QUESTION PAPER
2026 BOARD EXAM
CBSE Class 12 PCM Physics Board Paper 2026 — Set 2
2026
Physics
Class 12 PCM
CBSE EXAMINATION PAPER-2026
PHYSICS
(Solved)
General Instructions :
Read the following instructions carefully and follow them :
- This question paper contains 38 questions. All questions are compulsory.
- This question paper is divided into 5 sections.
- Section A – questions number 1 to 2 are case based questions
- Section B – questions number 3 to 18 are multiple choice questions
- Section C – questions number 19 to 24 are very short answer
- Section D – questions number 25 to 32 are short answer
- Section E – questions number 33 to 38 are long answer
- There is no overall choice given in the question paper. However, an internal choice has been provided in few questions.
- Use of calculator is NOT allowed.
Section A
(1) Silicon is doped with which of the following to obtain p-type semiconductor? (A) Phosphorus (B) Arsenic (C) Boron (D) Antimony
(2) A semiconductor has an electron concentration of 5 × 10²² m⁻³. The concentration of holes is (given nᵢ = 1.5 × 10¹⁶ m⁻³) (A) 5 × 10²² m⁻³ (B) 1.5 × 10⁶ m⁻³ (C) 9 × 10⁸ m⁻³ (D) 4.5 × 10⁹ m⁻³
(3) During forward biasing of a p-n junction diode, the (A) current is mainly due to drifting of majority carriers (B) current is mainly due to drifting of minority carriers (C) diffusion and drift currents are equal (D) current is of the order of 1 A
(4) The threshold voltage for silicon diode is about (A) 0.2 V (B) 0.5 V (C) 0.7 V (D) 1.5 V
(5) When we dope Ge with a pentavalent element, four of its electrons bond with four germanium neighbours but fifth electron remains weakly bound. The ionisation energy for this electron is about (A) 0.01 eV (B) 0.05 eV (C) 0.1 eV (D) 0.15 eV
(1) The value of d is (A) √D(D − 4f) (B) √D(D − 2f) (C) 2√(Df) (D) √D(D − f)
(2) Compared to the size of the object, the images formed in the two positions are respectively (A) reduced, enlarged (B) reduced, reduced (C) enlarged, enlarged (D) enlarged, reduced
(3) If the distance between object and screen is 80.00 cm and the lens forms sharp images at two positions separated by 20.00 cm, the focal length of convex lens is (A) 15.50 cm (B) 18.75 cm (C) 20.50 cm (D) 22.75 cm
(4) Consider a convex lens of focal length 15 cm. For which of the following values of object-screen distance, two positions of the lens can be found to obtain sharp image on the screen? (A) 45 cm (B) 50 cm (C) 55 cm (D) 65 cm
(5) A thin convex lens of focal length 10 cm and another thin lens of focal length ‘f’ are placed coaxially in contact. If the power of their combination is 10/ 3 D, the value of ‘f’ is (A)–15 cm (B) –10 cm (C) –20 cm (D) –30 cm
Section B
Three point charges 2q, –2q and q are kept at the vertices of an equilateral triangle of side l. The potential energy of the system is
Two metal spheres of radii r₁ and r₂ (r₁ > r₂) having charges q₁ and q₂ respectively kept in air, are brought in contact. Which of the following statements is not correct?
The maximum kinetic energy of the electrons emitted from a photosensitive surface depends on
In Bohr model of hydrogen, for large values of n, the distance between consecutive orbits is proportional to
A straight long wire lying along y-axis, carries a current of 1 A along –y direction. The magnetic field due to the conductor at a point (50 cm, 0, 0) will point along.
Which of the following materials has positive and small value of magnetic susceptibility?
A galvanometer of resistance 27 Ω is converted into an ammeter of range (0 – 10 mA) using a resistance of 3 Ω. The galvanometer will show full scale deflection for a current of about-
The magnetic flux ϕ (in Wb) linked with a coil is related to time t (in s) as ϕ = 5 At² + Bt – 2C The SI units of A and B are respectively
The figure shows the variation of capacitive reactance (X꜀) of two ideal capacitors of capacitances C₁ & C₂ with the reciprocal of angular frequency (1/ω) of ac source. The value of C₁/C₂ is
An electromagnetic wave is propagating along x-axis. At any instant, the phase difference (in radian) between the electric field (𝐄⃗) and the magnetic field (𝐁⃗) associated with the wave is
In Bohr model of hydrogen atom, the electron makes a transition from n = 5 to n = 1 state. As a result, a photon of wavelength λ is emitted in the process. The wavelength of the photon emitted when an electron makes a transition from energy level n = 5 to n = 2 will be
Assertion (A): On increasing the intensity of incident light of frequency (ν > ν₀) on a photosensitive surface, the photocurrent increases. Reason (R): The stopping potential for a photosensitive surface increases with increase of frequency (ν > ν₀) of incident light.
Assertion (A): On forward biasing a p-n junction diode, the height of the barrier potential increases. Reason (R): In forward biasing of a p-n junction diode, the direction of the applied voltage is in the same direction as the built-in potential.
Assertion (A): Two electric heaters of power P₁ and P₂ (P₁ > P₂) are joined in series across a dc source of voltage V. The power consumed by the combination will be less than that consumed by P₁ when connected across the same source. Reason (R): The power consumed by an electric device when connected to a dc source of voltage V is proportional to its resistance.
Section C
Write two points of difference between intrinsic and extrinsic semiconductors.
Find ratio (λₐ/λₚ) of the de Broglie wavelength λₐ and λₚ associated respectively with an alpha particle and a proton,
(i) if they are moving with the same kinetic energy.
(ii) just after they are accelerated through the same potential difference.
A ray of light in air is incident at angle ∠i on a face of an equilateral glass prism and is refracted through the prism. As ∠i is varied, it is observed that the ray undergoes minimum deviation, when the ∠i is three-fourth of the angle of the prism. Calculate the speed of light in the prism.
A heating element using nichrome is connected to a 220 V supply. Initially it draws a current of 2.9 A. After some time, the current attains a steady value of 2.5 A. Find the steady temperature of the heating element if the room temperature is 27 °C. The temperature coefficient of resistance of nichrome is 1.7 × 10⁻⁴ °C⁻¹.
A 5 cm long pencil is placed along the principal axis of a concave mirror of focal length 20 cm such that its nearest end is at a distance of 25 cm from the mirror. Calculate the length of the image of the pencil.
In a Young's double-slit experiment, a beam of light consisting of two wavelengths 500 nm and 600 nm is used. The interference fringes are observed at a screen placed 1.8 m away from the plane of slits (slit separation 0.3 mm). Calculate the least distance from the central maximum where the bright fringes due to both the wavelengths coincide.
Section D
(a) Consider the following nuclides:
¹²₆C, ¹⁹⁸₈₀Hg, ¹⁴₆C, ¹⁹⁷₇₉Au
Group them into isotopes and isotones.
(b) How does the size of a nucleus depend on its mass number A? Hence prove that the density of nucleus is a constant, independent of A, for all nuclei.
(a) An electric field 𝐄⃗ = E₀ î exists in a region of space. Draw three equipotential surfaces in the region.
(b) Two point charges –q and +q are located at points (–a, 0, 0) and (a, 0, 0) respectively. Find the electrostatic potential at point (x, 0, 0) where x >> a.
Name the electromagnetic waves which are used for
(i) detection of fractures in bones
(ii) physiotherapy
(iii) radar systems
Also write their wavelength range.
(i) Define mutual inductance of a pair of coils. Write its SI unit.
(ii) A long solenoid of radius R and length L has n turns per unit length. A circular loop of radius r(<R) is placed inside at the centre of the solenoid such that its axis coincides with the axis of the solenoid. Obtain the mutual inductance of the solenoid and the loop.
Two long straight parallel conductors A and B carrying steady currents Iₐ and I_b in the same direction are separated by a distance d. Deduce the expression for the force acting on length L of conductor B due to conductor A and show in figure. Write the expression for the force acting on length L of conductor A due to conductor B and show that it follows Newton’s third law.
(a) State Bohr’s second postulate and mention its significance.
(b) Prove that, in Bohr model of hydrogen atom as principal quantum number n becomes large, the energy levels get closer and closer.
(a) Explain the statement - “Current is a scalar although we represent current with an arrow.”
(b) Use Kirchhoff's rules to find the current through 3 Ω resistor in the circuit shown in the figure:
Derive an expression for the magnetic field 𝐁⃗, due to a circular coil of N turns, each of radius r carrying current I, at a distance ‘x’ from the centre along its axis.
Section E
(a) What are coherent sources? Why are they necessary for observing stable interference pattern? Draw a graph showing the variation of intensity of light with the position on the screen in Young’s double-slit experiment.
(b) Find the intensity of light at a point on the screen when two interfering waves of the same intensity (I₀) have a path difference of
(i) λ/4 and (ii) λ/3.
(a) Draw a labelled ray diagram of a refracting telescope when it forms image of a distant object at infinity. Derive expression for its magnifying power.
(b) (i) In a telescope the objective has much larger aperture than the eye piece. Why?
(ii) Write two advantages of reflecting telescope over refracting telescope.
(a) Derive an expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d with air present between the plates.
(b) Two air-filled capacitors of capacitances C₁ and C₂ are connected in parallel with a dc battery. After the capacitors are fully charged, a slab of dielectric constant K is inserted between the plates of each capacitor. How will the (i) charge on each capacitor and (ii) energy stored in the capacitor affected after the slab is introduced.
(a) An electric field 𝐄⃗ is established across the ends of a cylindrical conductor of length L and area of cross-section A. Discuss how electrons attain an average velocity, independent of time. Hence, obtain a relation between current in the conductor and this ‘average velocity’ of electrons.
(b) (i) This ‘average velocity’ is found be few mm/s for currents in range of a few amperes. How then is current established almost the instant a circuit is closed ?
(ii) Two copper wires having their radii in the ratio of 3 : 2 are connected in series across a battery. Find the ratio of the drift velocities of the electrons in the wires.
(a) A series combination of L, C and R is connected to an a.c. source. Using a phasor diagram, derive an expression for the impedance of the circuit and phase difference between V and I.
(b) Under what conditions the
(i) impedance of the circuit is minimum ?
(ii) Wattless current flows in the circuit ?
(i) With the help of a labelled diagram, explain the principle, construction and working of an a.c. generator.
(ii) Deduce an expression for the induced emf in the coil of the generator.
(iii) If T is the time period of the rotation of the coil, at what values of T in a cycle, the emf generator is maximum ?
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