CBSE Class 12 PCM Physics Board Paper 2026 — Set 4

Two wires of same length and same area of cross-section but made of different material of resistivities ρ₁ and ρ₂ are connected in series. The equivalent resistivity of the combination is:

Two particles of masses m₁ and m₂ having charges q₁ and q₂ respectively are projected with the same velocity in a region of uniform magnetic field 𝐁⃗ pointing vertically upward. If they describe circular paths as shown in the figure, one may conclude that:

An electron moves around the nucleus in a circular orbit of radius r and makes n revolutions per second. The value of equivalent current in the orbit is:

The dimensions of the rate of change of magnetic flux are:

Two identical conductors 1 and 2 are placed on two frictionless conducting rails R and S in a uniform magnetic field directed vertically downward into the plane of the page. If conductor 1 is moved with a constant velocity in the direction as shown in figure, the force on conductor 2 will be along:

An ac voltage is given as V = 14 sin (314t) V. The average and the effective value of the voltage (in V) over a cycle are respectively:

The ratio of amplitude of electric field to the amplitude of the magnetic field associated with an electromagnetic wave propagating in glass (n = 1.5) is:

While studying photoelectric emission from a given surface, the wavelength of the incident radiation is changed from 600 nm to 400 nm, keeping the intensity of radiation the same. Then:

Radiation of wavelength 331 nm irradiates the following metals: Which of the following statements is correct?

The kinetic energy of a charged particle is increased to four times of its initial value. The de Broglie wavelength associated with the particle will:

In a reversed-biased p-n junction diode, the applied voltage mostly drops across:

Assertion (A): When a ferromagnetic substance is heated to high temperature it becomes paramagnetic in nature. Reason (R): The disappearance of magnetisation of a ferromagnet is abrupt and not gradual.

Assertion (A): When a convex lens made of glass is immersed in water, its converging power increases. Reason (R): The focal length of a lens depends only on the radii of curvature of its two faces.

An electric dipole consists of two point charges +1 μC and –1 μC, held 10 cm apart. It is subjected to a uniform electric field of 100 N/C. Calculate the amount of work done in turning the dipole from its position of stable equilibrium to the position of unstable equilibrium, in the field.

State Huygens principle. How did Huygens justify the absence of the backward wave on a spherical wavefront?

In a single-slit diffraction experiment, light of wavelength λ illuminates the slit of width ‘a’. The diffraction pattern is observed on a screen kept at distance D from the slits.
(i) Depict variation in intensity in the fringe pattern with the angular position of the fringes.
(ii) How is the linear width of central maximum affected when separation between the slit and the screen is decreased?

A small bulb is placed at the bottom of a tank, containing a transparent liquid of refractive index √2, to a depth of 1 m. Calculate the area of the surface of the liquid through which light from the bulb emerges.

Draw the graph showing the variation of number of scattered alpha particles (N) detected with scattering angle (θ) in Geiger–Marsden experiment. Infer two conclusions from the graph.

The hole concentration in an intrinsic semiconductor is 5 × 10⁸ m⁻³. When it is doped with certain impurity, the electron concentration becomes 4 × 10¹² m⁻³. Find the new value of the hole concentration. Also identify the type of new semiconductor formed after doping.

State Kirchhoff’s rules. Using these rules, find the current flowing through branch FC in the given circuit.

The figure given below shows three straight long parallel conductors ①, ② and ③ kept in x-y plane, carrying currents 2I, I and 3I respectively as shown in figure.
Find the magnitude and direction of:
(i) net magnetic field at a point on conductor ① and
(ii) net magnetic force acting on unit length of conductor ①, due to conductors ② and ③.

A rectangular loop of sides l and b and resistance ‘R’ is kept in a region in which the magnetic field varies as B = B₀ sin ωt.
(i) Derive the expression for the emf induced in the loop.
(ii) Find the effective value of current that flows in the loop.

The figure given below shows a square-shaped loop MNOP of side 25 cm placed horizontally in a uniform magnetic field B(vector) directed vertically downward. The position of the loop at t = 0 s is as shown in figure. The loop is pulled with a constant velocity of 25 cm/s till it goes out of the field.
(a) What will be the direction of the induced current in the loop as it goes out of the field? For how long would the current in the loop persist?
(b) Plot graphs showing the variation of magnetic flux and magnitude of induced emf as a function of time.

What are infrared waves ? Why are these waves referred to as ‘heat waves’ ? Give any two uses of these waves.

(a) Explain how the dual aspect of matter is evident in the de Broglie relation.
(b) Radiation of wavelength λ is incident on a photosensitive surface. Find the de Broglie wavelength of electrons emitted from the surface. Assume that the work function of the surface is negligible.

In the nuclear reaction:
²₁H + ²₁H → ᴬ₂X + ¹₀n
(a) Find the value of A.
(b) Calculate the amount of energy released in the reaction.
Given: m(²₁H) = 2.014102 u, m(ᴬ₂X) = 3.016049 u,
m(¹₀n) = 1.008665 u, 1 u = 931.5 MeV/c²

With the help of a circuit diagram, explain the working of a full wave rectifier. Depict the input and output waveforms.

(i) Define refractive index of a medium in terms of speed of light.
(ii) Derive the relation for the refractive index (μ) of a prism in terms of angle of minimum deviation (δₘ) and angle of prism (A).
(iii) A ray of light QP is incident normally on the face BC of a triangular prism ABC of refractive index 1.5 kept in air, as shown in the figure. Trace the path of the ray as it passes through the prism and give relevant explanation.

(i) What is the difference between a ray and a wavefront ?

(ii) A plane wave is incident on a reflecting surface. Using Huygens principle, show how it is reflected from the surface. Hence, verify the law of reflection.

(iii) Depict refraction of a plane wave by a convex lens.

(i) Define the terms (I) resonant frequency, and (II) power factor of a series LCR circuit. For what value of the power factor will the power dissipated in the circuit be maximum?
(ii) An inductor of 5/π H, a capacitor of 50/π μF and a resistor of 400 Ω are connected in series across an ac voltage v = 140 sin (100πt) V. Calculate:
(I) impedance of the circuit, and
(II) rms value of current that flows in the circuit.
(Take √2 = 1.4)

(i) Draw a labelled diagram of a step-up transformer. Obtain the ratio of secondary voltage to primary voltage in terms of number of turns in the two coils.
(ii) The number of turns in the primary and the secondary coil of an ideal transformer are 100 and 5000 respectively. If 3.3 kW power is supplied to the transformer at 220 V, find
(I) current in the primary coil, and (II) output voltage.

(i) Explain the following statements giving reason:
(a) An equipotential surface through a point is normal to the electric field at that point.
(b) When a dielectric is placed in an external electric field, the electric field inside the dielectric is less than that outside it.
(c) The potential difference between the plates of a charged parallel plate capacitor decreases when its plates are brought closer.
(ii) Obtain an expression for the work done to dissociate the system of three charges q, –4q and 2q placed at the vertices A, B and C respectively of an equilateral triangle of side ‘a’.

(i) Answer the following giving reason:
(I) The electron drift speed is estimated to be only a few mm/s for currents in the range of a few amperes. How, then, is the current established almost the instant a circuit is closed?
(II) A low voltage supply from which one needs high currents must have very low internal resistance. Why?
(III) The assertion that V = IR is a statement of Ohm’s law is not true. Why?

(ii) Two cells of emfs 12 V and 6 V are connected in parallel as shown in the figure. Their internal resistances are 1 Ω and 0.5 Ω respectively. Calculate the emf and internal resistance of the equivalent cell between points A and B.