to that of the ionised donor.
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Section B
2 marks each
- Q.192 marksTwo identical dipoles are arranged in x-y plane as shown in the figure. Find the magnitude and the direction of net electric field at the origin O.
- Q.202 marksWrite two differences between the emf and terminal potential difference of a cell. What is the most important precaution that one should take while drawing current from a cell ?
- Q.212 marksA small magnetised needle P is placed at the origin of x-y plane with its magnetic moment pointing along the y-axis. Another identical magnetised needle Q is placed in two positions, one by one. Case 1 : at (a, 0) with its magnetic moment pointing along x-axis. Case 2 : at (0, a) with its magnetic moment pointing along y-axis. (a) In which case is the potential energy of P and Q minimum ? (b) In which case is P and Q not in equilibrium ? Justify your answers.
- Q.22 (a)2 marksWhat is a displacement current ? How is it different from a conduction current ?
OR
Q.22 (b)2 marksWrite any two characteristics of an electromagnetic wave. Why are microwaves used in radar systems ?- Q.232 marksThe figure shows versus graph for photoelectrons emitted from a surface where is the maximum speed of electrons and is the wavelength of incident radiation. Using this graph and Einstein's photoelectric equation, obtain the expression for Planck's constant and work function of the surface.
- Q.242 marksDraw the graph showing the variation of binding energy per nucleon with mass number A of nuclei . Use this graph to explain the release of energy in nuclear fission.
- Q.25 (a)2 marksObtain an expression for electrostatic potential energy of a system of three charges , and placed at the vertices of an equilateral triangle of side .
OR
Q.25 (b)2 marksTwo small conducting balls A and B of radius and have charges and respectively. They are connected by a wire. Obtain the expression for charges on A and B, in equilibrium.
Section C
3 marks each
- Q.263 marksTwo circular loops A and B, each of radius 3 m, are placed coaxially at a distance of 4 m. They carry currents of 3 A and 2 A in opposite directions respectively. Find the net magnetic field at the centre of loop A.
- Q.273 marks(a) The figure shows the variation of induced emf as a function of rate of change of current for two identical solenoids X and Y. One is air cored and the other is iron cored. Which one of them is iron cored ? Why ? (b) Obtain an expression for self-inductance of a long solenoid of length L and cross-sectional area A having N turns.
- Q.28 (a)3 marksA resistor of 30 and a capacitor of are connected in series to a 200 V, 50 Hz ac source. Calculate (i) the current in the circuit, and (ii) voltage drops across the resistor and the capacitor. (iii) Is the algebraic sum of these voltages more than the source voltage ? If yes, solve the paradox.
OR
Q.28 (b)3 marksA series LCR circuit with R = 20 , L = 2 H and C = 50 is connected to a 200 volts ac source of variable frequency. What is (i) the amplitude of the current, and (ii) the average power transferred to the circuit in one complete cycle, at resonance ? (iii) Calculate the potential drop across the capacitor.- Q.29 (a)3 marks(i) In diffraction due to a single slit, the phase difference between light waves reaching a point on the screen is . Explain whether a bright or a dark fringe will be formed at the point. (ii) What should the width (a) of each slit be to obtain eight maxima of two double-slit patterns (slit separation d) within the central maximum of the single slit pattern ? (iii) Draw the plot of intensity distribution in a diffraction pattern due to a single slit.
OR
Q.29 (b)3 marks(i) In a Young's double-slit experiment , where and are the two slits as shown in the figure. Find the path difference for constructive and destructive interference at P. (ii) What is the effect on the interference fringes in a Young's double-slit experiment, if the monochromatic source S is replaced by a source of white light ?- Q.303 marksBriefly explain Geiger-Marsden experiment. Show the variation of the number of particles scattered (N) with scattering angle in this experiment. What is the main conclusion that can be inferred from this plot ?
Section D
5 marks each
- Q.31 (a)5 marks(i) Define mobility of electrons. Give its SI units. (ii) A steady current flows through a wire AB, as shown in the figure. What happens to the electric field and the drift velocity along the wire ? Justify your answer. (iii) Consider the circuit shown in the figure. Find the effective resistance of the circuit and the current drawn from the battery.
OR
Q.31 (b)5 marks(i) Define electrical conductivity of a wire. Give its SI unit. (ii) High current is to be drawn safely from (1) a low-voltage battery, and (2) a high-voltage battery. What can you say about the internal resistance of the two batteries ? (iii) Calculate the total energy supplied by the batteries to the circuit shown in the figure, in one minute.- Q.32 (a)5 marks(i) Draw a ray diagram to show how the final image is formed at infinity in an astronomical refracting telescope. Obtain an expression for its magnifying power. (ii) Two thin lenses and , being a convex lens of focal length 24 cm and a concave lens of focal length 18 cm are placed coaxially at a separation of 45 cm. A 1 cm tall object is placed in front of the lens at a distance of 36 cm. Find the location and height of the image formed by the combination.
OR
Q.32 (b)5 marks(i) Explain the working principle of an optical fibre with the help of a diagram. Mention one use of a light pipe. (ii) A ray of light is incident at an angle of 60° on one face of a prism with the prism angle A = 60°. The ray passes symmetrically through the prism. Find the angle of minimum deviation and refractive index of the material of the prism. If the prism is immersed in water, how will be affected ? Justify your answer.- Q.33 (a)5 marks(i) A germanium crystal is doped with antimony. With the help of energy-band diagram, explain how the conductivity of the doped crystal is affected. (ii) Briefly explain the two processes involved in the formation of a p-n junction. (iii) What will the effect of (1) forward biasing, and (2) reverse biasing be on the width of depletion layer in a p-n junction diode ?
OR
Q.33 (b)5 marks(i) With the help of a circuit diagram, briefly explain the working of a full-wave rectifier using p-n junction diodes. (ii) Draw V – I characteristics of a p-n junction diode. Explain how these characteristics make a diode suitable for rectification. (iii) Carbon and silicon have the same lattice structure. Then why is carbon an insulator but silicon a semiconductor ?
Section E
- Electrostatics deals with the study of forces, fields and potentials arising from static charges. Force and electric field, due to a point charge is basically determined by Coulomb's law. For symmetric charge configurations, Gauss's law, which is also based on Coulomb's law, helps us to find the electric field. A charge/a system of charges like a dipole experience a force/torque in an electric field. Work is required to be done to provide a specific orientation to a dipole with respect to an electric field.Q.34 (a)1 markConsider a uniformly charged thin conducting shell of radius R. Plot a graph showing the variation of with distance r from the centre, for points .
- Q.34 (b)1 markThe figure shows the variation of potential V with for two point charges and , where V is the potential at a distance r due to a point charge. Find .
- Q.34 (c)2 marksAn electric dipole of dipole moment of C-m is kept in a uniform electric field of N/C such that the dipole moment and the electric field are parallel. Calculate the potential energy of the dipole.
OR
Q.34 (c) OR2 marksAn electric dipole of dipole moment is initially kept in a uniform electric field such that is perpendicular to . Find the amount of work done in rotating the dipole to a position at which becomes antiparallel to .- The lens maker's formula is useful to design lenses of desired focal lengths using surfaces of suitable radii of curvature. The focal length also depends on the refractive index of the material of the lens and the surrounding medium. The refractive index depends on the wavelength of the light used. The power of a lens is related to its focal length.Q.35 (a)1 markHow will the power of a lens be affected with an increase of wavelength of light ?
- Q.35 (b)1 markThe radius of curvature of two surfaces of a convex lens is R each. For what value of of its material will its focal length become equal to R ?
- Q.35 (c)2 marksThe focal length of a concave lens of is 20 cm in air. It is completely immersed in water of . Calculate its focal length in water.
OR
Q.35 (c) OR2 marksAn object is placed in front of a lens which forms its erect image of magnification 3. The power of the lens is 5 D. Calculate the distance of the object and the image from the lens.
Section A
1 mark each
- Q.11 markThe figure shows variation of current (I) with time (t) in four devices P, Q, R and S. The device in which an alternating current flows is :
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- Q.21 markThe electromagnetic waves used in radar systems are :
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- Q.31 markIn a Young's double-slit experiment, the fringe width is found to be . If the entire apparatus is immersed in a liquid of refractive index , the new fringe width will be :
Tap an option to check your answer.
- Q.41 markPhotons of energy eV are incident on a photosensitive surface of work function eV. The stopping potential for photoelectrons is :
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- Q.51 markWhich of the following statements is not true for nuclear forces ?
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- Q.61 markA point charge q is kept at a distance r from an infinitely long straight wire with charge density . The magnitude of the electrostatic force experienced by charge q is :
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- Q.71 markThe ratio of the magnitude of magnetic moment to that of angular momentum, of an electron revolving around the nucleus in a hydrogen atom is :
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- Q.81 markWhich one of the following has negative value of susceptibility ?
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- Q.91 markThe difference in mass of nucleus and total mass of its constituent nucleons is u. The binding energy per nucleon for this nucleus is equal to the energy equivalent of :
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- Q.101 markThe threshold voltage for a p-n junction diode used in the circuit is V. The type of biasing and current in the circuit are :
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- Q.111 markThe direction of induced current in the loop abc is :
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- Q.121 markAn ac voltage is applied to a series combination of a resistor R and an element X. The instantaneous current in the circuit is . Then which of the following is correct ?
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- Q.131 markA plane wavefront is incident on a concave mirror of radius of curvature R. The radius of the refracted wavefront will be :
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- Q.141 markA proton and an alpha particle have the same kinetic energy. The ratio of de Broglie wavelengths associated with the proton to that with the alpha particle is :
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- Q.151 markThe potential energy of an electron in the second excited state in hydrogen atom is :
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- Questions number 16 to 18 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.161 markAssertion (A) : A current carrying square loop made of a wire of length L is placed in a magnetic field. It experiences a torque which is greater than the torque on a circular loop made of the same wire carrying the same current in the same magnetic field. Reason (R) : A square loop occupies more area than a circular loop, both made of wire of the same length.
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- Q.171 markAssertion (A) : In 'n' type semiconductor, number density of electrons is greater than the number density of holes but the crystal maintains an overall charge neutrality. Reason (R) : The charge of electrons donated by donor atoms is just equal and opposite to that of the ionised donor.
Tap an option to check your answer.
- Q.181 markAssertion (A) : When three electric bulbs of power 200 W, 100 W and 50 W are connected in series to a source, the power consumed by the 50 W bulb is maximum. Reason (R) : In a series circuit, current is the same through each bulb, but the potential difference across each bulb is different.
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Section B
2 marks each
- Q.19 (a)2 marksObtain an expression for electrostatic potential energy of a system of three charges , and placed at the vertices of an equilateral triangle of side .
OR
Q.19 (b)2 marksTwo small conducting balls A and B of radius and have charges and respectively. They are connected by a wire. Obtain the expression for charges on A and B, in equilibrium.- Q.202 marksAnswer the following giving reasons : (a) Do the magnetic field lines also represent the 'lines of force' on a moving charged particle at every point ? (b) If magnetic monopoles existed, how would the Gauss's law of magnetism be modified ?
- Q.21 (a)2 marksWhat is a displacement current ? How is it different from a conduction current ?
OR
Q.21 (b)2 marksWrite any two characteristics of an electromagnetic wave. Why are microwaves used in radar systems ?- Q.222 marksThe figure shows versus graph for photoelectrons emitted from a surface where is the maximum speed of electrons and is the wavelength of incident radiation. Using this graph and Einstein's photoelectric equation, obtain the expression for Planck's constant and work function of the surface.
- Q.232 marksShow that the density of a nucleus is independent of its mass number. Why are lighter nuclei more stable than heavier nuclei ?
- Q.242 marksUse Gauss's law to obtain the expression for electric field due to a uniformly charged infinite plane thin sheet.
- Q.252 marksTwo identical cells, each of emf E and internal resistance r, are connected with a load resistance R, first in series and then in parallel. Obtain the condition under which the current through R is same in both cases.
Section C
3 marks each
- Q.26 (a)3 marksA resistor of 30 and a capacitor of are connected in series to a 200 V, 50 Hz ac source. Calculate (i) the current in the circuit, and (ii) voltage drops across the resistor and the capacitor. (iii) Is the algebraic sum of these voltages more than the source voltage ? If yes, solve the paradox.
OR
Q.26 (b)3 marksA series LCR circuit with R = 20 , L = 2 H and C = 50 is connected to a 200 volts ac source of variable frequency. What is (i) the amplitude of the current, and (ii) the average power transferred to the circuit in one complete cycle, at resonance ? (iii) Calculate the potential drop across the capacitor.- Q.27 (a)3 marks(i) In diffraction due to a single slit, the phase difference between light waves reaching a point on the screen is . Explain whether a bright or a dark fringe will be formed at the point. (ii) What should the width (a) of each slit be to obtain eight maxima of two double-slit patterns (slit separation d) within the central maximum of the single slit pattern ? (iii) Draw the plot of intensity distribution in a diffraction pattern due to a single slit.
OR
Q.27 (b)3 marks(i) In a Young's double-slit experiment , where and are the two slits as shown in the figure. Find the path difference for constructive and destructive interference at P. (ii) What is the effect on the interference fringes in a Young's double-slit experiment, if the monochromatic source S is replaced by a source of white light ?- Q.283 marks(a) Differentiate between 'impact parameter' and 'distance of closest approach' in alpha particle scattering experiment. Identify, situations when impact parameter is (i) minimum, and (ii) very large. (b) An electron cannot revolve around the nucleus in a hydrogen atom at an arbitrary distance. Explain.
- Q.293 marksTwo infinitely long parallel conductors A and B, separated by 2 cm, carry 6 A and 2 A currents in opposite directions respectively. Find : (a) the net magnetic field at a point midway between A and B. (b) the force acting per unit length on B.
- Q.303 marks(a) Two coplanar concentric circular loops of radii R and r (<< R) are arranged coaxially. Obtain the expression for their mutual inductance. (b) A square loop of side 20 cm starts moving at t = 0 with a velocity of 5 cm/s towards a region of uniform magnetic field as shown in the figure. Specify the time interval(s) during which induced emf is produced in the loop.
Section D
5 marks each
- Q.31 (a)5 marks(i) Draw a ray diagram to show how the final image is formed at infinity in an astronomical refracting telescope. Obtain an expression for its magnifying power. (ii) Two thin lenses and , being a convex lens of focal length 24 cm and a concave lens of focal length 18 cm are placed coaxially at a separation of 45 cm. A 1 cm tall object is placed in front of the lens at a distance of 36 cm. Find the location and height of the image formed by the combination.
OR
Q.31 (b)5 marks(i) Explain the working principle of an optical fibre with the help of a diagram. Mention one use of a light pipe. (ii) A ray of light is incident at an angle of 60° on one face of a prism with the prism angle A = 60°. The ray passes symmetrically through the prism. Find the angle of minimum deviation and refractive index of the material of the prism. If the prism is immersed in water, how will be affected ? Justify your answer.- Q.32 (a)5 marks(i) A germanium crystal is doped with antimony. With the help of energy-band diagram, explain how the conductivity of the doped crystal is affected. (ii) Briefly explain the two processes involved in the formation of a p-n junction. (iii) What will the effect of (1) forward biasing, and (2) reverse biasing be on the width of depletion layer in a p-n junction diode ?
OR
Q.32 (b)5 marks(i) With the help of a circuit diagram, briefly explain the working of a full-wave rectifier using p-n junction diodes. (ii) Draw V – I characteristics of a p-n junction diode. Explain how these characteristics make a diode suitable for rectification. (iii) Carbon and silicon have the same lattice structure. Then why is carbon an insulator but silicon a semiconductor ?- Q.33 (a)5 marks(i) Define mobility of electrons. Give its SI units. (ii) A steady current flows through a wire AB, as shown in the figure. What happens to the electric field and the drift velocity along the wire ? Justify your answer. (iii) Consider the circuit shown in the figure. Find the effective resistance of the circuit and the current drawn from the battery.
OR
Q.33 (b)5 marks(i) Define electrical conductivity of a wire. Give its SI unit. (ii) High current is to be drawn safely from (1) a low-voltage battery, and (2) a high-voltage battery. What can you say about the internal resistance of the two batteries ? (iii) Calculate the total energy supplied by the batteries to the circuit shown in the figure, in one minute.
Section E
- The lens maker's formula is useful to design lenses of desired focal lengths using surfaces of suitable radii of curvature. The focal length also depends on the refractive index of the material of the lens and the surrounding medium. The refractive index depends on the wavelength of the light used. The power of a lens is related to its focal length.Q.34 (a)1 markHow will the power of a lens be affected with an increase of wavelength of light ?
- Q.34 (b)1 markThe radius of curvature of two surfaces of a convex lens is R each. For what value of of its material will its focal length become equal to R ?
- Q.34 (c)2 marksThe focal length of a concave lens of is 20 cm in air. It is completely immersed in water of . Calculate its focal length in water.
OR
Q.34 (c) OR2 marksAn object is placed in front of a lens which forms its erect image of magnification 3. The power of the lens is 5 D. Calculate the distance of the object and the image from the lens.- Electrostatics deals with the study of forces, fields and potentials arising from static charges. Force and electric field, due to a point charge is basically determined by Coulomb's law. For symmetric charge configurations, Gauss's law, which is also based on Coulomb's law, helps us to find the electric field. A charge/a system of charges like a dipole experience a force/torque in an electric field. Work is required to be done to provide a specific orientation to a dipole with respect to an electric field.Q.35 (a)1 markConsider a uniformly charged thin conducting shell of radius R. Plot a graph showing the variation of with distance r from the centre, for points .
- Q.35 (b)1 markThe figure shows the variation of potential V with for two point charges and , where V is the potential at a distance r due to a point charge. Find .
- Q.35 (c)2 marksAn electric dipole of dipole moment of C-m is kept in a uniform electric field of N/C such that the dipole moment and the electric field are parallel. Calculate the potential energy of the dipole.
OR
Q.35 (c) OR2 marksAn electric dipole of dipole moment is initially kept in a uniform electric field such that is perpendicular to . Find the amount of work done in rotating the dipole to a position at which becomes antiparallel to .
Section A
1 mark each
- Q.11 markIn a Young's double-slit experiment, the fringe width is found to be . If the entire apparatus is immersed in a liquid of refractive index , the new fringe width will be :
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- Q.21 markA light of frequency is incident on a metal surface whose work function is . The kinetic energy of emitted electron is K. If the frequency of the incident light is doubled then the kinetic energy of emitted electron will be :
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- Q.31 markWhich of the following statements is not true for nuclear forces ?
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- Q.41 markA particle of mass m and charge is moving with a uniform speed v in a circle of radius r, with another charge q at the centre of the circle. The value of r is :
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- Q.51 markPhotons of energy eV are incident on a photosensitive surface. If the stopping potential for the emitted electrons is V, the work function for the surface is :
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- Q.61 markWhich one of the following has relative magnetic permeability between 0 and 1 ?
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- Q.71 markThe figure shows variation of current (I) with time (t) in four devices P, Q, R and S. The device in which an alternating current flows is :
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- Q.81 markName the electromagnetic waves also known as 'heat waves'.
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- Q.91 markA plane wavefront is incident on a concave mirror of radius of curvature R. The radius of the refracted wavefront will be :
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- Q.101 markA proton and an alpha particle have the same kinetic energy. The ratio of de Broglie wavelengths associated with the proton to that with the alpha particle is :
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- Q.111 markThe direction of induced current in the loop abc is :
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- Q.121 markAn ac voltage is applied to a series combination of a resistor R and an element X. The instantaneous current in the circuit is . Then which of the following is correct ?
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- Q.131 markThe threshold voltage for a p-n junction diode used in the circuit is V. The type of biasing and current in the circuit are :
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- Q.141 markThe potential energy of an electron in the second excited state in hydrogen atom is :
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- Q.151 markThe difference in mass of nucleus and total mass of its constituent nucleons is u. The binding energy per nucleon for this nucleus is equal to the energy equivalent of :
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- Questions number 16 to 18 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.161 markAssertion (A) : In 'n' type semiconductor, number density of electrons is greater than the number density of holes but the crystal maintains an overall charge neutrality. Reason (R) : The charge of electrons donated by donor atoms is just equal and opposite to that of the ionised donor.
Tap an option to check your answer.
- Q.171 markAssertion (A) : When three electric bulbs of power 200 W, 100 W and 50 W are connected in series to a source, the power consumed by the 50 W bulb is maximum. Reason (R) : In a series circuit, current is the same through each bulb, but the potential difference across each bulb is different.
Tap an option to check your answer.
- Q.181 markAssertion (A) : A current carrying square loop made of a wire of length L is placed in a magnetic field. It experiences a torque which is greater than the torque on a circular loop made of the same wire carrying the same current in the same magnetic field. Reason (R) : A square loop occupies more area than a circular loop, both made of wire of the same length.
Tap an option to check your answer.
Section B
2 marks each
- Q.192 marksThe figure shows versus graph for photoelectrons emitted from a surface where is the maximum speed of electrons and is the wavelength of incident radiation. Using this graph and Einstein's photoelectric equation, obtain the expression for Planck's constant and work function of the surface.
- Q.202 marksBriefly describe the multi-step process involved in the generation of energy in the Sun.
- Q.212 marksUse Gauss's law to obtain the expression for electric field due to a thin infinitely long straight uniformly charged wire.
- Q.222 marksA cell of emf E and internal resistance r is connected to a variable resistance R. Draw plots showing the variation of (a) terminal voltage V with R, and (b) V with current I, in the circuit.
- Q.232 marksA particle of charge q and mass m starts moving with uniform velocity . Specify the direction of magnetic field which should be set up in the region so that the particle moves (a) straight undeviated, and (b) in a circle. Justify your answers.
- Q.24 (a)2 marksObtain an expression for electrostatic potential energy of a system of three charges , and placed at the vertices of an equilateral triangle of side .
OR
Q.24 (b)2 marksTwo small conducting balls A and B of radius and have charges and respectively. They are connected by a wire. Obtain the expression for charges on A and B, in equilibrium.- Q.25 (a)2 marksWhat is a displacement current ? How is it different from a conduction current ?
OR
Q.25 (b)2 marksWrite any two characteristics of an electromagnetic wave. Why are microwaves used in radar systems ?
Section C
3 marks each
- Q.263 marksDraw a plot showing the variation of potential energy of two nucleons as a function of distance between them. Identify the regions in which the force between the nucleons is (i) attractive, and (ii) repulsive. Justify your answers.
- Q.273 marksA current carrying circular loop and a straight wire bent partly in the form of a semicircle are placed as shown in the figure. Find the magnitude and direction of net magnetic field at point O.
- Q.28 (a)3 marks(i) In diffraction due to a single slit, the phase difference between light waves reaching a point on the screen is . Explain whether a bright or a dark fringe will be formed at the point. (ii) What should the width (a) of each slit be to obtain eight maxima of two double-slit patterns (slit separation d) within the central maximum of the single slit pattern ? (iii) Draw the plot of intensity distribution in a diffraction pattern due to a single slit.
OR
Q.28 (b)3 marks(i) In a Young's double-slit experiment , where and are the two slits as shown in the figure. Find the path difference for constructive and destructive interference at P. (ii) What is the effect on the interference fringes in a Young's double-slit experiment, if the monochromatic source S is replaced by a source of white light ?- Q.29 (a)3 marksA resistor of 30 and a capacitor of are connected in series to a 200 V, 50 Hz ac source. Calculate (i) the current in the circuit, and (ii) voltage drops across the resistor and the capacitor. (iii) Is the algebraic sum of these voltages more than the source voltage ? If yes, solve the paradox.
OR
Q.29 (b)3 marksA series LCR circuit with R = 20 , L = 2 H and C = 50 is connected to a 200 volts ac source of variable frequency. What is (i) the amplitude of the current, and (ii) the average power transferred to the circuit in one complete cycle, at resonance ? (iii) Calculate the potential drop across the capacitor.- Q.303 marksA rectangular conductor MNPQ with a movable arm MN (resistance r) is kept in a uniform magnetic field as shown in the figure. Resistance of arms MQ, QP and PN are negligible. Obtain the expression for the : (a) current induced in the loop specifying its direction, and (b) power required to move the arm.
Section D
5 marks each
- Q.31 (a)5 marks(i) A germanium crystal is doped with antimony. With the help of energy-band diagram, explain how the conductivity of the doped crystal is affected. (ii) Briefly explain the two processes involved in the formation of a p-n junction. (iii) What will the effect of (1) forward biasing, and (2) reverse biasing be on the width of depletion layer in a p-n junction diode ?
OR
Q.31 (b)5 marks(i) With the help of a circuit diagram, briefly explain the working of a full-wave rectifier using p-n junction diodes. (ii) Draw V – I characteristics of a p-n junction diode. Explain how these characteristics make a diode suitable for rectification. (iii) Carbon and silicon have the same lattice structure. Then why is carbon an insulator but silicon a semiconductor ?- Q.32 (a)5 marks(i) Define mobility of electrons. Give its SI units. (ii) A steady current flows through a wire AB, as shown in the figure. What happens to the electric field and the drift velocity along the wire ? Justify your answer. (iii) Consider the circuit shown in the figure. Find the effective resistance of the circuit and the current drawn from the battery.
OR
Q.32 (b)5 marks(i) Define electrical conductivity of a wire. Give its SI unit. (ii) High current is to be drawn safely from (1) a low-voltage battery, and (2) a high-voltage battery. What can you say about the internal resistance of the two batteries ? (iii) Calculate the total energy supplied by the batteries to the circuit shown in the figure, in one minute.- Q.33 (a)5 marks(i) Draw a ray diagram to show how the final image is formed at infinity in an astronomical refracting telescope. Obtain an expression for its magnifying power. (ii) Two thin lenses and , being a convex lens of focal length 24 cm and a concave lens of focal length 18 cm are placed coaxially at a separation of 45 cm. A 1 cm tall object is placed in front of the lens at a distance of 36 cm. Find the location and height of the image formed by the combination.
OR
Q.33 (b)5 marks(i) Explain the working principle of an optical fibre with the help of a diagram. Mention one use of a light pipe. (ii) A ray of light is incident at an angle of 60° on one face of a prism with the prism angle A = 60°. The ray passes symmetrically through the prism. Find the angle of minimum deviation and refractive index of the material of the prism. If the prism is immersed in water, how will be affected ? Justify your answer.
Section E
- Electrostatics deals with the study of forces, fields and potentials arising from static charges. Force and electric field, due to a point charge is basically determined by Coulomb's law. For symmetric charge configurations, Gauss's law, which is also based on Coulomb's law, helps us to find the electric field. A charge/a system of charges like a dipole experience a force/torque in an electric field. Work is required to be done to provide a specific orientation to a dipole with respect to an electric field.Q.34 (a)1 markConsider a uniformly charged thin conducting shell of radius R. Plot a graph showing the variation of with distance r from the centre, for points .
- Q.34 (b)1 markThe figure shows the variation of potential V with for two point charges and , where V is the potential at a distance r due to a point charge. Find .
- Q.34 (c)2 marksAn electric dipole of dipole moment of C-m is kept in a uniform electric field of N/C such that the dipole moment and the electric field are parallel. Calculate the potential energy of the dipole.
OR
Q.34 (c) OR2 marksAn electric dipole of dipole moment is initially kept in a uniform electric field such that is perpendicular to . Find the amount of work done in rotating the dipole to a position at which becomes antiparallel to .- The lens maker's formula is useful to design lenses of desired focal lengths using surfaces of suitable radii of curvature. The focal length also depends on the refractive index of the material of the lens and the surrounding medium. The refractive index depends on the wavelength of the light used. The power of a lens is related to its focal length.Q.35 (a)1 markHow will the power of a lens be affected with an increase of wavelength of light ?
- Q.35 (b)1 markThe radius of curvature of two surfaces of a convex lens is R each. For what value of of its material will its focal length become equal to R ?
- Q.35 (c)2 marksThe focal length of a concave lens of is 20 cm in air. It is completely immersed in water of . Calculate its focal length in water.
OR
Q.35 (c) OR2 marksAn object is placed in front of a lens which forms its erect image of magnification 3. The power of the lens is 5 D. Calculate the distance of the object and the image from the lens.