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CBSE Class 12 Physics 2024 question paper (55/1)

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

  1. Q.11 mark
    A thin plastic rod is bent into a circular ring of radius R. It is uniformly charged with charge density λ\lambda. The magnitude of the electric field at its centre is :

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  2. Q.21 mark
    Ten capacitors, each of capacitance 1 μF\mu\mathrm{F}, are connected in parallel to a source of 100 V. The total energy stored in the system is equal to :

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  3. Q.31 mark
    Consider the circuit shown in the figure. The potential difference between points A and B is :

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  4. Q.41 mark
    A loop carrying a current I clockwise is placed in x−yx - y plane, in a uniform magnetic field directed along z-axis. The tendency of the loop will be to :

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  5. Q.51 mark
    A 10 cm long wire lies along y-axis. It carries a current of 1⋅01{\cdot}0 A in positive y-direction. A magnetic field B⃗=(5 mT)j^−(8 mT)k^\vec{\mathrm{B}} = (5\ \mathrm{mT})\hat{j} - (8\ \mathrm{mT})\hat{k} exists in the region. The force on the wire is :

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  6. Q.61 mark
    A galvanometer of resistance G Ω\Omega is converted into an ammeter of range 0 to I A. If the current through the galvanometer is 0⋅1%0{\cdot}1\% of I A, the resistance of the ammeter is :

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  7. Q.71 mark
    The reactance of a capacitor of capacitance C connected to an ac source of frequency ω\omega is ‘X’. If the capacitance of the capacitor is doubled and the frequency of the source is tripled, the reactance will become :

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  8. Q.81 mark
    In the four regions, I, II, III and IV, the electric fields are described as : Region I : Ex=E0sin⁡(kz−ωt)\mathrm{E}_x = \mathrm{E}_0 \sin (kz - \omega t) Region II : Ex=E0\mathrm{E}_x = \mathrm{E}_0 Region III : Ex=E0sin⁡kz\mathrm{E}_x = \mathrm{E}_0 \sin kz Region IV : Ex=E0cos⁡kz\mathrm{E}_x = \mathrm{E}_0 \cos kz The displacement current will exist in the region :

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  9. Q.91 mark
    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 :

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  10. Q.101 mark
    Ge is doped with As. Due to doping,

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  11. Q.111 mark
    Two beams, A and B whose photon energies are 3⋅33{\cdot}3 eV and 11⋅311{\cdot}3 eV respectively, illuminate a metallic surface (work function 2⋅32{\cdot}3 eV) successively. The ratio of maximum speed of electrons emitted due to beam A to that due to beam B is :

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  12. Q.121 mark
    The waves associated with a moving electron and a moving proton have the same wavelength λ\lambda. It implies that they have the same :

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  13. 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 mark
    Assertion (A) : In photoelectric effect, the kinetic energy of the emitted photoelectrons increases with increase in the intensity of the incident light. Reason (R) : Photoelectric current depends on the wavelength of the incident light.

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  14. Q.141 mark
    Assertion (A) : The mutual inductance between two coils is maximum when the coils are wound on each other. Reason (R) : The flux linkage between two coils is maximum when they are wound on each other.

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  15. Q.151 mark
    Assertion (A) : Two long parallel wires, freely suspended and connected in series to a battery, move apart. Reason (R) : Two wires carrying current in opposite directions repel each other.

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  16. Q.161 mark
    Assertion (A) : Plane and convex mirrors cannot produce real images under any circumstance. Reason (R) : A virtual image cannot serve as an object to produce a real image.

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Section B

2 marks each

  1. Q.172 marks
    Find the temperature at which the resistance of a wire made of silver will be twice its resistance at 20°C. Take 20°C as the reference temperature and temperature coefficient of resistance of silver at 20°C = 4⋅0×10−3 K−14{\cdot}0 \times 10^{-3}\ \mathrm{K^{-1}}.
  2. Q.18 (a)2 marks
    Monochromatic light of frequency 5⋅0×10145{\cdot}0 \times 10^{14} Hz passes from air into a medium of refractive index 1⋅51{\cdot}5. Find the wavelength of the light (i) reflected, and (ii) refracted at the interface of the two media.
  3. OR

    Q.18 (b)2 marks
    A plano-convex lens of focal length 16 cm is made of a material of refractive index 1⋅41{\cdot}4. Calculate the radius of the curved surface of the lens.
  4. Q.192 marks
    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.
  5. Q.202 marks
    Consider a neutron (mass m) of kinetic energy E and a photon of the same energy. Let λn\lambda_n and λp\lambda_p be the de Broglie wavelength of neutron and the wavelength of photon respectively. Obtain an expression for λnλp\dfrac{\lambda_n}{\lambda_p}.
  6. Q.212 marks
    Plot a graph showing the variation of current with voltage for the material GaAs. On the graph, mark the region where : (a) resistance is negative, and (b) Ohm's law is obeyed.

Section C

3 marks each

  1. Q.223 marks
    A cube of side 0⋅10{\cdot}1 m is placed, as shown in the figure, in a region where electric field E⃗=500 x i^\vec{\mathrm{E}} = 500\,x\,\hat{i} exists. Here x is in meters and E in NC−1\mathrm{NC^{-1}}. Calculate : (a) the flux passing through the cube, and (b) the charge within the cube.
  2. Q.23 (a)3 marks
    Define ‘current density’. Is it a scalar or a vector ? An electric field E⃗\vec{\mathrm{E}} is maintained in a metallic conductor. If n be the number of electrons (mass m, charge −e- e) per unit volume in the conductor and τ\tau its relaxation time, show that the current density j⃗=αE⃗\vec{j} = \alpha \vec{\mathrm{E}}, where α=(ne2m)τ\alpha = \left(\dfrac{ne^2}{m}\right)\tau.
  3. OR

    Q.23 (b)3 marks
    What is a Wheatstone bridge ? Obtain the necessary conditions under which the Wheatstone bridge is balanced.
  4. Q.243 marks
    A proton with kinetic energy 1⋅3384×10−141{\cdot}3384 \times 10^{-14} J moving horizontally from north to south, enters a uniform magnetic field B of 2⋅02{\cdot}0 mT directed eastward. Calculate : (a) the speed of the proton (b) the magnitude of acceleration of the proton (c) the radius of the path traced by the proton [Take (q/m) for proton = 1⋅0×1081{\cdot}0 \times 10^{8} C/kg]
  5. Q.253 marks
    An inductor, a capacitor and a resistor are connected in series with an ac source v=vmsin⁡ωtv = v_m \sin \omega t. Derive an expression for the average power dissipated in the circuit. Also obtain the expression for the resonant frequency of the circuit.
  6. Q.263 marks
    (a) “The wavelength of the electromagnetic wave is often correlated with the characteristic size of the system that radiates.” Give two examples to justify this statement. (b) (i) Long distance radio broadcasts use short-wave bands. Why ? (ii) Optical and radio telescopes are built on the ground, but X-ray astronomy is possible only from satellites orbiting the Earth. Why ?
  7. Q.273 marks
    Write the drawbacks of Rutherford's atomic model. How did Bohr remove them ? Show that different orbits in Bohr's atom are not equally spaced.
  8. Q.283 marks
    (a) State any two properties of a nucleus. (b) Why is the density of a nucleus much more than that of an atom ? (c) Show that the density of the nuclear matter is the same for all nuclei.

Section D

1 mark each

  1. A lens is a transparent medium bounded by two surfaces, with one or both surfaces being spherical. The focal length of a lens is determined by the radii of curvature of its two surfaces and the refractive index of its medium with respect to that of the surrounding medium. The power of a lens is reciprocal of its focal length. If a number of lenses are kept in contact, the power of the combination is the algebraic sum of the powers of the individual lenses.
    Q.29 (i)1 mark
    A double-convex lens, with each face having same radius of curvature R, is made of glass of refractive index n. Its power is :

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  2. Q.29 (ii)1 mark
    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 :

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  3. Q.29 (iii)1 mark
    The above two parts are kept in contact with each other as shown in the figure. The power of the combination will be :

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  4. Q.29 (iv) (a)1 mark
    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 :

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  5. OR

    Q.29 (iv) (b)1 mark
    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 :

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  6. 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.
    Q.30 (i)1 mark
    The root mean square value of an alternating voltage applied to a full-wave rectifier is V02\dfrac{\mathrm{V}_0}{\sqrt{2}}. Then the root mean square value of the rectified output voltage is :

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  7. Q.30 (ii)1 mark
    In a full-wave rectifier, the current in each of the diodes flows for :

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  8. Q.30 (iii)1 mark
    In a full-wave rectifier :

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  9. Q.30 (iv) (a)1 mark
    An alternating voltage of frequency of 50 Hz is applied to a half-wave rectifier. Then the ripple frequency of the output will be :

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  10. OR

    Q.30 (iv) (b)1 mark
    A signal, as shown in the figure, is applied to a p-n junction diode. Identify the output across resistance RL\mathrm{R_L} :

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Section E

5 marks each

  1. Q.31 (a)5 marks
    (i) Derive an expression for potential energy of an electric dipole p⃗\vec{p} in an external uniform electric field E⃗\vec{\mathrm{E}}. When is the potential energy of the dipole (1) maximum, and (2) minimum ? (ii) An electric dipole consists of point charges −1⋅0- 1{\cdot}0 pC and +1⋅0+ 1{\cdot}0 pC located at (0, 0) and (3 mm, 4 mm) respectively in x−yx - y plane. An electric field E⃗=(1000 Vm)i^\vec{\mathrm{E}} = \left(\dfrac{1000\ \mathrm{V}}{\mathrm{m}}\right)\hat{i} is switched on in the region. Find the torque τ⃗\vec{\tau} acting on the dipole.
  2. OR

    Q.31 (b)5 marks
    (i) An electric dipole (dipole moment p⃗=p i^\vec{p} = p\,\hat{i}), consisting of charges −q- 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 14πε0⋅p⃗⋅i^x2\dfrac{1}{4\pi\varepsilon_0} \cdot \dfrac{\vec{p} \cdot \hat{i}}{x^2}. (ii) Two isolated metallic spheres S1\mathrm{S_1} and S2\mathrm{S_2} of radii 1 cm and 3 cm respectively are charged such that both have the same charge density (2π×10−9)C/m2\left(\dfrac{2}{\pi} \times 10^{-9}\right) \mathrm{C/m^2}. They are placed far away from each other and connected by a thin wire. Calculate the new charge on sphere S1\mathrm{S_1}.
  3. Q.32 (a)5 marks
    (i) A resistor and a capacitor are connected in series to an ac source v=vmsin⁡ωtv = v_m \sin \omega t. Derive an expression for the impedance of the circuit. (ii) When does an inductor act as a conductor in a circuit ? Give reason for it. (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.
  4. OR

    Q.32 (b)5 marks
    (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. (ii) A step-up transformer converts a low voltage into high voltage. Does it violate the principle of conservation of energy ? Explain. (iii) 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 : (1) The output voltage across the secondary coil (2) The current in the primary coil if the current in the secondary coil is 2⋅02{\cdot}0 A.
  5. Q.33 (a)5 marks
    (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 δ\delta. Prove that the refractive index n of the material of the prism is given by n=sin⁡ (A+δ)sin⁡An = \dfrac{\sin\,(\mathrm{A} + \delta)}{\sin \mathrm{A}}. (iii) The refractive index of the material of a prism is 2\sqrt{2}. If the refracting angle of the prism is 60°, find the (1) Angle of minimum deviation, and (2) Angle of incidence.
  6. OR

    Q.33 (b)5 marks
    (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. (ii) What are the coherent sources of light ? Can two independent sodium lamps act like coherent sources ? Explain. (iii) A beam of light consisting of a known wavelength 520 nm and an unknown wavelength λ\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 λ\lambda.