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CBSE Class 12 Physics 2025 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

  1. Q.11 mark
    A body acquires charge 8⋅0×10−128{\cdot}0 \times 10^{-12} C. The mass of the body :

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  2. Q.21 mark
    A current flows through a cylindrical conductor of radius R. The current density at a point in the conductor is j=αrj = \alpha r (along its axis), here α\alpha is a constant and r is distance from the axis of the conductor. The current flowing through the portion of the conductor from r=0r = 0 to r=R2r = \dfrac{R}{2} is proportional to :

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  3. Q.31 mark
    A particle having charge +q enters a uniform magnetic field B⃗\vec{B} as shown in the figure. The particle will describe :

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  4. Q.41 mark
    A bar magnet is initially at right angles to a uniform magnetic field. The magnet is rotated till the torque acting on it becomes one-half of its initial value. The angle through which the bar magnet is rotated is :

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  5. Q.51 mark
    Which one out of the following materials is not paramagnetic ?

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  6. Q.61 mark
    An ammeter connected in series in an ac circuit reads 10 A. The maximum value of current at any instant in the circuit is :

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  7. Q.71 mark
    The amplitude of electric field in an electromagnetic wave in free space is 1000 Vm−1\mathrm{Vm^{-1}}. The amplitude of the magnetic field in this electromagnetic wave is :

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  8. Q.81 mark
    The magnification produced by a spherical mirror is −2⋅0-2{\cdot}0. The mirror used and the nature of the image formed will be

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  9. Q.91 mark
    Choose the correct statement :

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  10. Q.101 mark
    A beam of red light and a beam of blue light have equal intensities. Which of the following statements is true ?

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  11. Q.111 mark
    Which of the following is an electrical conductor at room temperature ?

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  12. Q.121 mark
    A long straight wire is held vertically and carries a steady current in upward direction. The shape of magnetic field lines produced by the current-carrying wire are :

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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) : n-type semiconductor is not negatively charged. Reason (R) : Neutral pentavalent impurity atom doped in intrinsic semiconductor (neutral) donates its fifth unpaired electron to the crystal lattice and becomes a positive donor.

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  14. Q.141 mark
    Assertion (A) : A series LCR circuit behaves as a pure resistive circuit at resonance. Reason (R) : At resonance, XL=XCX_L = X_C gives ω=1LC\omega = \dfrac{1}{\sqrt{LC}}.

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  15. Q.151 mark
    Assertion (A) : In double slit experiment if one slit is closed, diffraction pattern due to the other slit will appear on the screen. Reason (R) : For interference, at least two waves are required.

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  16. Q.161 mark
    Assertion (A) : For monochromatic incident radiation, the emitted photoelectrons from a given metal have speed ranging from zero to a certain maximum value. Reason (R) : Each metal has a definite work function.

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Section B

2 marks each

  1. Q.17 (a)2 marks
    In the given figure, three identical bulbs P, Q and S are connected to a battery. (i) Compare the brightness of bulbs P and Q with that of bulb S when key K is closed. (ii) Compare the brightness of the bulbs S and Q when the key K is opened. Justify your answer in both cases.
  2. OR

    Q.17 (b)2 marks
    Two cells of emf 10 V each, two resistors of 20 Ω\Omega and 10 Ω\Omega and a bulb B of 10 Ω\Omega resistance are connected together as shown in the figure. Find the current that flows through the bulb.
  3. Q.182 marks
    Find the angle of diffraction (in degrees) for first secondary maximum of the pattern due to diffraction at a single slit. The width of the slit and wavelength of light used are 0⋅550{\cdot}55 mm and 550 nm, respectively.
  4. Q.192 marks
    An equiconvex lens is made of glass of refractive index 1⋅551{\cdot}55. If the focal length of the lens is 15⋅015{\cdot}0 cm, calculate the radius of curvature of its surfaces.
  5. Q.202 marks
    Calculate the mass of an α\alpha-particle in atomic mass unit (u). Given, Mass of a normal helium atom = 4⋅0026034{\cdot}002603 u Mass of carbon atom = 1⋅9926×10−261{\cdot}9926 \times 10^{-26} kg
  6. Q.212 marks
    In an intrinsic semiconductor, carrier's concentration is 5×108 m−35 \times 10^{8}\ \mathrm{m^{-3}}. On doping with impurity atoms, the hole concentration becomes 8×1012 m−38 \times 10^{12}\ \mathrm{m^{-3}}. (a) Identify (i) the type of dopant and (ii) the extrinsic semiconductor so formed. (b) Calculate the electron concentration in the extrinsic semiconductor.

Section C

3 marks each

  1. Q.22 (a)3 marks
    (i) Derive an expression for the resistivity of a conductor in terms of number density of free electrons and relaxation time. (ii) The figure shows the plot of current through a cross-section of wire over two different time intervals. Compare the charges (Q1Q_1 and Q2Q_2) that pass through the cross-section during these time intervals.
  2. OR

    Q.22 (b)3 marks
    (i) A battery of emf E and internal resistance r is connected to a variable external resistance R. (I) Obtain the expression for current I in the circuit and the value of maximum current the battery can supply. (II) Obtain the terminal voltage V across the battery and its maximum possible value. (ii) The above battery sends a current I1I_1 when R=R1R = R_1 and a current I2I_2 when R=R2R = R_2. Obtain the internal resistance of the battery in terms of I1I_1, I2I_2, R1R_1 and R2R_2.
  3. Q.233 marks
    (a) Write vector form of Biot-Savart law. (b) Two insulated long straight wires, each carrying 2⋅02{\cdot}0 A current are kept along xx′xx' and yy′yy' axis as shown in the figure. Find the magnitude and direction of resultant magnetic field at point P (4m, 5m).
  4. Q.243 marks
    Two coils '1' and '2' are placed close to each other as shown in the figure. Find the direction of induced current in coil '1' in each of the following situations, justifying your answers : (a) Coil '2' is moving towards coil '1'. (b) Coil '2' is moving away from coil '1'. (c) The resistance connected with coil '2' is increased keeping both the coils stationary.
  5. Q.253 marks
    (a) State any three characteristics of electromagnetic waves. (b) Briefly explain how and where the displacement current exists during the charging of a capacitor.
  6. Q.263 marks
    A double slit set-up was initially placed in a tank filled with water and the interference pattern was obtained using a laser light. When water is replaced by a transparent liquid of refractive index n>nwatern > n_{\text{water}}, what will be the effect on the following ? (a) Speed, frequency and wavelength of the light of laser beam. (b) The fringe width, shape of interference fringes and shift in the position of central maximum.
  7. Q.273 marks
    Explain the following observations using Einstein's photoelectric equation : (a) Photoelectric emission does not occur from a surface when the frequency of the light incident on it is less than a certain minimum value. (b) It is the frequency, and not the intensity of the incident light which affects the maximum kinetic energy of the photoelectrons. (c) The cut-off voltage (V0V_0) versus frequency (ν\nu) of the incident light curve is a straight line with a slope he\dfrac{h}{e}.
  8. Q.283 marks
    (a) What are majority and minority charge carriers of p-type and n-type semiconductors ? (b) Explain briefly the formation of diffusion current and drift current in a p-n junction diode.

Section D

1 mark each

  1. A parallel plate capacitor consists of two conducting plates kept generally parallel to each other at a distance. When the capacitor is charged, the charge resides on the inner surfaces of the plates and an electric field is set up between them. Thus, electrostatic energy is stored in the capacitor. The figure shows three large square metallic plates, each of side 'L' held parallel and equidistant from each other. The space between P1P_1 and P2P_2 and P2P_2 and P3P_3 is completely filled with mica sheets of dielectric constant 'K'. The plate P2P_2 is connected to point A and other plates P1P_1 and P3P_3 are connected to point B. Point A is maintained at a positive potential with respect to point B and the potential difference between A and B is V.
    Q.29 (i)1 mark
    The capacitance of the system between A and B will be :

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  2. Q.29 (ii)1 mark
    The charge on plate P1P_1 is :

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  3. Q.29 (iii)1 mark
    The electric field in the region between P1P_1 and P2P_2 is :

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  4. Q.29 (iv) (a)1 mark
    The separation between the plates of same area (L2L^2) of a parallel plate air capacitor having capacitance equal to that of this system, will be :

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  5. OR

    Q.29 (iv) (b)1 mark
    If the source of potential difference applied between A and B is removed, and then A and B are connected by a conducting wire, the net charge on the system will be :

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  6. A hydrogen atom consists of an electron revolving in a circular orbit of radius r with certain velocity v around a proton located at the nucleus of the atom. The electrostatic force of attraction between the revolving electron and the proton provides the requisite centripetal force to keep it in the orbit. According to Bohr's model, an electron can revolve only in certain stable orbits. The angular momentum of the electron in these orbits is some integral multiple of h2π\dfrac{h}{2\pi}, where h is the Planck's constant. Further, when an electron makes a transition from one orbit of higher energy to that of lower energy, a photon is emitted having energy equal to the difference between energies of the initial and final states. Assuming the mass and charge of an electron as m and e respectively, answer the following questions.
    Q.30 (i)1 mark
    The expression for the speed of electron v in terms of radius of the orbit (r) and physical constant (K=14πε0K = \dfrac{1}{4\pi\varepsilon_0}) is :

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  7. Q.30 (ii)1 mark
    The total energy of the atom in terms of r and physical constant K is :

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  8. Q.30 (iii)1 mark
    A photon of wavelength 500 nm is emitted when an electron makes a transition from one state to the other state in an atom. The change in the total energy of the electron and change in its kinetic energy in eV as per Bohr's model, respectively will be :

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  9. Q.30 (iv) (a)1 mark
    In Bohr's model of hydrogen atom, the frequency of revolution of electron in its nthn^{\text{th}} orbit is proportional to :

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  10. OR

    Q.30 (iv) (b)1 mark
    An electron makes a transition from −3⋅4-3{\cdot}4 eV state to the ground state in hydrogen atom. Its radius of orbit changes by : (radius of orbit of electron in ground state = 0⋅530{\cdot}53 Å)

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Section E

5 marks each

  1. Q.31 (a)5 marks
    (i) Two point charges +q and -q are held at (a, 0) and (-a, 0) in x-y plane. Obtain an expression for the net electric field due to the charges at a point (0, y). Hence, find electric field at a far off point (y >> a). (ii) Three point charges of -2 nC, -1 nC, and +5 nC are kept at the vertices A, B and C of an equilateral triangle of side 0⋅20{\cdot}2 m. Find the total amount of work done in shifting the charges from A to A1A_1, B to B1B_1 and C to C1C_1. Here A1A_1, B1B_1 and C1C_1 are the midpoints of sides AB, BC and CA, respectively.
  2. OR

    Q.31 (b)5 marks
    (i) Show that Gauss's theorem is consistent with Coulomb's law. Using it, derive an expression for the electric field due to a uniformly charged thin spherical shell of radius r at a point at a distance y from the centre of the shell such that (I) y>ry > r, and (II) y<ry < r. (ii) A point charge of +2+2 nC is kept at the origin of a three-dimensional coordinate system. Find the type and magnitude of the charge which should be kept at (0, 0, -6m) so that the potential due to the system becomes zero at (0, 0, 2m).
  3. Q.32 (a)5 marks
    (i) State Lenz's law and explain how this law is a consequence of conservation of energy principle. (ii) A square shaped loop of side l2\dfrac{l}{2} is initially lying outside a region of uniform magnetic field B⃗\vec{B} as shown in the figure. The loop is moved towards right with a constant velocity v⃗\vec{v} till it goes out of the region of magnetic field. (I) What will be the directions of induced current when the loop enters the field and when it leaves the field ? (II) Draw the plots showing the variation of magnetic flux ϕ\phi linked with the loop with time t and variation of induced emf E with time t. Mark the relevant values of E, ϕ\phi and t on the graphs.
  4. OR

    Q.32 (b)5 marks
    (i) Differentiate between peak and rms values of alternating current. How are they related ? (ii) A current element X is connected across an ac source of emf V=V0sin⁡2πνtV = V_0 \sin 2\pi\nu t. It is found that the voltage leads the current in phase by π2\dfrac{\pi}{2} radian. If element X was replaced by element Y, the voltage lags behind the current in phase by π2\dfrac{\pi}{2} radian. (I) Identify elements X and Y by drawing phasor diagrams. (II) Obtain the condition of resonance when both elements X and Y are connected in series to the source and obtain expression for resonant frequency. What is the impedance value in this case ?
  5. Q.33 (a)5 marks
    (i) An object is placed 30 cm from a thin convex lens of focal length 10 cm. The lens forms a sharp image on a screen. If a thin concave lens is placed in contact with the convex lens, the sharp image on the screen is formed when the screen is moved by 45 cm from its initial position. Calculate the focal length of the concave lens. (ii) Calculate the angle of minimum deviation of an equilateral prism. The refractive index of the prism is 3\sqrt{3}. Calculate the angle of incidence for this case of minimum deviation also.
  6. OR

    Q.33 (b)5 marks
    (i) A physics teacher wants to demonstrate interference with the help of double slit experiment using a laser beam of 633 nm wavelength. Since the hall is large enough, interference pattern is formed on the wall 5⋅05{\cdot}0 m from the slits. For clear and comfortable view by all the students they want the fringe width 5 mm. (I) Find the slit separation for obtaining the desired interference pattern. (II) How far will the first minimum be from the central maximum ? (ii) A parallel beam of light of wavelength 650 nm passes through a slit of width 0⋅60{\cdot}6 mm. The diffraction pattern is obtained on a screen kept 60 cm away from the slit. Find the distance between first order minima on both sides of the central maximum.