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Class 12 Physics: questions from CBSE board papers, by chapter

Every question of the 4 CBSE board exam papers Shishya has solved (2026 Q.P. 55/1/1, 2025 Q.P. 55/1/1, 2024 Q.P. 55/1/1, 2023 Q.P. 55/1/1), listed under the NCERT chapter it was asked from. The question lines are in Shishya's own shorter words; each links to its step-by-step solution, and the paper page links CBSE's own question paper. Marks per chapter count every listed question, including both sides of an either/or choice.

Electric Charges and Fields

9 questions, 27 marks across 4 papers

Asked in CBSE 2026 · 55/1/1 · Q22 · 3 marks(a) Use Gauss's law to get the field of a uniformly charged infinite thin sheet. (b) Two large parallel sheets, each with charge density σ, are close together in air: field (i) between and (ii) outside them?
Asked in CBSE 2026 · 55/1/1 · Q24 · 3 marksElectrons enter midway between two horizontal plates 2 cm apart at 3 × 10⁷ m/s. Plates are 3 cm long. What plate voltage makes the beam just hit the far end of the lower plate?
Asked in CBSE 2026 · 55/1/1 · Q31 · 5 marks(a) Charges q and −q are 2a apart. Derive the field at distance r on the equatorial plane, and its form for r ≫ a. (b) q sits at x = a and −q at x = b; field E = 2î N/C. Find the force and torque on the dipole.
Asked in CBSE 2025 · 55/1/1 · Q1 · 1 markA graph of force F against 1/r² for charge pairs (q1, q2) and (q2, q3) is given. q2 is positive and has the smallest magnitude. Order the magnitudes of q1, q2, q3.
Asked in CBSE 2024 · 55/1/1 · Q1 · 1 markA thin plastic ring of radius R carries a uniform linear charge density λ. Find the electric field magnitude at its centre.
Asked in CBSE 2024 · 55/1/1 · Q22 · 3 marksA cube of edge 0.1 m sits in a field E = 500x î N/C (x in m), placed as in the figure. Find (a) the net flux through the cube and (b) the charge inside it.
Asked in CBSE 2023 · 55/1/1 · Q1 · 1 markA point charge on the axis of a short dipole, at distance r, feels force F. What is the force when it is moved to 2r?
Asked in CBSE 2023 · 55/1/1 · Q31(a) · 5 marks(i) State Coulomb's law and give its vector form for two charges. (ii) Explain why Gauss's law relies on the 1/r² dependence in Coulomb's law. (iii) Charge q at A(0, 0) and charge 2q at B(a, a): find the force of A on B in terms of î and ĵ.
Asked in CBSE 2023 · 55/1/1 · Q31(b) · 5 marks(i) For a dipole of +q and −q, 2a apart, derive E at an equatorial point. (ii) For a far point on this plane, what happens to the field if its distance is halved? (iii) Charges +q at A, −q at B, −q at C, +q at D sit at the corners of a square ABCD (side √2 m), making two identical dipoles on its diagonals. Find the size and direction of the net field at the centre O.

Electrostatic Potential and Capacitance

14 questions, 34 marks across 4 papers

Asked in CBSE 2026 · 55/1/1 · Q1 · 1 markPotential in a region is V = 10 − 50x (V in volts, x in metres). Find the electric field.
Asked in CBSE 2026 · 55/1/1 · Q2 · 1 markTwo far-apart charged metal spheres A and B (radii r1, r2) are joined by a conducting wire. Find E_A/E_B at their surfaces.
Asked in CBSE 2026 · 55/1/1 · Q23 · 3 marksA capacitor C with a dielectric slab is charged to V, then the battery is removed and the slab pulled out. Effect on (a) capacitance, (b) stored energy, (c) voltage? Justify.
Asked in CBSE 2025 · 55/1/1 · Q29(i) · 1 markRC circuit with R = 20 kΩ, C = 500 μF, battery V = 10 V. Closing S1 (S2 open) charges C. What is its final charge?
Asked in CBSE 2025 · 55/1/1 · Q29(ii) · 1 markIn the same RC circuit, after C is fully charged, S2 is closed and S1 opened. What is the final charge on C?
Asked in CBSE 2025 · 55/1/1 · Q29(iii) · 1 markGive the dimensional formula of the product RC.
Asked in CBSE 2025 · 55/1/1 · Q29(iv)(A) · 1 markWith S1 closed and S2 open (R = 20 kΩ, C = 500 μF, V = 10 V), find the current in R 5 s after closing.
Asked in CBSE 2025 · 55/1/1 · Q29(iv)(B) · 1 markWith S1 closed and S2 open (R = 20 kΩ, V = 10 V), find the charging current in R just after closing.
Asked in CBSE 2025 · 55/1/1 · Q31(a) · 5 marks(i) Charges 5 μC at (−3 cm, 0, 0) and −1 μC at (3 cm, 0, 0) are placed in an external field E = (A/r²) r̂ with A = 3 × 10⁵ V m. Find the change in the system's electrostatic energy due to this field. (ii) Two conductors in air carry +80 μC and −80 μC with 16 V between them. (1) Capacitance? (2) New voltage if a dielectric of K = 3 fills the space? (3) Does the capacitance change if the charges become ±160 μC? Why?
Asked in CBSE 2025 · 55/1/1 · Q31(b) · 5 marks(i) Shells A, B, C (radius R) each hold a concentric metal ball of radius R/10. Shell charges are +6q, −4q, 14q and ball charges −2q, +8q, −10q. Compare the field magnitudes due to A, B, C at 3R from their centres. (ii) −6 μC sits at the centre B of a semicircle of radius 5 cm and +6 μC at D, 10 cm from B on the diameter line beyond C. Find the work done in taking +5 μC from C to A along the arc.
Asked in CBSE 2024 · 55/1/1 · Q2 · 1 markTen 1 μF capacitors are joined in parallel across a 100 V supply. Find the total stored energy.
Asked in CBSE 2024 · 55/1/1 · Q31(a) · 5 marks(i) Derive the potential energy of a dipole p in a uniform field E; when is it maximum and minimum? (ii) Charges −1.0 pC at (0, 0) and +1.0 pC at (3 mm, 4 mm) in the x-y plane form a dipole in a field E = (1000 V/m) î. Find the torque on it.
Asked in CBSE 2024 · 55/1/1 · Q31(b) · 5 marks(i) A dipole p = p î (charges −q and q, 2a apart) lies on the x-axis centred at the origin. Show that at a point x with x >> a, V = (1/4πε₀)(p·î)/x². (ii) Isolated metal spheres S₁ and S₂ of radii 1 cm and 3 cm both have surface charge density (2/π) × 10⁻⁹ C/m². They are far apart and joined by a thin wire. Find the new charge on S₁.
Asked in CBSE 2023 · 55/1/1 · Q26 · 3 marks(a) Twelve equal negative charges (each −q) sit equally spaced on a circle of radius R. Taking V = 0 at infinity, find V and E at the centre C. (b) The same charges are instead bunched unevenly along a 120° arc (radius R); find V at C.

Current Electricity

20 questions, 40 marks across 4 papers

Asked in CBSE 2026 · 55/1/1 · Q11 · 1 markHeaters rated (P1, V) and (P2, V) are joined in series across a dc supply of V/2. Total power drawn?
Asked in CBSE 2026 · 55/1/1 · Q20 · 2 marksGive the typical order of the electron drift speed in a conductor and derive how current depends on it.
Asked in CBSE 2026 · 55/1/1 · Q22-OR · 3 marks(a) Derive the balance condition of a Wheatstone bridge. (b) Find the resistance between A and B of the network in the figure.
Asked in CBSE 2026 · 55/1/1 · Q31-OR · 5 marks(a) Cells (E1, r1) and (E2, r2) are joined in parallel, like terminals together. Derive the equivalent emf and internal resistance. (b) Such a pair with emfs E and 3E, each of internal resistance R, feeds a 2R resistor. Current in 2R?
Asked in CBSE 2025 · 55/1/1 · Q2 · 1 markWires P and Q are of the same material. Q has double the diameter and half the length of P. If P has resistance R, find Q's resistance.
Asked in CBSE 2025 · 55/1/1 · Q17 · 2 marksA cell (emf E, internal resistance r) feeds a rheostat. The rheostat voltage is 5 V at 2 A and 4 V at 4 A. Find E and r.
Asked in CBSE 2025 · 55/1/1 · Q22(a) · 3 marksCells of 3 V (0.2 Ω) and 6 V (0.4 Ω) are joined in parallel and connected to a 4 Ω resistor. Find (i) the equivalent emf, (ii) the equivalent internal resistance, (iii) the current drawn.
Asked in CBSE 2025 · 55/1/1 · Q22(b) · 3 marks(i) A wire of length l across an ideal cell (emf E) is slowly stretched to 2l with the cell still connected. Relate the final resistance R' to R and the final drift speed v_d' to v_d. (ii) If electrons drift from lower to higher potential, are all free electrons moving the same way?
Asked in CBSE 2024 · 55/1/1 · Q3 · 1 markBetween points A and B, a 12 V cell with 1 Ω and a 6 V cell with 0.5 Ω are connected in parallel (same polarity). Find the potential difference between A and B.
Asked in CBSE 2024 · 55/1/1 · Q17 · 2 marksSilver has α = 4.0 × 10⁻³ K⁻¹ at the reference temperature 20°C. At what temperature does a silver wire's resistance become double its value at 20°C?
Asked in CBSE 2024 · 55/1/1 · Q21 · 2 marksSketch the current-voltage curve of GaAs and mark (a) the negative-resistance region and (b) the region obeying Ohm's law.
Asked in CBSE 2024 · 55/1/1 · Q23(a) · 3 marksDefine current density and say whether it is scalar or vector. For a metal in a field E, with electron density n, electron mass m, charge −e and relaxation time τ, show that j = αE with α = ne²τ/m.
Asked in CBSE 2024 · 55/1/1 · Q23(b) · 3 marksWhat is a Wheatstone bridge? Derive the condition for it to be balanced.
Asked in CBSE 2023 · 55/1/1 · Q2 · 1 markWhich R–T graph correctly shows how the resistance of a metallic conductor changes with temperature?
Asked in CBSE 2023 · 55/1/1 · Q3 · 1 markA cell reads 8 V on open circuit and 4 V while delivering 4 A. Find its internal resistance.
Asked in CBSE 2023 · 55/1/1 · Q4 · 1 markA steady current flows in a metal wire whose cross-section area A grows steadily along its length. Which graph shows the drift speed v_d against A?
Asked in CBSE 2023 · 55/1/1 · Q34(a) · 1 markIn the circuit described, which points have equal potential?
Asked in CBSE 2023 · 55/1/1 · Q34(b) · 1 markIn the same circuit (6.0 V cell with 1.0 Ω; 10 Ω in branch bg; 5.0 Ω + 5.0 Ω in branch cf), find the current in arm bg.
Asked in CBSE 2023 · 55/1/1 · Q34(c) · 2 marksIn the same circuit, find the voltage across R₃ = 5.0 Ω.
Asked in CBSE 2023 · 55/1/1 · Q34(c)-OR · 2 marksIn the same circuit, find the power dissipated in R₂ = 5.0 Ω.

Moving Charges and Magnetism

20 questions, 42 marks across 4 papers

Asked in CBSE 2026 · 55/1/1 · Q3 · 1 markA long wire of radius a carries current I spread uniformly over its cross-section. Find the magnetic field magnitude at distance a/2 from its axis.
Asked in CBSE 2026 · 55/1/1 · Q19 · 2 marksA wire of length L is wound into an N-turn square coil, and again into an N-turn circular coil; same current, same uniform field. Ratio of maximum torques (square : circle)?
Asked in CBSE 2026 · 55/1/1 · Q29(I) · 1 markWhy does the torque on a galvanometer coil stay the same at every orientation?
Asked in CBSE 2026 · 55/1/1 · Q29(II) · 1 markBest practical way to raise a galvanometer's current sensitivity?
Asked in CBSE 2026 · 55/1/1 · Q29(III) · 1 markA 50-turn coil of area 4.0 × 10⁻³ m² in a 0.25 T field carries 5 A. Torque on it?
Asked in CBSE 2026 · 55/1/1 · Q29(III)-OR · 1 markA 15 Ω galvanometer gives full deflection at 3 mA. Series resistance needed to make a 0–12 V voltmeter?
Asked in CBSE 2026 · 55/1/1 · Q29(IV) · 1 markA 20 Ω galvanometer gives full deflection at 5 mA. What shunt makes it a 0–10 A ammeter, and how is it connected?
Asked in CBSE 2025 · 55/1/1 · Q3 · 1 markA 1 cm wire segment on the x-axis carries 0.5 A in the +x direction in a field B = (0.4 mT) ĵ + (0.6 mT) k̂. Find the force on it.
Asked in CBSE 2025 · 55/1/1 · Q14 · 1 markA: Galvanometer deflection is proportional to current. R: Its coil hangs in a uniform radial magnetic field.
Asked in CBSE 2025 · 55/1/1 · Q23 · 3 marksUse the Biot–Savart law to find B on the axis of a current loop, and then at its centre.
Asked in CBSE 2025 · 55/1/1 · Q32(a) · 5 marks(i) A proton moving right reaches P and then follows a curved path through Q up to a crest at R, staying in the paper's plane. Give the field direction near P, Q, R and compare field strengths there. (ii) A circular loop of area A gives field B at its centre. Show its magnetic moment is (2BA/μ₀)√(A/π).
Asked in CBSE 2025 · 55/1/1 · Q32(b) · 5 marks(i) Derive the torque on a rectangular current loop in a uniform magnetic field. (ii) A charged particle circling in a uniform field passes through a lead sheet and loses half its kinetic energy without changing direction. How do (1) its path radius and (2) its period change?
Asked in CBSE 2024 · 55/1/1 · Q4 · 1 markA loop in the x-y plane carries current I clockwise (seen from +z) in a uniform magnetic field along the z-axis. What does the loop tend to do?
Asked in CBSE 2024 · 55/1/1 · Q5 · 1 markA 10 cm wire on the y-axis carries 1.0 A in the +y direction in a field B = (5 mT) ĵ − (8 mT) k̂. Find the force on the wire.
Asked in CBSE 2024 · 55/1/1 · Q6 · 1 markA galvanometer of resistance G Ω is made into a 0 to I A ammeter, with 0.1% of I passing through the galvanometer. Find the ammeter's resistance.
Asked in CBSE 2024 · 55/1/1 · Q15 · 1 markAssertion: Two long, freely hung parallel wires joined in series to a battery move away from each other. Reason: Wires with oppositely directed currents repel.
Asked in CBSE 2024 · 55/1/1 · Q24 · 3 marksA proton of KE 1.3384 × 10⁻¹⁴ J travels horizontally north to south into a uniform 2.0 mT field pointing east. Taking proton mass 1.673 × 10⁻²⁷ kg and q/m = 1.0 × 10⁸ C/kg, find (a) its speed, (b) its acceleration and (c) its path radius.
Asked in CBSE 2023 · 55/1/1 · Q19 · 2 marksAn alpha particle enters a region with velocity (3.0 × 10⁵ m/s) î where B = (0.4 T) î + (0.3 T) ĵ. With q/m = 4.8 × 10⁷ C/kg, find its acceleration.
Asked in CBSE 2023 · 55/1/1 · Q32(a) · 5 marks(i) State the Biot–Savart law and use it to find B at the centre of a circular loop of radius a carrying current I; sketch the field lines of a current loop showing their direction. (ii) An electron circles a nucleus at 10⁷ m/s in an orbit of radius 10⁻¹⁰ m. Find the equivalent current.
Asked in CBSE 2023 · 55/1/1 · Q32(b) · 5 marks(i) Derive the force on a straight current-carrying conductor in a magnetic field, name the rule that gives its direction, and state when the force is greatest and least. (ii) Long parallel wires A and B, 2.5 cm apart in air, have opposite currents, 5.0 A in A and 2.5 A in B. Find the force of A on 10 cm of B.

Magnetism and Matter

3 questions, 3 marks across 2 papers

Asked in CBSE 2026 · 55/1/1 · Q13 · 1 markAssertion: every atom has a net magnetic moment. Reason: a current loop is not always a magnetic dipole.
Asked in CBSE 2023 · 55/1/1 · Q5 · 1 markHow does a diamagnetic sample behave when brought close to either pole of a bar magnet?
Asked in CBSE 2023 · 55/1/1 · Q16 · 1 markA: Field lines crowd into a copper bar kept in an external magnetic field. R: Copper is paramagnetic.

Electromagnetic Induction

9 questions, 17 marks across 4 papers

Asked in CBSE 2026 · 55/1/1 · Q33 · 5 marks(a) State Faraday's law of induction. (b) Derive the self-inductance of a long air-core solenoid (length l, area A, N turns). (c) A 50 cm rod pivoted at one end spins at 60 rpm in a 4.0 mT field normal to its rotation plane. Induced emf?
Asked in CBSE 2025 · 55/1/1 · Q4 · 1 markA 100-turn coil (each turn 0.05 m², total resistance 1.5 Ω) is suddenly put into a 90 mT field with its axis along the field. Find the charge that flows.
Asked in CBSE 2025 · 55/1/1 · Q5 · 1 markAn air-cored solenoid must have L = 0.016 H, length 0.81 m and radius 0.02 m. How many turns does it need?
Asked in CBSE 2025 · 55/1/1 · Q13 · 1 markA: Pushing a magnet into a closed coil with many turns is hard. R: The induced current in the closed coil opposes the magnet's motion that causes it.
Asked in CBSE 2025 · 55/1/1 · Q24 · 3 marks(a) Show that setting up current I in an inductor L needs energy LI²/2. (b) Using an air-cored solenoid, show that magnetic energy density is B²/(2μ₀).
Asked in CBSE 2024 · 55/1/1 · Q14 · 1 markAssertion: Two coils have the greatest mutual inductance when one is wound over the other. Reason: Their flux linkage is greatest in that arrangement.
Asked in CBSE 2023 · 55/1/1 · Q6 · 1 markA 40-turn coil of radius 8.0 cm spins about a vertical diameter at 25/π rad/s in a horizontal uniform field of 3.0 × 10⁻² T. Find the peak induced emf.
Asked in CBSE 2023 · 55/1/1 · Q7 · 1 markArm PQ (resistance r) slides with velocity v on a rectangular frame PSRQ of negligible resistance in a uniform field. The size of the induced emf is independent of which quantity: B, v, r or the length of PQ?
Asked in CBSE 2023 · 55/1/1 · Q28 · 3 marksA long solenoid (radius r, n turns per unit length) carries I = I₀ sin ωt. A coil of N turns is wound closely round its middle. Find (a) the emf induced in the coil and (b) the mutual inductance.

Alternating Current

9 questions, 27 marks across 4 papers

Asked in CBSE 2026 · 55/1/1 · Q6 · 1 markIn a series LCR circuit, the resistor, capacitor and inductor each have 10 V across them. If the capacitor is shorted, what is the inductor voltage?
Asked in CBSE 2026 · 55/1/1 · Q33-OR · 5 marks(a) Draw and label a step-up transformer, give its working principle, and Vs/Vp in terms of turns and currents. (b) Ideal transformer, turns ratio primary : secondary = 1 : 5, input 5 kW at 200 V. Find (i) primary current, (ii) output voltage.
Asked in CBSE 2025 · 55/1/1 · Q6 · 1 markVoltage v = v₀ sin ωt drives current i = i₀ sin(ωt + φ). Find the average power over one cycle.
Asked in CBSE 2024 · 55/1/1 · Q7 · 1 markA capacitor has reactance X at angular frequency ω. Its capacitance is doubled and the frequency tripled. New reactance?
Asked in CBSE 2024 · 55/1/1 · Q25 · 3 marksAn L, a C and an R are in series with v = vm sin ωt. Derive the average power dissipated and the resonant frequency.
Asked in CBSE 2024 · 55/1/1 · Q32(a) · 5 marks(i) Derive the impedance of a series RC circuit on v = vm sin ωt. (ii) When does an inductor behave as a plain conductor, and why? (iii) A lamp rated 110 V dc, 11 A is run from a 220 V, 50 Hz supply with a coil in series. Find the coil's inductance.
Asked in CBSE 2024 · 55/1/1 · Q32(b) · 5 marks(i) Draw a labelled step-up transformer, state its working principle and three causes of energy loss in a real one. (ii) Does stepping up voltage violate energy conservation? Explain. (iii) Primary 200 turns, secondary 3000 turns, input 90 V. Find (1) the secondary voltage and (2) the primary current when the secondary current is 2.0 A.
Asked in CBSE 2023 · 55/1/1 · Q27(a) · 3 marksHow is impedance different from resistance? Using a phasor diagram, find the impedance of a series LCR circuit fed by v = v_m sin ωt.
Asked in CBSE 2023 · 55/1/1 · Q27(b) · 3 marksFor a series LCR circuit on v = v_m sin ωt with variable ω, find the resonance condition, list what the resonant frequency depends on, and sketch current against frequency.

Electromagnetic Waves

8 questions, 13 marks across 4 papers

Asked in CBSE 2026 · 55/1/1 · Q5 · 1 markAn EM wave goes from vacuum into a medium with relative permittivity 3/2 and relative permeability 8/3. What happens to its wavelength and frequency?
Asked in CBSE 2026 · 55/1/1 · Q7 · 1 markWhat wavelength range do EM waves used as a medical diagnostic tool (X-rays) have?
Asked in CBSE 2025 · 55/1/1 · Q7 · 1 markOn a falling curve of photon energy against wavelength, P is at short wavelength (high energy), R in the middle and Q at long wavelength. Which radiations could P, Q, R be?
Asked in CBSE 2025 · 55/1/1 · Q25 · 3 marks(a) A parallel-plate capacitor is charged by an ac source. Show that I_c + I_d is the same everywhere in the circuit. (b) Does Kirchhoff's junction rule hold at each plate? Explain.
Asked in CBSE 2024 · 55/1/1 · Q8 · 1 markElectric fields in four regions: I: Ex = E₀ sin(kz − ωt); II: Ex = E₀; III: Ex = E₀ sin kz; IV: Ex = E₀ cos kz. In which region is there a displacement current?
Asked in CBSE 2024 · 55/1/1 · Q26 · 3 marks(a) Give two examples showing that an EM wave's wavelength matches the size of the system emitting it. (b)(i) Why are short-wave bands chosen for radio broadcasting over long distances? (ii) Why is X-ray astronomy possible only from satellites, while optical and radio telescopes work on the ground?
Asked in CBSE 2023 · 55/1/1 · Q8 · 1 markWhile a capacitor charges, what expression gives the current that exists in the gap between its plates?
Asked in CBSE 2023 · 55/1/1 · Q20 · 2 marksCompare a magnetic field produced by a changing electric field with an electric field produced by a changing magnetic field. Which is easier to observe, and why?

Ray Optics and Optical Instruments

29 questions, 59 marks across 4 papers

Asked in CBSE 2026 · 55/1/1 · Q9 · 1 markA diverging lens of focal length 10 cm is sliced into two equal plano-concave pieces. What is the focal length of each piece?
Asked in CBSE 2026 · 55/1/1 · Q27 · 3 marks(a) Ray diagram of a refracting telescope and its angular magnification in normal adjustment. (b) Two reasons a reflecting telescope is preferred.
Asked in CBSE 2026 · 55/1/1 · Q28 · 3 marks(a) Two conditions for total internal reflection. (b) Liquids A, B, C (indices n, 3n/4, 2n/3) are layered; a laser in A meets the A–B boundary at angle θ. Show it never enters C when sin θ ≥ 2/3.
Asked in CBSE 2026 · 55/1/1 · Q32 · 5 marks(a) Derive the lens maker's formula from refraction at a spherical surface. (b) Lenses L1, L2, L3 (each f = 40 cm) are coaxial; L1–L2 gap 120 cm, L2–L3 gap 20 cm. Object 80 cm left of L1. How far is the final image from the object?
Asked in CBSE 2026 · 55/1/1 · Q32-OR · 5 marks(a) Ray diagram for a concave mirror with the object between F and C; derive the mirror formula from it. (b) A concave mirror gives a virtual image twice the size of an object 10 cm in front. Focal length?
Asked in CBSE 2025 · 55/1/1 · Q8 · 1 markA coin lies at the bottom of water (n = 4/3) of depth H. Its apparent depth when seen nearly normally?
Asked in CBSE 2025 · 55/1/1 · Q19 · 2 marksA ray enters the flat end face of a cylindrical rod (n = 2/√3, in air) at angle θ to the axis and then just grazes along the curved surface. Find θ.
Asked in CBSE 2025 · 55/1/1 · Q30(i) · 1 markA glass plate painted with an upward arrow and a crossing line ending in a ball on the right is lit, and a convex lens forms its real image on a screen. Which picture shows the image?
Asked in CBSE 2025 · 55/1/1 · Q30(ii) · 1 markFour statements give the sign of magnification for a convex mirror, virtual mirror images, a concave lens and real inverted images. Which one is wrong?
Asked in CBSE 2025 · 55/1/1 · Q30(iii)(A) · 1 markA convex lens of focal length f is split into two equal halves by a cut perpendicular to its principal axis. Focal length of each half?
Asked in CBSE 2025 · 55/1/1 · Q30(iii)(B) · 1 markIn the set-up of part (i), the object is 20 cm from the lens and the screen is 50 cm from the object. Find the focal length.
Asked in CBSE 2025 · 55/1/1 · Q30(iv) · 1 markFor a biconvex lens, the object is X₁ from the first focal point and the image is X₂ from the second focal point. Find the focal length.
Asked in CBSE 2025 · 55/1/1 · Q33(b) · 5 marks(i) Define a wavefront and sketch a plane wavefront refracted by a convex lens. (ii) Light from a distant source passes through a glass sphere (n = 1.5) of radius 15 cm. Draw the ray diagram and locate the final image.
Asked in CBSE 2024 · 55/1/1 · Q16 · 1 markAssertion: A plane or convex mirror can never form a real image. Reason: A virtual image can never act as the object for a real image.
Asked in CBSE 2024 · 55/1/1 · Q18(b) · 2 marksA plano-convex lens has focal length 16 cm and refractive index 1.4. Find the radius of its curved face.
Asked in CBSE 2024 · 55/1/1 · Q19 · 2 marksA concave mirror (R = 40 cm) has an object 30 cm before it. Find (i) the image position and (ii) the magnification.
Asked in CBSE 2024 · 55/1/1 · Q29(i) · 1 markCase study on lenses. A double-convex lens of glass with index n has both radii equal to R. Its power?
Asked in CBSE 2024 · 55/1/1 · Q29(ii) · 1 markAn equiconvex lens of power P is cut into two equal halves by a plane perpendicular to the principal axis. Power of each half?
Asked in CBSE 2024 · 55/1/1 · Q29(iii) · 1 markThe two plano-convex halves from (ii) are put in contact as in the figure. Power of the combination?
Asked in CBSE 2024 · 55/1/1 · Q29(iv)(a) · 1 markAn equiconvex lens of power P is cut along its principal axis and the two halves are placed one after the other on the axis as in the figure. Power of the combination?
Asked in CBSE 2024 · 55/1/1 · Q29(iv)(b) · 1 markTwo convex lenses (f = 60 cm and f = 20 cm) touch each other coaxially. Power of the pair?
Asked in CBSE 2024 · 55/1/1 · Q33(a) · 5 marks(i) Sketch how deviation through a prism varies with angle of incidence and define minimum deviation. (ii) A ray falls normally on one face of a prism of angle A and is deviated by δ. Prove n = sin(A + δ)/sin A. (iii) A prism of index √2 has refracting angle 60°. Find (1) the minimum deviation and (2) the angle of incidence.
Asked in CBSE 2023 · 55/1/1 · Q9 · 1 markFor a concave mirror of focal length f, what is the least possible gap between an object and its real image?
Asked in CBSE 2023 · 55/1/1 · Q21(b) · 2 marksGive two reasons, with justification, why astronomers prefer a reflecting telescope to a refracting one.
Asked in CBSE 2023 · 55/1/1 · Q33(b) · 5 marks(i) A spherical surface of radius R divides media of indices n₁ and n₂; an object at distance u in n₁ gives an image at distance v in n₂. Derive the u–v relation. (ii) A glass sphere (radius 6.0 cm, μ = 1.5) has an air bubble 3.0 cm from its centre. Find where the bubble appears when viewed from air through the nearer surface.
Asked in CBSE 2023 · 55/1/1 · Q35(a) · 1 markStrontium titanate has refractive index 2.41 and critical angle 24.5°. A ray falls normally on one face of an equilateral prism made of it. Trace the ray through the prism.
Asked in CBSE 2023 · 55/1/1 · Q35(b) · 1 markFind the speed of light inside the strontium titanate prism (n = 2.41).
Asked in CBSE 2023 · 55/1/1 · Q35(c) · 2 marksBriefly explain two uses of total internal reflection.
Asked in CBSE 2023 · 55/1/1 · Q35(c)-OR · 2 marksDefine total internal reflection and give the two conditions needed for it.

Wave Optics

13 questions, 32 marks across 4 papers

Asked in CBSE 2026 · 55/1/1 · Q4 · 1 markIn Young's double-slit set-up with screen distance much larger than slit separation, what shape are the fringes nearly?
Asked in CBSE 2026 · 55/1/1 · Q10 · 1 markWaves: y1 = A1 sin ωt, y2 = A2 sin 2ωt, y3 = A3 cos ωt, y4 = A4 sin(ωt + π/3). Which of them can interfere with each other?
Asked in CBSE 2026 · 55/1/1 · Q18(a) · 2 marksLight of 400 nm and 600 nm falls on a 1 mm wide single slit; screen 1.5 m away. Least distance from the central maximum where minima of both coincide?
Asked in CBSE 2026 · 55/1/1 · Q18(b) · 2 marksDouble-slit set-up: slits 0.6 mm apart, screen 1.5 m away, light of 440 nm and 660 nm. Least distance from the central maximum where bright fringes of both coincide?
Asked in CBSE 2025 · 55/1/1 · Q18(a) · 2 marksLight of 600 nm passes a single slit; the first minimum is at θ = 30°. Find the slit width.
Asked in CBSE 2025 · 55/1/1 · Q18(b) · 2 marksTwo waves, each of intensity I₀, meet at a point with path difference λ/8 in a double-slit set-up. Find the resultant intensity there.
Asked in CBSE 2025 · 55/1/1 · Q33(a) · 5 marks(i) (1) What are coherent sources and why are they needed for steady interference? (2) Why are two independent lamps not coherent? (ii) Slits 0.1 mm apart, screen 1.20 m away, λ = 600 nm. Find (1) the fringe spacing, (2) the angular width of a bright fringe in degrees.
Asked in CBSE 2024 · 55/1/1 · Q18(a) · 2 marksLight of frequency 5.0 × 10¹⁴ Hz goes from air into a medium with n = 1.5. Find the wavelength of (i) the reflected light and (ii) the refracted light.
Asked in CBSE 2024 · 55/1/1 · Q33(b) · 5 marks(i) State Huygens' principle; construct the reflected wavefront for a plane wave meeting a mirror at angle i and prove reflection angle = incidence angle. (ii) Define coherent sources; can two separate sodium lamps be coherent? (iii) In YDSE with light of 520 nm and an unknown λ, the 4th bright fringe of λ falls on the 5th bright fringe of 520 nm. Find λ.
Asked in CBSE 2023 · 55/1/1 · Q17 · 1 markA: Any two points on one wavefront have zero phase difference. R: Points of a wavefront are equally far from the source, so they vibrate in step.
Asked in CBSE 2023 · 55/1/1 · Q21(a) · 2 marksWith Huygens' construction, draw how a plane wavefront refracts at a flat boundary between two media, and use it to prove the law of refraction.
Asked in CBSE 2023 · 55/1/1 · Q22 · 2 marksCoherent single-wavelength beams of intensity I and 4I overlap. Find I_max : I_min of the combined beam.
Asked in CBSE 2023 · 55/1/1 · Q33(a) · 5 marks(i) Give two differences between interference and diffraction patterns, and two factors that set the fringe width in Young's experiment. (ii) In Young's experiment the slit gap is 100 times the wavelength. Find (1) the angle in radians between the central and the next maximum and (2) their separation on a screen 50 cm away.

Dual Nature of Radiation and Matter

16 questions, 22 marks across 4 papers

Asked in CBSE 2026 · 55/1/1 · Q14 · 1 markAssertion: accelerated electrons sent through a narrow slit give a diffraction pattern. Reason: electrons show both particle and wave nature.
Asked in CBSE 2026 · 55/1/1 · Q17 · 2 marksLight of 200 nm falls on an emitter; photocurrent stops at a collector potential of −0.80 V. Find the work function in eV.
Asked in CBSE 2026 · 55/1/1 · Q30(I) · 1 markFrom the stopping-potential versus frequency graph, what are the work functions of metals A and B?
Asked in CBSE 2026 · 55/1/1 · Q30(II) · 1 markFor frequency ν > ν₂ falling on both metals, which gives electrons of higher maximum KE?
Asked in CBSE 2026 · 55/1/1 · Q30(III) · 1 markIf the light intensity on both metals is doubled at fixed frequency, what changes?
Asked in CBSE 2026 · 55/1/1 · Q30(IV) · 1 markThreshold frequency is ν₀. Max KE is E1 at frequency 3ν₀ and E2 at 6ν₀. Find E1/E2.
Asked in CBSE 2026 · 55/1/1 · Q30(IV)-OR · 1 markIf m is the slope of metal B's Vs–ν line, express h in terms of m and e.
Asked in CBSE 2025 · 55/1/1 · Q9 · 1 markThe graph of stopping potential V₀ against frequency ν has slope m. Express the electron's charge using m and Planck's constant h.
Asked in CBSE 2025 · 55/1/1 · Q10 · 1 markAn electron, a proton and a deuteron move at equal speeds. Compare their de Broglie wavelengths λe, λp, λd.
Asked in CBSE 2025 · 55/1/1 · Q26 · 3 marksGive reasons: (a) photoelectrons from monochromatic light have a spread of kinetic energies; (b) saturation current changes with intensity; (c) at fixed intensity, raising the wavelength eventually stops emission.
Asked in CBSE 2024 · 55/1/1 · Q11 · 1 markPhotons of 3.3 eV (beam A) and 11.3 eV (beam B) fall in turn on a metal with work function 2.3 eV. Find the ratio of maximum photoelectron speeds, A to B.
Asked in CBSE 2024 · 55/1/1 · Q12 · 1 markAn electron and a proton in motion have equal de Broglie wavelength λ. What quantity must they share?
Asked in CBSE 2024 · 55/1/1 · Q13 · 1 markAssertion: In the photoelectric effect, photoelectron kinetic energy rises with the intensity of light. Reason: Photocurrent depends on the wavelength of the light.
Asked in CBSE 2024 · 55/1/1 · Q20 · 2 marksA neutron (mass m) and a photon both have energy E. With λn the neutron's de Broglie wavelength and λp the photon's wavelength, find λn/λp.
Asked in CBSE 2023 · 55/1/1 · Q18 · 1 markA: The photoelectric effect shows light behaves as particles. R: Above the threshold frequency, photocurrent is proportional to the light's intensity.
Asked in CBSE 2023 · 55/1/1 · Q29 · 3 marksBriefly explain electron emission from a metal using Einstein's photoelectric equation. Plot photocurrent against (a) collector potential for different intensities and (b) intensity of the light.

Atoms

10 questions, 16 marks across 4 papers

Asked in CBSE 2026 · 55/1/1 · Q8 · 1 markAn alpha particle moving head-on at speed v has distance of closest approach d. What is it if the speed is halved?
Asked in CBSE 2026 · 55/1/1 · Q16 · 1 markAssertion: in Bohr's hydrogen model, energy levels are discrete. Reason: the Coulomb force on the electron supplies its centripetal force.
Asked in CBSE 2025 · 55/1/1 · Q16 · 1 markA: The electron's potential energy in any stationary orbit of hydrogen is positive. R: A charged particle always has positive total energy.
Asked in CBSE 2025 · 55/1/1 · Q20 · 2 marksShow that in Bohr's hydrogen model the period of the electron in the nth orbit varies as n³.
Asked in CBSE 2024 · 55/1/1 · Q9 · 1 markWhich electron transition in hydrogen produces the second line of the Balmer series?
Asked in CBSE 2024 · 55/1/1 · Q27 · 3 marksState the shortcomings of Rutherford's atom model, how Bohr overcame them, and show that Bohr orbits are not evenly spaced.
Asked in CBSE 2023 · 55/1/1 · Q10 · 1 markIn Bohr's hydrogen model, the radius of orbit number n varies as which power of n?
Asked in CBSE 2023 · 55/1/1 · Q11 · 1 markA ground-state hydrogen atom takes in one photon and goes to the n = 5 level. Find the photon's wavelength.
Asked in CBSE 2023 · 55/1/1 · Q23 · 2 marksHydrogen's ground-state energy is −13.6 eV. Find the electron's potential energy and kinetic energy in the third excited state.
Asked in CBSE 2023 · 55/1/1 · Q30(a) · 3 marksDraw hydrogen's energy level diagram and mark the transitions of the series in the ultraviolet, visible and infrared regions.

Nuclei

7 questions, 14 marks across 4 papers

Asked in CBSE 2026 · 55/1/1 · Q15 · 1 markAssertion: a nucleus weighs less than its separate nucleons. Reason: energy is absorbed when nucleons bind into a nucleus.
Asked in CBSE 2026 · 55/1/1 · Q21 · 2 marksSketch potential energy of two nucleons versus their separation and give two conclusions from it.
Asked in CBSE 2025 · 55/1/1 · Q11 · 1 markPick the correct shape of the binding energy per nucleon vs mass number A curve.
Asked in CBSE 2025 · 55/1/1 · Q27 · 3 marks(a) Define mass defect and binding energy, and explain fission using binding energy per nucleon. (b) A deuteron (one p, one n) has mass 2.013553 u. With m_p = 1.007277 u, m_n = 1.008665 u and 1 u = 931.5 MeV/c², find its mass defect and energy equivalent.
Asked in CBSE 2024 · 55/1/1 · Q28 · 3 marks(a) Name two nuclear properties. (b) Why is a nucleus far denser than an atom? (c) Show that nuclear density does not depend on the nucleus.
Asked in CBSE 2023 · 55/1/1 · Q12 · 1 markHow does the mass density of a nucleus depend on its mass number A?
Asked in CBSE 2023 · 55/1/1 · Q30(b) · 3 marksSketch binding energy per nucleon against mass number, give two features of the curve, and say why light nuclei tend to fuse.

Semiconductor Electronics: Materials, Devices and Simple Circuits

19 questions, 29 marks across 4 papers

Asked in CBSE 2026 · 55/1/1 · Q12 · 1 markFor an unbiased p-n junction in equilibrium, how are diffusion and drift currents related?
Asked in CBSE 2026 · 55/1/1 · Q25 · 3 marksAn ac input Vi = 12 sin(100πt) V acts across A and B of the diode–resistor network in the figure. In the positive half-cycle: (a) which diode conducts and why, (b) redraw the circuit, (c) voltage across each resistor at peak input.
Asked in CBSE 2026 · 55/1/1 · Q26 · 3 marksBriefly explain the two key processes in forming a p-n junction.
Asked in CBSE 2025 · 55/1/1 · Q12 · 1 markWhat happens to barrier height and depletion width when a p-n junction is forward biased?
Asked in CBSE 2025 · 55/1/1 · Q15 · 1 markA: Simply pressing a p-type slab against an n-type slab does not make a p-n junction. R: Electrons outnumber holes in p-type, and holes outnumber electrons in n-type.
Asked in CBSE 2025 · 55/1/1 · Q21 · 2 marksSi is doped with one acceptor atom per 5 × 10⁷ Si atoms; Si atom density is 5 × 10²⁸ m⁻³. Find holes per cm³ due to doping and name one such dopant.
Asked in CBSE 2025 · 55/1/1 · Q28 · 3 marks(a) Draw the circuit to study a p-n diode's V-I characteristics. (b) Sketch the characteristic curves. (c) State two things learnt from them.
Asked in CBSE 2024 · 55/1/1 · Q10 · 1 markWhat happens when germanium is doped with arsenic?
Asked in CBSE 2024 · 55/1/1 · Q30(i) · 1 markCase study on rectifiers. An ac input of rms value V₀/√2 feeds a full-wave rectifier. RMS value of the rectified output?
Asked in CBSE 2024 · 55/1/1 · Q30(ii) · 1 markFor how long does current flow through each diode of a full-wave rectifier?
Asked in CBSE 2024 · 55/1/1 · Q30(iii) · 1 markIn a full-wave rectifier, how are the two diodes biased at any instant?
Asked in CBSE 2024 · 55/1/1 · Q30(iv)(a) · 1 markA 50 Hz ac voltage feeds a half-wave rectifier. Ripple frequency of the output?
Asked in CBSE 2024 · 55/1/1 · Q30(iv)(b) · 1 markA square wave switching between +5 V and −5 V is applied to a diode in series with a load R_L (output taken across R_L). What output appears?
Asked in CBSE 2023 · 55/1/1 · Q13 · 1 markAn ac supply drives a p-n diode and a load resistor joined in series. Which graph shows the voltage across the load?
Asked in CBSE 2023 · 55/1/1 · Q14 · 1 markWhat happens when a pure semiconductor gets a little trivalent impurity added?
Asked in CBSE 2023 · 55/1/1 · Q15 · 1 markIn the band diagram of n-type silicon, roughly how far below the conduction band edge E_C is the donor level E_D?
Asked in CBSE 2023 · 55/1/1 · Q24(a) · 2 marksState two differences between intrinsic and extrinsic semiconductors.
Asked in CBSE 2023 · 55/1/1 · Q24(b) · 2 marksSketch the circuits used to study a p-n diode's V–I behaviour in forward and in reverse bias, and plot the V–I curve of a silicon diode.
Asked in CBSE 2023 · 55/1/1 · Q25 · 2 marksExplain in brief the roles of diffusion current and drift current in building up the barrier potential of a p-n junction.

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