CBSE Class 12 2025 Physics 55-4-3 Question Paper Set-3: Download Solutions with Answer Key

Two point charges Q and \( -q \) are held \( r \) distance apart in free space. A uniform electric field \( \vec{E} \) is applied in the region perpendicular to the line joining the two charges. Which one of the following angles will the direction of the net force acting on charge \( -q \) make with the line joining Q and \( -q \)?

• (A) \( \tan^{-1} \left( \frac{4\pi \epsilon_0 E r^2}{Q} \right) \)
• (B) \( \cot^{-1} \left( \frac{4\pi \epsilon_0 E r^2}{Q} \right) \)
• (C) \( \tan^{-1} \left( \frac{QE}{4\pi \epsilon_0 r^2} \right) \)
• (D) \( \cot^{-1} \left( \frac{QE}{4\pi \epsilon_0 r^2} \right) \)

Three wires A, B, and C of the same material have lengths and area of cross-sections as \( (2l, \frac{A}{2}) \), \( (l, A) \) and \( (\frac{l}{2}, 2A) \), respectively. If the resistances of these wires are \( R_A, R_B, R_C \) respectively, then:

• (A) \( R_A > R_B > R_C \)
• (B) \( R_B > R_C > R_A \)
• (C) \( R_C > R_A > R_B \)
• (D) \( R_A > R_C > R_B \)

A particle of mass \( m \) and charge \( q \) moves along the y-axis in a region in which a uniform magnetic field \( \vec{B} \) is pointing along the x-axis. The Lorentz force acting on the charge will point along:

• (A) x-axis
• (B) y-axis
• (C) z-axis
• (D) negative z-axis

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:

• (A) 30°
• (B) 45°
• (C) 60°
• (D) 75°

Which of the following substances has magnetic permeability less than that of free space?

• (A) Sodium
• (B) Iron
• (C) Aluminium
• (D) Copper

The magnetic flux linked with a closed coil (in Wb) varies with time \( t \) (in s) as \( \phi = 5t^2 + 4t - 2 \). If the resistance of the circuit is 14 \( \Omega \), the magnitude of induced current in the coil at \( t = 1 \) s will be:

• (A) 0.5 A
• (B) 1.0 A
• (C) 1.5 A
• (D) 2.0 A

In an electromagnetic wave travelling in free space, the amplitude of magnetic field is \( 6.0 \times 10^{-4} \ T \). The amplitude of its electric field is:

• (A) \( 2 \times 10^4 \ Vm^{-1} \)
• (B) \( 1.5 \times 10^{12} \ Vm^{-1} \)
• (C) \( 1.8 \times 10^5 \ Vm^{-1} \)
• (D) \( 0.3 \times 10^4 \ Vm^{-1} \)

In an electromagnetic wave travelling in free space, the amplitude of magnetic field is \( 6.0 \times 10^{-4} \ T \). The amplitude of its electric field is:

• (A) \( 2 \times 10^4 \ Vm^{-1} \)
• (B) \( 1.5 \times 10^{12} \ Vm^{-1} \)
• (C) \( 1.8 \times 10^5 \ Vm^{-1} \)
• (D) \( 0.3 \times 10^4 \ Vm^{-1} \)

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:

• (A) horizontal straight lines directed radially out from the wire.
• (B) straight lines parallel to the current-carrying wire.
• (C) concentric horizontal circles around the wire.
• (D) coaxial helices around the wire.

The magnification produced by a spherical mirror is -2.0. The mirror used and the nature of the image formed will be:

• (A) Convex and virtual
• (B) Concave and real
• (C) Concave and virtual
• (D) Convex and real

Choose the correct statement:

• (A) Photons of light show diffraction whereas electrons do not show diffraction.
• (B) Electrons have momentum whereas photons do not have momentum.
• (C) Photons of light and electrons both exhibit dual nature.
• (D) All electromagnetic radiations do not have photons.

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

• (A) The blue beam has more number of photons than the red beam.
• (B) The red beam has more number of photons than the blue beam.
• (C) Wavelength of red light is lesser than wavelength of blue light.
• (D) The blue light beam has lesser energy per photon than that in the red light beam.

Which of the following is an electrical conductor at room temperature?

• (A) Sn
• (B) Mica
• (C) Si
• (D) C

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.


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.

• (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• (C) Assertion (A) is true, but Reason (R) is false.
• (D) Both Assertion (A) and Reason (R) are false.

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.


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.

• (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• (C) Assertion (A) is true, but Reason (R) is false.
• (D) Both Assertion (A) and Reason (R) are false.

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.


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.

• (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• (C) Assertion (A) is true, but Reason (R) is false.
• (D) Both Assertion (A) and Reason (R) are false.

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.


Assertion (A): A series LCR circuit behaves as a pure resistive circuit at resonance.

Reason (R): At resonance, \( X_L = X_C \) gives \( \omega = \frac{1}{\sqrt{LC}} \).

• (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• (C) Assertion (A) is true, but Reason (R) is false.
• (D) Both Assertion (A) and Reason (R) are false.

In an intrinsic semiconductor, carrier’s concentration is \( 5 \times 10^8 \ m^{-3} \). On doping with impurity atoms, the hole concentration becomes \( 8 \times 10^{12} \ m^{-3} \).

(a) Identify (i) the type of dopant and (ii) the extrinsic semiconductor so formed.

(b) Calculate the electron concentration in the extrinsic semiconductor.

In Young's double slit experiment, the screen is moved 30 cm towards the slits. As a consequence, the fringe width of the pattern changes by 0.09 mm. If the slits separation used is 2 mm, calculate the wavelength of light used in the experiment.

The two surfaces of a biconvex lens are of radius of curvature \( R \) each. Obtain the condition under which its focal length \( f \) is equal to \( R \). If one of the two surfaces of this lens is made plane, what will be the new focal length of the lens?

In Bohr’s model of hydrogen atom, find the percentage change in the radius of its orbit when an electron makes a transition from \( n = 3 \) state to \( n = 2 \) state.

(a) 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.

(b) Two cells of emf 10 V each, two resistors of 20 \( \Omega \) and 10 \( \Omega \), and a bulb B of 10 \( \Omega \) resistance are connected together as shown in the figure. Find the current that flows through the bulb.

What are majority and minority charge carriers of p-type and n-type semiconductors?

Explain briefly the formation of diffusion current and drift current in a p-n junction diode.

In which cases does a charged particle not experience a force in a magnetic field?

A square loop MNPK of side \( l \) carrying a current \( I_2 \) is kept close to a long straight wire in the same plane and the wire carries a steady current \( I_1 \) as shown in the figure. Obtain the magnitude of magnetic force exerted by the wire on the loop.

The figure shows the plot of magnitude of induced emf (\( \varepsilon \)) versus the rate of change of current in two coils ‘1’ and ‘2’. Which coil has a greater value of self-inductance and why?

Photoelectric emission does not occur from a surface when the frequency of the light incident on it is less than a certain minimum value. Explain this observation using Einstein’s photoelectric equation.

It is the frequency, and not the intensity of the incident light which affects the maximum kinetic energy of the photoelectrons. Explain this observation using Einstein’s photoelectric equation.

The cut-off voltage \( V_0 \) versus frequency \( \nu \) of the incident light curve is a straight line with a slope of \( \frac{h}{e} \). Explain this observation.

Write the conditions under which two light waves originating from two coherent sources can interfere each other (i) constructively, and (ii) destructively, in terms of wavelength. Can these be applied for two lights originating from two sodium lamps? Give reason.

Monochromatic light of green color is used in Young’s double slit experiment and an interference pattern is observed on a screen. If the green light is replaced by red monochromatic light of the same intensity, how will the fringe width of the interference pattern be affected? Justify your answer.

Derive an expression for the resistivity of a conductor in terms of number density of free electrons and relaxation time.

The figure shows the plot of current through a cross-section of wire over two different time intervals. Compare the charges \( Q_1 \) and \( Q_2 \) that pass through the cross-section during these time intervals.

The above battery sends a current \( I_1 \) when \( R = R_1 \) and a current \( I_2 \) when \( R = R_2 \). Obtain the internal resistance of the battery in terms of \( I_1 \), \( I_2 \), \( R_1 \), and \( R_2 \).

State any three characteristics of electromagnetic waves.

Briefly explain how and where the displacement current exists during the charging of a capacitor.

The expression for the speed of electron \( v \) in terms of radius of the orbit (\( r \)) and physical constant \[ K = \frac{1}{4 \pi \varepsilon_0} \] is:

• (A) \( \frac{Ke^2}{mr} \)
• (B) \( \frac{Ke^2}{mr^2} \)
• (C) \( \sqrt{\frac{Ke^2}{mr}} \)
• (D) \( \sqrt{\frac{Ke^2}{mr^2}} \)

The total energy of the atom in terms of \( r \) and physical constant \( K \) is:

• (A) \( \frac{Ke^2}{r} \)
• (B) \( -\frac{Ke^2}{2r} \)
• (C) \( \frac{Ke^2}{2r} \)
• (D) \( \frac{3}{2} \cdot \frac{Ke^2}{r} \)

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:

• (A) \( 2.48, -2.48 \)
• (B) \( -1.24, 1.24 \)
• (C) \( -2.48, 2.48 \)
• (D) \( 1.24, -1.24 \)

In Bohr’s model of hydrogen atom, the frequency of revolution of electron in its \( n^th \) orbit is proportional to:

• (A) \( n \)
• (B) \( \frac{1}{n} \)
• (C) \( \frac{1}{n^2} \)
• (D) \( \frac{1}{n^3} \)

An electron makes a transition from \(-3.4\ eV\) state to the ground state in hydrogen atom. Its radius of orbit changes by: (radius of orbit of electron in ground state = \(0.53\ \AA\))

• (A) \(0.53\ \AA\)
• (B) \(1.06\ \AA\)
• (C) \(1.59\ \AA\)
• (D) \(2.12\ \AA\)

The capacitance of the system between A and B will be:

• (A) \( \frac{\varepsilon_0 K L^2}{d} \)
• (B) \( \frac{\varepsilon_0 K L^2}{2d} \)
• (C) \( \frac{2\varepsilon_0 K L^2}{d} \)
• (D) \( \frac{2\varepsilon_0 K d}{L^2} \)

The charge on plate \( P_1 \) is:

• (A) \( \frac{\varepsilon_0 V K L^2}{2d} \)
• (B) \( \frac{\varepsilon_0 V K L^2}{d} \)
• (C) \( \frac{2\varepsilon_0 V K L^2}{d} \)
• (D) \( \frac{\varepsilon_0 V K L^2}{4d} \)

The electric field in the region between \( P_1 \) and \( P_2 \) is:

• (A) \( \frac{V}{d} \)
• (B) \( \frac{2V}{d} \)
• (C) \( \frac{V}{2d} \)
• (D) \( \frac{d}{V} \)

The separation between the plates of same area (\( L^2 \)) of a parallel plate air capacitor having capacitance equal to that of this system, will be:

• (A) \( \frac{d}{K} \)
• (B) \( \frac{2d}{K} \)
• (C) \( \frac{d}{2K} \)
• (D) \( \frac{d}{4K} \)

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:

• (A) \( \frac{\varepsilon_0 VKL^2}{4d} \)
• (B) \( \frac{\varepsilon_0 VKL^2}{2d} \)
• (C) \( \frac{\varepsilon_0 VKL^2}{d} \)
• (D) Zero