CBSE Class 12 PCM Physics Board Paper 2026 — Set 3

A charged particle +q in an electric field 𝐄⃗ experiences a force in the direction of the electric field. As a result, its kinetic energy changes. Similarly, the charged particle also experiences a force when it moves in a magnetic field 𝐁⃗ . But this magnetic force is perpendicular to both velocity 𝐯⃗ of the charged particle and the magnetic field 𝐁⃗, so it cannot change the kinetic energy of the charged particle. Consider two charged particles 1 and 2 of masses m and m/2 having charges −q and +2q respectively. They are accelerated from rest through the same potential difference V and acquire kinetic energies K₁ and K₂. Then they enter in a region of uniform magnetic field 𝐁⃗ perpendicular to their velocities.

A particle of mass m and charge q starts from rest and moves in an electric field 𝐄⃗ = E₀ î. After travelling a distance x in the field along x-axis, the kinetic energy of the particle will be:

A square loop of side 50 cm is placed in a uniform magnetic field of 3.0 T acting perpendicular to the plane of the loop. If the loop is rotated through an angle of 90° in 0.3 s, the value of emf induced in the loop would be:

A thin plano-convex lens and a thin equi-concave lens are kept coaxially in contact as shown in the figure. Assuming both the lenses are made of glass of refractive index μ, and R is the radius of curvature of each curved surface, the focal length of the combination is:

A telescope has an objective lens of focal length 144 cm and an eyepiece of focal length 6.0 cm. The magnifying power and the length of telescope tube will be respectively:

Radiation of wavelength 200 nm is incident on a photosensitive surface of work function 4.2 eV. The kinetic energy of fastest photoelectrons emitted from this surface will be close to:

A proton and an alpha particle have equal momentum. The ratio of their kinetic energies (Eₚ/Eₐ) and de Broglie wavelengths associated with them (λₚ/λₐ) respectively are:

If r₁ and r₂ are the radii of atomic nuclei of mass number 64 and 27 respectively, then the value of (r₁/r₂) is:

When the forward bias voltage in a semiconductor diode is changed from 0.8 V to 1.0 V, the forward current changes by 2.0 mA. The forward bias resistance of the diode will be:

Assertion (A): In a Wheatstone bridge circuit, if we interchange the position of the cell and the galvanometer, the balance condition P/Q = R/S remains unchanged. Reason (R): P/Q = R/S ⇒ Q/S = P/R, so balance condition remains same.

Assertion (A): The cylindrical soft iron core in a moving coil galvanometer only makes the magnetic field radial and does not affect the strength of the magnetic field. Reason (R): In a moving coil galvanometer, the plane of the coil is always perpendicular to the magnetic field.

Assertion (A): Photoelectric current depends upon the intensity of the incident radiation. Reason (R): Stopping potential is independent of the intensity of the incident radiation.

Assertion (A): Nuclear forces are always attractive. Reason (R): The nuclear force between protons and neutrons in a nucleus is a weak force.

In the given figure, a steady current I flows through the circuit when points A and C are connected by a wire of negligible resistance. Find the potential difference between points B and C.

A battery of emf 21 V and internal resistance 3Ω is connected to a resistor. If the current in the circuit is 3 A, find :

(i) the resistance of the resistor.

(ii) the terminal voltage of the battery.

Explain why diffraction of sound is more common in daily experience than that of light.

Explain the terms mass defect and binding energy. How are they related ?

A particle of mass M at rest splits up into two particles of masses m₁ and m₂ having non-zero velocities. Calculate the ratio of the de Broglie wavelengths associated with the two particles.

How are charge carriers created in an intrinsic semiconductor? Explain.

(a) Establish the relation between drift velocity of electrons (v_d) and electric current (I) in a conductor.
(b) How is v_d affected when the length of the conductor is doubled, keeping the voltage applied across the conductor constant?

A circular coil of 30 turns and radius 8.0 cm carrying a current of 6 A is suspended vertically in a uniform horizontal magnetic field of 1.0 T. The field lines make an angle of 30° with the plane of the coil. Calculate the magnitude of the external torque that must be applied to prevent the coil from turning. What would happen if the circular coil is replaced by a planar coil of irregular shape that encloses the same area, keeping other parameters unchanged?

An alpha particle (mass 6.4 × 10⁻²⁷ kg and charge 3.2 × 10⁻¹⁹ C) having 8.0 MeV energy, enters a region of uniform magnetic field of 0.5 T. If the field is directed perpendicular to the velocity of the particle, find the radius of the circular path described by the particle. Mention the conditions under which the particle in this region (i) describes a helical path, and (ii) goes straight undeviated.

(a) Discuss the behaviour of an inductor connected to (i) a dc source, and (ii) a high frequency ac source.

(b) What is the phase relation between current and voltage in an ideal inductor connected to an ac source ? Draw a phasor diagram for the circuit.

(a) Depict the variation of electric field (𝐄⃗ ) and magnetic field (𝐁⃗) with respect to the direction of propagation of an electromagnetic wave. Write their two important characteristics.
(b) Show that 1/√(ε₀μ₀) gives the velocity of an electromagnetic wave in free space.

A ray of light is travelling through a rectangular glass slab (refractive index 3/2) and is incident on the horizontal glass-air surface at the critical angle for the two media. The slab is then brought in contact with water (refractive index 4/3) such that a thin horizontal layer of water is formed on the surface of the slab. Find the angle at which the ray will emerge into air from the water-air surface.

Differentiate between nuclear fission and nuclear fusion. Give one example for each with nuclear reaction.

With the help of circuit diagrams, briefly explain the forward biasing and the reverse biasing of a p-n junction diode.

(i) In the figure, OA and OB show the variation of electric potential V at a point due to two point charges Q₁ and Q₂ with 1/r respectively. Here r represents the distance of the point from the two point charges.
(a) Identify the nature of the two charges Q₁ and Q₂.
(b) What is the value of (Q₁/Q₂)? Justify your answer.
(ii) Two point charges –2 μC and 5 μC are placed at (–30 cm, 0) and (30 cm, 0) respectively and an external electric field 𝐄⃗= (A/x²) î, where A = 9 × 10⁵ N m² C⁻¹.
Find the electrostatic potential energy of this configuration.

(i) Two infinitely long straight wires having linear charge densities –λ and 3λ are held vertically parallel to each other, distance r apart in free space. Find the nature and magnitude of the force/length exerted by one wire on the other.

(ii) A small hollow conducting sphere of radius r₁ is given a charge Q. It is surrounded by a concentric conducting spherical shell of inner radius r₂ and outer radius r₃, having charge –3q.
If a point charge 2q were kept at the centre, find:
(I) the electric flux through a concentric spherical Gaussian surface of radius x for (1) x < r₁, and (2) r₁ < x < r₂.
(II) electric field at a point distant x from the centre for (1) x > r₃, and (2) r₁ < x < r₂.
(III) surface charge density on the inner surface of (1) sphere, and (2) shell.

(i) A light bulb and an open coil inductor are connected in series across a source of variable frequency. How will the glow of the bulb be affected when:
(I) an iron bar is inserted inside the coil, and
(II) the frequency of the source is decreased?
Justify your answers. Assume that in each above case other changes remain unchanged.
(ii) An ac voltage V = 280 sin (100πt) volt is connected across a series LCR circuit in which R = 400 Ω, L = 5/π H, and C = 50/(π) μF. Taking √2 = 1.4, calculate:
(I) impedance of the circuit.
(II) rms value of current that flows in the circuit.
(III) power factor of the circuit.

(i) State Lenz’s law and explain that it follows the law of conservation of energy.
(ii) Write the dimensional formula for self-inductance.
The current in a coil changes from 8.0 A to 2.0 A in 0.6 s. If an average emf induced in the coil is 50 V, calculate the self-inductance of the coil.

(i) A point object is kept in front of a convex spherical surface of curvature radius R. Draw the ray diagram to show the formation of image and derive the relation between object and image distance (u and v) in terms of refractive index n of the medium and R.
(ii) A convex lens of focal length of 20 cm is used to form the image of an object placed 30 cm away from the lens. Find the position and nature of the image formed.

(i) Two thin converging lenses of focal length f₁ and f₂ are placed coaxially in contact. Derive expression for the focal length of the combination.
(ii) A beam of coherent light of wavelength 550 nm is incident normal to the plane of a pair of two slits S₁ and S₂, each of width 1.2 × 10⁻⁶ m separated by 1.1 mm. Dark and bright fringes are observed on a screen 2.2 m away from the plane of the slits.
Calculate:
(I) fringe width.
(II) distance of the second dark fringe from the central maximum.
(III) what will happen when the entire apparatus is immersed in water.