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CBSE Class 12 Physics 2024 question paper (55/2)

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
    Two charged particles P and Q, having the same charge but different masses mPm_P and mQm_Q, start from rest and travel equal distances in a uniform electric field E⃗\vec{E} in time tPt_P and tQt_Q respectively. Neglecting the effect of gravity, the ratio (tPtQ)\left(\dfrac{t_P}{t_Q}\right) is :

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  2. Q.21 mark
    Electrons drift with speed vdv_d in a conductor with potential difference V across its ends. If V is reduced to (V2)\left(\dfrac{V}{2}\right), their drift speed will become :

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  3. Q.31 mark
    A wire of length 4⋅44{\cdot}4 m is bent round in the shape of a circular loop and carries a current of 1⋅01{\cdot}0 A. The magnetic moment of the loop will be :

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  4. Q.41 mark
    A circular coil of radius 10 cm is placed in a magnetic field B⃗=(1⋅0 i^+0⋅5 j^)\vec{B} = (1{\cdot}0\,\hat{i} + 0{\cdot}5\,\hat{j}) mT such that the outward unit vector normal to the surface of the coil is (0⋅6 i^+0⋅8 j^)(0{\cdot}6\,\hat{i} + 0{\cdot}8\,\hat{j}). The magnetic flux linked with the coil is :

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  5. Q.51 mark
    Which of the following quantity/quantities remains same in primary and secondary coils of an ideal transformer ? Current, Voltage, Power, Magnetic flux

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  6. Q.61 mark
    A resistor and an ideal inductor are connected in series to a 1002100\sqrt{2} V, 50 Hz ac source. When a voltmeter is connected across the resistor or the inductor, it shows the same reading. The reading of the voltmeter is :

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  7. Q.71 mark
    Electromagnetic waves with wavelength 10 nm are called :

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  8. Q.81 mark
    The work function for a photosensitive surface is 3⋅3153{\cdot}315 eV. The cut-off wavelength for photoemission of electrons from this surface is :

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  9. Q.91 mark
    Energy levels A, B and C of an atom correspond to increasing values of energy i.e. EA<EB<ECE_A < E_B < E_C. Let λ1\lambda_1, λ2\lambda_2 and λ3\lambda_3 be the wavelengths of radiation corresponding to the transitions C to B, B to A and C to A, respectively. The correct relation between λ1\lambda_1, λ2\lambda_2 and λ3\lambda_3 is :

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  10. Q.101 mark
    An alpha particle approaches a gold nucleus in Geiger-Marsden experiment with kinetic energy K. It momentarily stops at a distance d from the nucleus and reverses its direction. Then d is proportional to :

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  11. Q.111 mark
    An n-type semiconducting Si is obtained by doping intrinsic Si with :

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  12. Q.121 mark
    When a p-n junction diode is subjected to reverse biasing :

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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) : Photoelectric current increases with an increase in intensity of incident radiation, for a given frequency of incident radiation and the accelerating potential. Reason (R) : Increase in the intensity of incident radiation results in an increase in the number of photoelectrons emitted per second and hence an increase in the photocurrent.

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  14. Q.141 mark
    Assertion (A) : Lenz's law is a consequence of the law of conservation of energy. Reason (R) : There is no power loss in an ideal inductor.

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  15. Q.151 mark
    Assertion (A) : An electron and a proton enter with the same momentum p⃗\vec{p} in a magnetic field B⃗\vec{B} such that p⃗⊥B⃗\vec{p} \perp \vec{B}. Then both describe a circular path of the same radius. Reason (R) : The radius of the circular path described by the charged particle (charge q, mass m) moving in the magnetic field B⃗\vec{B} is given by r=mvqBr = \dfrac{mv}{qB}.

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  16. Q.161 mark
    Assertion (A) : The magnifying power of a compound microscope is negative. Reason (R) : The final image formed is erect with respect to the object.

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Section B

2 marks each

  1. Q.172 marks
    Define resistivity of a conductor. How does the resistivity of a conductor depend upon the following : (a) Number density of free electrons in the conductor (n) (b) Their relaxation time τ\tau
  2. Q.18 (a)2 marks
    Two waves, each of amplitude 'a' and frequency 'ω\omega' emanating from two coherent sources of light superpose at a point. If the phase difference between the two waves is ϕ\phi, obtain an expression for the resultant intensity at that point.
  3. OR

    Q.18 (b)2 marks
    What is the effect on the interference pattern in Young's double-slit experiment when (i) the source slit is moved closer to the plane of the slits, and (ii) the separation between the two slits is increased ? Justify your answers.
  4. Q.192 marks
    A convex lens (n = 1⋅521{\cdot}52) has a focal length of 15⋅015{\cdot}0 cm in air. Find its focal length when it is immersed in liquid of refractive index 1⋅651{\cdot}65. What will be the nature of the lens ?
  5. Q.202 marks
    The carbon isotope 612C^{12}_{6}\mathrm{C} has a nuclear mass of 12⋅00000012{\cdot}000000 u. Calculate the binding energy of its nucleus. Given mp=1⋅007825m_p = 1{\cdot}007825 u; mn=1⋅008665m_n = 1{\cdot}008665 u.
  6. Q.212 marks
    How does the energy gap of an intrinsic semiconductor effectively change when doped with a (a) trivalent impurity, and (b) pentavalent impurity ? Justify your answer in each case.

Section C

3 marks each

  1. Q.223 marks
    The figure shows a circuit with three ideal batteries. Find the magnitude and direction of currents in the branches AG, BF and CD.
  2. Q.233 marks
    (a) On what factors does the speed of an electromagnetic wave in a medium depend ? (b) How is an electromagnetic wave produced ? (c) Sketch a schematic diagram depicting the electric and magnetic fields for an electromagnetic wave propagating along z-axis.
  3. Q.243 marks
    A 100-turn coil of radius 1⋅61{\cdot}6 cm and resistance 5⋅0 Ω5{\cdot}0\ \Omega is co-axial with a solenoid of 250 turns/cm and radius 1⋅81{\cdot}8 cm. The solenoid current drops from 1⋅51{\cdot}5 A to zero in 25 ms. Calculate the current induced in the coil in this duration. (Take π2=10\pi^2 = 10)
  4. Q.25 (a)3 marks
    Two long, straight, parallel conductors carry steady currents in opposite directions. Explain the nature of the force of interaction between them. Obtain an expression for the magnitude of the force between the two conductors. Hence define one ampere.
  5. OR

    Q.25 (b)3 marks
    Obtain an expression for the torque τ⃗\vec{\tau} acting on a current carrying loop in a uniform magnetic field B⃗\vec{B}. Draw the necessary diagram.
  6. Q.263 marks
    Using Bohr's postulates, derive the expression for the radius of the nthn^{th} orbit of an electron in a hydrogen atom. Also find the numerical value of Bohr's radius a0a_0.
  7. Q.273 marks
    de Broglie wavelength λ\lambda as a function of 1K\dfrac{1}{\sqrt{K}}, for two particles of masses m1m_1 and m2m_2 are shown in the figure. Here, K is the energy of the moving particles. (a) What does the slope of a line represent ? (b) Which of the two particles is heavier ? (c) Is this graph also valid for a photon ? Justify your answer in each case.
  8. Q.283 marks
    With the help of a circuit diagram, explain the working of a p-n junction diode as a full wave rectifier. Draw its input and output waveforms.

Section D

1 mark each

  1. When the terminals of a cell are connected to a conductor of resistance R, an electric current flows through the circuit. The electrolyte of the cell also offers some resistance in the path of the current, like the conductor. This resistance offered by the electrolyte is called internal resistance of the cell (r). It depends upon the nature of the electrolyte, the area of the electrodes immersed in the electrolyte and the temperature. Due to internal resistance, a part of the energy supplied by the cell is wasted in the form of heat. When no current is drawn from the cell, the potential difference between the two electrodes in known as emf of the cell ε\varepsilon. With a current drawn from the cell, the potential difference between the two electrodes is termed as terminal potential difference (V).
    Q.29 (i)1 mark
    Choose the incorrect statement :

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  2. Q.29 (ii)1 mark
    Two cells of emfs 2⋅02{\cdot}0 V and 6⋅06{\cdot}0 V and internal resistances 0⋅1 Ω0{\cdot}1\ \Omega and 0⋅4 Ω0{\cdot}4\ \Omega respectively, are connected in parallel. The equivalent emf of the combination will be :

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  3. Q.29 (iii)1 mark
    Dipped in the solution, the electrode exchanges charges with the electrolyte. The positive electrode develops a potential V+V_+ (V+>0)(V_+ > 0), and the negative electrode develops a potential −(V−)-(V_-) (V−≥0)(V_- \geq 0), relative to the electrolyte adjacent to it. When no current is drawn from the cell then :

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  4. Q.29 (iv) (a)1 mark
    Five identical cells, each of emf 2 V and internal resistance 0⋅1 Ω0{\cdot}1\ \Omega are connected in parallel. This combination in turn is connected to an external resistor of 9⋅98 Ω9{\cdot}98\ \Omega. The current flowing through the resistor is :

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  5. OR

    Q.29 (iv) (b)1 mark
    Potential difference across a cell in the open circuit is 6 V. It becomes 4 V when a current of 2 A is drawn from it. The internal resistance of the cell is :

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  6. When a ray of light propagates from a denser medium to a rarer medium, it bends away from the normal. When the incident angle is increased, the refracted ray deviates more from the normal. For a particular angle of incidence in the denser medium, the refracted ray just grazes the interface of the two surfaces. This angle of incidence is called the critical angle for the pair of media involved.
    Q.30 (i)1 mark
    For a ray incident at the critical angle, the angle of reflection is :

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  7. Q.30 (ii)1 mark
    A ray of light of wavelength 600 nm is incident in water (n=43)\left(n = \dfrac{4}{3}\right) on the water-air interface at an angle less than the critical angle. The wavelength associated with the refracted ray is :

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  8. Q.30 (iii) (a)1 mark
    The interface AB between the two media A and B is shown in the figure. In the denser medium A, the incident ray PQ makes an angle of 30∘30^\circ with the horizontal. The refracted ray is parallel to the interface. The refractive index of medium B w.r.t. medium A is :

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  9. OR

    Q.30 (iii) (b)1 mark
    Two media A and B are separated by a plane boundary. The speed of light in medium A and B is 2×1082 \times 10^8 ms−1^{-1} and 2⋅5×1082{\cdot}5 \times 10^8 ms−1^{-1} respectively. The critical angle for a ray of light going from medium A to medium B is :

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  10. Q.30 (iv)1 mark
    The figure shows the path of a light ray through a triangular prism. In this phenomenon, the angle θ\theta is given by :

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Section E

5 marks each

  1. Q.31 (a)5 marks
    (i) Obtain an expression for the electric potential due to a small dipole of dipole moment p⃗\vec{p}, at a point r⃗\vec{r} from its centre, for much larger distances compared to the size of the dipole. (ii) Three point charges q, 2q and nq are placed at the vertices of an equilateral triangle. If the potential energy of the system is zero, find the value of n.
  2. OR

    Q.31 (b)5 marks
    (i) State Gauss's Law in electrostatics. Apply this to obtain the electric field E⃗\vec{E} at a point near a uniformly charged infinite plane sheet. (ii) Two long straight wires 1 and 2 are kept as shown in the figure. The linear charge density of the two wires are λ1=10 μC/m\lambda_1 = 10\ \mu\mathrm{C/m} and λ2=−20 μC/m\lambda_2 = -20\ \mu\mathrm{C/m}. Find the net force F⃗\vec{F} experienced by an electron held at point P.
  3. Q.32 (a)5 marks
    (i) A particle of mass m and charge q is moving with a velocity v⃗\vec{v} in a magnetic field B⃗\vec{B} as shown in the figure. Show that it follows a helical path. Hence, obtain its frequency of revolution. (ii) In a hydrogen atom, the electron moves in an orbit of radius 2 A˚2\ \mathring{\mathrm{A}} making 8×10148 \times 10^{14} revolutions per second. Find the magnetic moment associated with the orbital motion of the electron.
  4. OR

    Q.32 (b)5 marks
    (i) What is current sensitivity of a galvanometer ? Show how the current sensitivity of a galvanometer may be increased. "Increasing the current sensitivity of a galvanometer may not necessarily increase its voltage sensitivity." Explain. (ii) A moving coil galvanometer has a resistance 15 Ω15\ \Omega and takes 20 mA to produce full scale deflection. How can this galvanometer be converted into a voltmeter of range 0 to 100 V ?
  5. Q.33 (a)5 marks
    (i) Give any two differences between the interference pattern obtained in Young's double-slit experiment and a diffraction pattern due to a single slit. (ii) Draw an intensity distribution graph in case of a double-slit interference pattern. (iii) In Young's double-slit experiment using monochromatic light of wavelength λ\lambda, the intensity of light at a point on the screen, where path difference is λ\lambda, is K units. Find the intensity of light at a point on the screen where the path difference is λ6\dfrac{\lambda}{6}.
  6. OR

    Q.33 (b)5 marks
    (i) Draw a labelled ray diagram of a compound microscope showing image formation at least distance of distinct vision. Derive an expression for its magnifying power. (ii) A telescope consists of two lenses of focal length 100 cm and 5 cm. Find the magnifying power when the final image is formed at infinity.