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CBSE Class 12 Physics 2025 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
    Figure shows variation of Coulomb force (F) acting between two point charges with 1r2\frac{1}{r^2}, r being the separation between the two charges (q1,q2)(q_1, q_2) and (q2,q3)(q_2, q_3). If q2q_2 is positive and least in magnitude, then the magnitudes of q1q_1, q2q_2 and q3q_3 are such that

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  2. Q.21 mark
    Two wires P and Q are made of the same material. The wire Q has twice the diameter and half the length as that of wire P. If the resistance of wire P is R, the resistance of the wire Q will be

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  3. Q.31 mark
    A 1 cm segment of a wire lying along x-axis carries current of 0.5 A along +x direction. A magnetic field B⃗=(0.4 mT) j^+(0.6 mT) k^\vec{B} = (0.4\ \text{mT})\,\hat{j} + (0.6\ \text{mT})\,\hat{k} is switched on, in the region. The force acting on the segment is

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  4. Q.41 mark
    A coil has 100 turns, each of area 0.05 m2\mathrm{m^2} and total resistance 1.5 Ω\Omega. It is inserted at an instant in a magnetic field of 90 mT, with its axis parallel to the field. The charge induced in the coil at that instant is :

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  5. Q.51 mark
    You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m. The number of turns in the solenoid should be

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  6. Q.61 mark
    A voltage v=v0sin⁡ωtv = v_0 \sin \omega t applied to a circuit drives a current i=i0sin⁡(ωt+ϕ)i = i_0 \sin (\omega t + \phi) in the circuit. The average power consumed in the circuit over a cycle is

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  7. Q.71 mark
    The given diagram exhibits the relationship between the wavelength of the electromagnetic waves and the energy of photon associated with them. The three points P, Q and R marked on the diagram may correspond respectively to :

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  8. Q.81 mark
    A beaker is filled with water (refractive index 43\frac{4}{3}) upto a height H. A coin is placed at its bottom. The depth of the coin, when viewed along the near normal direction, will be

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  9. Q.91 mark
    The stopping potential V0V_0 measured in a photoelectric experiment for a metal surface is plotted against frequency ν\nu of the incident radiation. Let m be the slope of the straight line so obtained. Then the value of charge of an electron is given by (h is the Planck's constant.)

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  10. Q.101 mark
    Let λe\lambda_e, λp\lambda_p and λd\lambda_d be the wavelengths associated with an electron, a proton and a deuteron, all moving with the same speed. Then the correct relation between them is

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  11. Q.111 mark
    Which of the following figures correctly represent the shape of curve of binding energy per nucleon as a function of mass number ?

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  12. Q.121 mark
    When a p-n junction diode is forward biased

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  13. Note : Question numbers 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) : It is difficult to move a magnet into a coil of large number of turns when the circuit of the coil is closed. Reason (R) : The direction of induced current in a coil with its circuit closed, due to motion of a magnet, is such that it opposes the cause.

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  14. Q.141 mark
    Assertion (A) : The deflection in a galvanometer is directly proportional to the current passing through it. Reason (R) : The coil of a galvanometer is suspended in a uniform radial magnetic field.

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  15. Q.151 mark
    Assertion (A) : We cannot form a p-n junction diode by taking a slab of a p-type semiconductor and physically joining it to another slab of a n-type semiconductor. Reason (R) : In a p-type semiconductor ηe≫ηh\eta_e \gg \eta_h while in a n-type semiconductor ηh≫ηe\eta_h \gg \eta_e.

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  16. Q.161 mark
    Assertion (A) : The potential energy of an electron revolving in any stationary orbit in a hydrogen atom is positive. Reason (R) : The total energy of a charged particle is always positive.

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Section B

2 marks each

  1. Q.172 marks
    A battery of emf E and internal resistance r is connected to a rheostat. When a current of 2A is dawn from the battery, the potential difference across the rheostat is 5V. The potential difference becomes 4V when a current of 4A is drawn from the battery. Calculate the value of E and r.
  2. Q.18 (a)2 marks
    In a diffraction experiment, the slit is illuminated by light of wavelength 600 nm. The first minimum of the pattern falls at θ=30∘\theta = 30^\circ. Calculate the width of the slit.
  3. OR

    Q.18 (b)2 marks
    In a Young's double-slit experiment, two light waves, each of intensity Io\mathrm{I_o}, interfere at a point, having a path difference λ8\frac{\lambda}{8} on the screen. Find the intensity at this point.
  4. Q.192 marks
    A transparent solid cylindrical rod (refractive index 23\frac{2}{\sqrt{3}}) is kept in air. A ray of light incident on its face travels along the surface of the rod, as shown in figure. Calculate the angle θ\theta.
  5. Q.202 marks
    Prove that, in Bohr model of hydrogen atom, the time period of revolution of an electron in nthn^{\mathrm{th}} orbit is proportional to n3n^3.
  6. Q.212 marks
    A p-type Si semiconductor is made by doping an average of one dopant atom per 5×1075 \times 10^7 silicon atoms. If the number density of silicon atoms in the specimen is 5×10285 \times 10^{28} atoms m−3\mathrm{m^{-3}}, find the number of holes created per cubic centimetre in the specimen due to doping. Also give one example of such dopants.

Section C

3 marks each

  1. Q.22 (a)3 marks
    Two batteries of emf's 3V & 6V and internal resistances 0.2 Ω\Omega & 0.4 Ω\Omega are connected in parallel. This combination is connected to a 4 Ω\Omega resistor. Find : (i) the equivalent emf of the combination (ii) the equivalent internal resistance of the combination (iii) the current drawn from the combination
  2. OR

    Q.22 (b)3 marks
    (i) A conductor of length ll is connected across an ideal cell of emf E. Keeping the cell connected, the length of the conductor is increased to 2l2l by gradually stretching it. If R and R′\mathrm{R}' are initial and final values of resistance and vdv_d and vd′v_d' are initial and final values of drift velocity, find the relation between (i) R′\mathrm{R}' and R and (ii) vd′v_d' and vdv_d. (ii) When electrons drift in a conductor from lower to higher potential, does it mean that all the 'free electrons' of the conductor are moving in the same direction ?
  3. Q.233 marks
    Using Biot-Savart law, derive expression for the magnetic field (B⃗)(\vec{B}) due to a circular current carrying loop at a point on its axis and hence at its centre.
  4. Q.243 marks
    (a) Show that the energy required to build up the current I in a coil of inductance L is 12LI2\frac{1}{2}\mathrm{LI}^2. (b) Considering the case of magnetic field produced by air-filled current carrying solenoid, show that the magnetic energy density of a magnetic field B is B22μ0\frac{\mathrm{B}^2}{2\mu_0}.
  5. Q.253 marks
    (a) A parallel plate capacitor is charged by an ac source. Show that the sum of conduction current (Ic)(\mathrm{I_c}) and the displacement current (Id)(\mathrm{I_d}) has the same value at all points of the circuit. (b) In case (a) above, is Kirchhoff's first rule (junction rule) valid at each plate of the capacitor ? Explain.
  6. Q.263 marks
    Answer the following giving reason : (a) All the photo electrons do not eject with the same kinetic energy when monochromatic light is incident on a metal surface. (b) The saturation current in case (a) is different for different intensity. (c) If one goes on increasing the wavelength of light incident on a metal surface, keeping its intensity constant, emission of photo electrons stop at a certain wavelength for this metal.
  7. Q.273 marks
    (a) Define 'Mass defect' and 'Binding energy' of a nucleus. Describe 'Fission process' on the basis of binding energy per nucleon. (b) A deuteron contains a proton and a neutron and has a mass of 2.013553 u. Calculate the mass defect for it in u and its energy equivalence in MeV. (mp=1.007277 u, mn=1.008665 u, 1u=931.5 MeV/c2)(\mathrm{m_p} = 1.007277\ \mathrm{u},\ \mathrm{m_n} = 1.008665\ \mathrm{u},\ 1\mathrm{u} = 931.5\ \mathrm{MeV/c^2})
  8. Q.283 marks
    (a) Draw circuit arrangement for studying V-I characteristics of a p-n junction diode. (b) Show the shape of the characteristics of a diode. (c) Mention two information that you can get from these characteristics.

Section D

1 mark each

  1. A circuit consisting of a capacitor C, a resistor of resistance R and an ideal battery of emf V, as shown in figure is known as RC series circuit. As soon as the circuit is completed by closing key S1\mathrm{S_1} (keeping S2\mathrm{S_2} open) charges begin to flow between the capacitor plates and the battery terminals. The charge on the capacitor increases and consequently the potential difference VcV_c (= q/C) across the capacitor also increases with time. When this potential difference equals the potential difference across the battery, the capacitor is fully charged (Q = VC). During this process of charging, the charge q on the capacitor changes with time t as q=Q[1−e−t/RC]q = Q[1 - e^{-t/RC}] The charging current can be obtained by differentiating it and using ddx(emx)=memx\frac{d}{dx}(e^{mx}) = m e^{mx}. Consider the case when R = 20 kΩ\Omega, C = 500 μ\muF and V = 10 V.
    Q.29 (i)1 mark
    The final charge on the capacitor, when key S1\mathrm{S_1} is closed and S2\mathrm{S_2} is open, is

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  2. Q.29 (ii)1 mark
    For sufficient time the key S1\mathrm{S_1} is closed and S2\mathrm{S_2} is open. Now key S2\mathrm{S_2} is closed and S1\mathrm{S_1} is open. What is the final charge on the capacitor ?

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  3. Q.29 (iii)1 mark
    The dimensional formula for RC is

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  4. Q.29 (iv) (a)1 mark
    The key S1\mathrm{S_1} is closed and S2\mathrm{S_2} is open. The value of current in the resistor after 5 seconds, is

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  5. OR

    Q.29 (iv) (b)1 mark
    The key S1\mathrm{S_1} is closed and S2\mathrm{S_2} is open. The initial value of charging current in the resistor, is

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  6. A thin lens is a transparent optical medium bounded by two surfaces, at least one of which should be spherical. Applying the formula for image formation by a single spherical surface successively at the two surfaces of a lens, one can obtain the 'lens maker formula' and then the 'lens formula'. A lens has two foci – called 'first focal point' and 'second focal point' of the lens, one on each side.
    Q.30 (i)1 mark
    Consider the arrangement shown in figure. A black vertical arrow and a horizontal thick line with a ball are painted on a glass plate. It serves as the object. When the plate is illuminated, its real image is formed on the screen. Which of the following correctly represents the image formed on the screen ?

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  7. Q.30 (ii)1 mark
    Which of the following statements is incorrect ?

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  8. Q.30 (iii) (a)1 mark
    A convex lens of focal length 'f' is cut into two equal parts perpendicular to the principal axis. The focal length of each part will be :

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  9. OR

    Q.30 (iii) (b)1 mark
    If an object in case (i) above is 20 cm from the lens and the screen is 50 cm away from the object, the focal length of the lens used is

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  10. Q.30 (iv)1 mark
    The distance of an object from first focal point of a biconvex lens is X1\mathrm{X_1} and distance of the image from second focal point is X2\mathrm{X_2}. The focal length of the lens is

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Section E

5 marks each

  1. Q.31 (a)5 marks
    (i) Two point charges 5 μ\muC and −1-1 μ\muC are placed at points (−3 cm,0,0)(-3\ \text{cm}, 0, 0) and (3 cm,0,0)(3\ \text{cm}, 0, 0) respectively. An external electric field E⃗=Ar2r^\vec{E} = \frac{A}{r^2}\hat{r} where A=3×105A = 3 \times 10^5 Vm is switched on in the region. Calculate the change in electrostatic energy of the system due to the electric field. (ii) A system of two conductors is placed in air and they have net charge of +80μ+80\muC and −80μ-80\muC which causes a potential difference of 16 V between them. (1) Find the capacitance of the system. (2) If the air between the capacitor is replaced by a dielectric medium of dielectric constant 3, what will be the potential difference between the two conductors ? (3) If the charges on two conductors are changed to +160+160 μ\muC and −160-160 μ\muC, will the capacitance of the system change ? Give reason for your answer.
  2. OR

    Q.31 (b)5 marks
    (i) Consider three metal spherical shells A, B and C, each of radius R. Each shell is having a concentric metal ball of radius R/10. The spherical shells A, B and C are given charges +6q+6q, −4q-4q, and 14q14q respectively. Their inner metal balls are also given charges −2q-2q, +8q+8q and −10q-10q respectively. Compare the magnitude of the electric fields due to shells A, B and C at a distance 3R from their centres. (ii) A charge −6-6 μ\muC is placed at the centre B of a semicircle of radius 5 cm, as shown in the figure. An equal and opposite charge is placed at point D at a distance of 10 cm from B. A charge +5+5 μ\muC is moved from point 'C' to point 'A' along the circumference. Calculate the work done on the charge.
  3. Q.32 (a)5 marks
    (i) A proton moving with velocity V⃗\vec{V} in a non-uniform magnetic field traces a path as shown in the figure. The path followed by the proton is always in the plane of the paper. What is the direction of the magnetic field in the region near points P, Q and R ? What can you say about relative magnitude of magnetic fields at these points ? (ii) A current carrying circular loop of area A produces a magnetic field B at its centre. Show that the magnetic moment of the loop is 2BAμ0Aπ\frac{2\mathrm{BA}}{\mu_0}\sqrt{\frac{\mathrm{A}}{\pi}}.
  4. OR

    Q.32 (b)5 marks
    (i) Derive an expression for the torque acting on a rectangular current loop suspended in a uniform magnetic field. (ii) A charged particle is moving in a circular path with velocity V⃗\vec{V} in a uniform magnetic field B⃗\vec{B}. It is made to pass through a sheet of lead and as a consequence, it looses one half of its kinetic energy without change in its direction. How will (1) the radius of its path (2) its time period of revolution change ?
  5. Q.33 (a)5 marks
    (i) (1) What are coherent sources ? Why are they necessary for observing a sustained interference pattern ? (2) Lights from two independent sources are not coherent. Explain. (ii) Two slits 0.1 mm apart are arranged 1.20 m from a screen. Light of wavelength 600 nm from a distant source is incident on the slits. (1) How far apart will adjacent bright interference fringes be on the screen ? (2) Find the angular width (in degree) of the first bright fringe.
  6. OR

    Q.33 (b)5 marks
    (i) Define a wavefront. An incident plane wave falls on a convex lens and gets refracted through it. Draw a diagram to show the incident and refracted wavefront. (ii) A beam of light coming from a distant source is refracted by a spherical glass ball (refractive index 1.5) of radius 15 cm. Draw the ray diagram and obtain the position of the final image formed.