Class 12 Physics · 3 hours · 70 marks

CBSE Class 12 Physics Sample Paper 2

Set in the pattern of CBSE's 2026-27 sample question papers. Write it in 3 hours, then check with the marking scheme and solutions.

There are 33 questions in all. All questions are compulsory.
Section A has 16 questions of 1 mark each: 12 multiple-choice and 4 assertion-reason. Section B has 5 questions of 2 marks, Section C 7 questions of 3 marks, Section D 2 case study-based questions of 4 marks and Section E 3 long answer questions of 5 marks.
There is no overall choice. Internal choice is given in two questions in Section B, one in Section C and all three in Section E; attempt only one of the alternatives.
Calculators are not allowed. Use the values of physical constants given in a question wherever they are needed.
For the assertion-reason questions, choose: (a) Both A and R are true, and R is the correct explanation of A. (b) Both A and R are true, but R is not the correct explanation of A. (c) A is true, but R is false. (d) A is false, but R is true.

Section A (16 × 1 mark)

Question 1 · 1 mark

A beam of light passes from glass into air. The quantity that does not change is its

(a) frequency(b) wavelength(c) speed(d) direction of travel, for oblique incidence

Question 2 · 1 mark

With ε₀ the permittivity and μ₀ the permeability of free space, and c the speed of light in vacuum, the product ε₀μ₀ equals

(a) 1/c(b) c²(c) 1/c²(d) c

Question 3 · 1 mark

To plot the reverse-bias characteristic of a silicon diode, the current should be measured with

(a) a milliammeter, since the reverse current is large(b) a microammeter, since the reverse current is of the order of microamperes(c) an ammeter reading in amperes, since breakdown may occur(d) a voltmeter in series with the diode

Question 4 · 1 mark

A solid has an electrical conductivity of 2.0 × 10⁻³ S m⁻¹ at room temperature. On the indicative ranges of resistivity, the solid is

(a) a metal, since its resistivity is 2.0 × 10⁻³ Ω m(b) a semiconductor, since its resistivity is 500 Ω m(c) an insulator, since its resistivity is 500 Ω m(d) a metal, since its resistivity is 500 Ω m

Question 5 · 1 mark

The binding energy of the 42He nucleus is 28.3 MeV. Its mass defect is (take 1 u = 931.5 MeV/c²)

(a) 0.304 u(b) 0.0304 u(c) 0.0152 u(d) 0.0076 u

Question 6 · 1 mark

The SI unit of magnetisation M is

(a) T m A⁻¹(b) A m²(c) T(d) A m⁻¹

Question 7 · 1 mark

Equal point charges +Q are fixed at two vertices of an equilateral triangle of side a in vacuum. The magnitude of the electric field at the third vertex is (k = 1/4πε₀)

(a) 2kQ/a²(b) √3 kQ/a²(c) kQ/a²(d) zero

Question 8 · 1 mark

The SI unit of resistivity is

(a) S m⁻¹(b) Ω m⁻¹(c) Ω m⁻²(d) Ω m

Question 9 · 1 mark

In a spark plug, electrons are pulled out of a metal electrode by an electric field of the order of 10⁸ V m⁻¹. This process is called

(a) thermionic emission(b) photoelectric emission(c) secondary emission(d) field emission

Question 10 · 1 mark

An ac voltage is applied across an ideal inductor. The current in the inductor

(a) lags the voltage by π/2(b) leads the voltage by π/2(c) is in phase with the voltage(d) lags the voltage by π

Question 11 · 1 mark

Infrared waves are often called heat waves because they

(a) ionise the molecules they strike(b) travel faster than visible light in vacuum(c) are produced only by the sun(d) set entire atoms and molecules vibrating, raising the internal energy of matter

Question 12 · 1 mark

An object on the axis of a concave mirror of focal length 10 cm is moved from 30 cm to 20 cm in front of the mirror. During this move the image shifts through

(a) 5 cm, towards the mirror(b) 10 cm, away from the mirror(c) 10 cm, towards the mirror(d) 5 cm, away from the mirror

Question 13 · 1 mark

Assertion (A): The binding energy per nucleon is nearly constant for nuclei with 30 < A < 170. Reason (R): The nuclear force between two nucleons does not depend on their electric charge.

(a) Both A and R are true, and R is the correct explanation of A.(b) Both A and R are true, but R is not the correct explanation of A.(c) A is true, but R is false.(d) A is false, but R is true.

Question 14 · 1 mark

Assertion (A): While a storage cell is being charged, the voltmeter across its terminals reads more than its emf. Reason (R): During charging, the current flows through the cell from its positive terminal to its negative terminal, so V = ε + Ir.

(a) Both A and R are true, and R is the correct explanation of A.(b) Both A and R are true, but R is not the correct explanation of A.(c) A is true, but R is false.(d) A is false, but R is true.

Question 15 · 1 mark

Assertion (A): A convex lens of glass of refractive index 1.5 behaves as a diverging lens when immersed in a liquid of refractive index 1.7. Reason (R): For a lens of index n₂ in a medium of index n₁, 1/f = (n₂/n₁ − 1)(1/R₁ − 1/R₂), and the factor (n₂/n₁ − 1) is negative when n₂ < n₁.

(a) Both A and R are true, and R is the correct explanation of A.(b) Both A and R are true, but R is not the correct explanation of A.(c) A is true, but R is false.(d) A is false, but R is true.

Question 16 · 1 mark

Assertion (A): The average power supplied by an ac source to an ideal inductor over a complete cycle is zero. Reason (R): In an ideal inductor the current lags the voltage by π/2, so the instantaneous power p = −(i_m v_m/2) sin 2ωt is positive for half the time and negative for the other half.

(a) Both A and R are true, and R is the correct explanation of A.(b) Both A and R are true, but R is not the correct explanation of A.(c) A is true, but R is false.(d) A is false, but R is true.

Section B (5 × 2 marks)

Question 17 · 2 marks

On the wave picture of light, how long would one expect an electron to take to escape from a metal under very dim light? How does this compare with what is observed?

Or On the wave picture of light, how should the maximum kinetic energy of photoelectrons change when the intensity of light is increased? How does this compare with what is observed?

Question 18 · 2 marks

Two coherent sources each produce an intensity I₀ at a point on a screen. Find the resultant intensity at points where the phase difference between the two waves is (i) π/2, (ii) 5π/3.

Or In a double-slit experiment, light of wavelength 600 nm falls on slits 0.30 mm apart and the screen is 1.5 m away. Each slit alone gives an intensity I₀ on the screen. Find the resultant intensity at points (i) 0.50 mm, (ii) 4.5 mm from the central bright fringe.

Question 19 · 2 marks

A proton and an alpha particle (charge 2e, mass four times the proton's) enter the same uniform magnetic field with the same speed, perpendicular to the field. Find the ratio of the radius of the alpha particle's path to that of the proton's.

Question 20 · 2 marks

A plastic comb run through dry hair attracts small bits of neutral paper. Explain why.

Question 21 · 2 marks

In a half-wave rectifier, why must the diode's reverse breakdown voltage be sufficiently higher than the peak of the ac voltage from the transformer?

Section C (7 × 3 marks)

Question 22 · 3 marks

An iron nail is made of many magnetic domains, yet on its own it attracts nothing. (a) Explain why it shows no net magnetisation. (b) Explain how it becomes strongly magnetised when a magnet is brought near. (c) Why does it stay magnetised for only a short time after the magnet is removed, while a lodestone stays magnetised?

Or Describe the state of the domains in a ferromagnetic sample (a) with no external field, (b) in a strong external field B₀, and (c) after the field is removed, for a hard and for a soft ferromagnet.

Question 23 · 3 marks

A coil of metal X (temperature coefficient of resistivity 5.0 × 10⁻³ °C⁻¹, referred to 20 °C) and a manganin coil Y each have a resistance of 10.0 Ω at 20 °C. Treat the resistance of Y as constant and ignore changes in dimensions. (a) At what temperature is the resistance of X 1.5 times that of Y? (b) What is the resistance of X and Y in parallel at that temperature?

Question 24 · 3 marks

An aluminium ring rests on the top of a vertical coil wound on a soft-iron core. When the switch in the coil's circuit is closed, the ring jumps up. (a) Explain why. (b) Why does it fall back while the switch is kept closed? (c) What would happen if the ring had a narrow cut in it?

Question 25 · 3 marks

Two germanium samples, X and Y, are doped with indium and kept at the same temperature: X at 1 atom in 10⁷ and Y at 1 atom in 10⁶. Taking every acceptor as ionised and nₕ ≈ Nₐ, (a) by what factor is the ratio nₕ/nₑ in Y larger than in X? (b) Find the ratio of the electron concentration in Y to that in X. (c) Explain why heavier doping lowers the minority concentration.

Question 26 · 3 marks

A parallel plate capacitor has plates of area A a distance d apart (d² much smaller than A), carrying charges +Q and −Q. Using the field of a large plane sheet of charge, find the field inside and outside the plates and show that C = ε₀A/d.

Question 27 · 3 marks

A capacitor with circular plates of radius R is being charged by a current i, the electric field between the plates being uniform. Using the Ampere–Maxwell law, obtain the magnetic field at a distance r (r ≤ R) from the axis, between the plates. How does it vary from the axis to the rim?

Question 28 · 3 marks

An α-particle (charge 2e) of kinetic energy K is aimed head-on at a nucleus of charge Ze. (a) Show that its distance of closest approach is d = 2Ze²/(4πε₀K), stating the assumption made about the nucleus. (b) The radius of a gold nucleus (Z = 79) is about 6 fm. Neglecting the size of the α-particle, find the least kinetic energy, in MeV, with which an α-particle must approach head-on to just reach the surface of the gold nucleus. (1/4πε₀ = 9 × 10⁹ N m² C⁻², e = 1.6 × 10⁻¹⁹ C, 1 MeV = 1.6 × 10⁻¹³ J)

Section D (2 × 4 marks)

Question 29 · 4 marks

Ananya, a student in Kochi, plots the binding energy per nucleon E_bn of stable nuclei against mass number A from a table of data. Her graph is shown, with a few points marked and their E_bn values in MeV in brackets. P and Q are nuclei of mass numbers 90 and 180. She wants to compare the energy available from fusing very light nuclei with that from splitting heavy ones, reading the values from her graph.

(a) The curve is nearly flat between A = 30 and A = 170 because the nuclear force [1]

(a) is much stronger than the gravitational force(b) is short-ranged, so an interior nucleon is bound only by its near neighbours(c) does not depend on electric charge(d) becomes repulsive below 0.8 fm

(b) Using the marked values, the energy released per nucleon of fuel when two ²H nuclei fuse into ⁴He is about how many times that released per nucleon when nucleus Q splits into two nuclei like P? [1]

(a) 1.0(b) 0.19(c) 8.6(d) 12

Question 30 · 4 marks

A doctor in a Chennai hospital examines a patient's stomach with an endoscope, a bundle of thin optical fibres. Each fibre has a glass core of refractive index 1.60 inside a cladding of refractive index 1.50 (see figure). Light sent into one end meets the core–cladding boundary again and again, and travels along the fibre even where the bundle bends. In good silica fibres more than 95% of the light comes through a kilometre of fibre, which is why such fibres also carry telephone and video signals between cities.

(a) The critical angle at the core–cladding boundary is about [1]

(a) 38.7°(b) 41.8°(c) 69.6°(d) 20.4°

(b) If the cladding were replaced by glass of refractive index 1.60, the same as the core, light would [1]

(a) pass into the cladding, since total internal reflection at the boundary could not occur(b) still be totally reflected, since the core is glass(c) be totally reflected only where the fibre bends(d) travel faster in the core than in the cladding

(c) In the figure a ray meets the boundary at 75°. Is it totally reflected? What happens to a ray that meets the boundary at 60°? [2]

Section E (3 × 5 marks)

Question 31 · 5 marks

(a) What is a polaroid? Describe an experiment with two polaroids which shows that light is a transverse wave. (b) Unpolarised light of intensity 64 W m⁻² passes through three polaroids P₁, P₂, P₃ in turn. The pass-axis of P₂ is at 30° to that of P₁, and the pass-axis of P₃ is at a further 30° beyond P₂, that is at 60° to P₁. Find the intensity emerging from P₃. Then find the intensity when P₂ is removed, and comment on the result.

Or (a) Light polarised by a polaroid P₁ falls on a polaroid P₂ whose pass-axis makes an angle θ with that of P₁. Show that the intensity transmitted by P₂ is I = I₀ cos²θ, where I₀ is the intensity between them, and state between what limits two polaroids can control the intensity of unpolarised light. (b) Unpolarised light of intensity 48 W m⁻² falls on P₁. (i) Find θ for which the light emerging from P₂ is one-eighth of the incident intensity. (ii) With P₂ at this angle, a third polaroid P₃ is placed after P₂ with its pass-axis parallel to that of P₁. Find the intensity emerging from P₃. (iii) Would the light from P₂ change if P₃ were placed instead between P₁ and P₂, still parallel to P₁? Give a reason.

Question 32 · 5 marks

Point charges +2 μC, +3 μC and −8 μC are placed in vacuum at the vertices A, B and C of a right-angled triangle, with the right angle at A, AB = 0.30 m and AC = 0.40 m (see figure). (a) Find the force on the +2 μC charge due to each of the other two. (b) Find the magnitude and direction of the net force on it. (c) Find the electric field at A due to the charges at B and C. (Take 1/4πε₀ = 9 × 10⁹ N m² C⁻².)

Or Charges +2 μC are placed at three corners A, B and D of a square ABCD of side 0.30 m, and −1 μC at the fourth corner C (see figure). (a) Find the force on the −1 μC charge due to each of the other three. (b) Find the magnitude and direction of the net force on it. (c) Find the electric field at C due to the three +2 μC charges. (Take 1/4πε₀ = 9 × 10⁹ N m² C⁻².)

Question 33 · 5 marks

(a) A series LCR circuit is connected to an ac source v = v_m sin ωt. Draw its phasor diagram for X_L > X_C, and use it to obtain the impedance of the circuit and the phase angle between the current and the source voltage. (b) A circuit with R = 50 Ω, X_L = 150 Ω and X_C = 30 Ω is connected to a 130 V (rms) supply. Find the rms current and the power factor.

Or (a) In a series LCR circuit the source voltage is v = v_m sin ωt and the current is i = i_m sin(ωt + φ). Show that the average power over a cycle is P = VI cos φ, V and I being rms values. (b) A circuit with R = 50 Ω, X_L = 40 Ω and X_C = 160 Ω is connected to a 260 V (rms) supply. Find the average power and state whether the current leads or lags.