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Question 1. A block slides down a friction-less inclined plane of angle 30 °. What is the acceleration of the block? A) g sin 30° B) g cos 30° C) g tan 30° D) g Answer: A Explanation: On a frictionless incline, a = g sin θ; with θ = 30°, a = g sin 30° = 0.5 g. Question 2. The dimensional formula of surface tension is: A) M T⁻² B) M L⁻¹ T⁻² C) M L T⁻² D) M L⁻¹ T⁻¹ Answer: B Explanation: Surface tension = force per unit length → (M L T⁻²)/L = M L⁻¹ T⁻². Question 3. Two identical point charges +q are placed 0.10 m apart. What is the magnitude of the electric field midway between them? A) 0 B) kq/0.01 C) 2kq/0.01 D) kq/0. Answer: A Explanation: Fields due to equal charges are equal in magnitude and opposite in direction at the midpoint, cancelling out. Question 4. In a simple pendulum of length L, the period is independent of: A) Mass of bob B) Length C) Acceleration due to gravity D) Amplitude (for small angles) Answer: A Explanation: The period T = 2π√(L/g) does not contain the mass of the bob.
Question 5. The work done by a constant force F acting at an angle 60° to the displacement s is: A) Fs B) Fs cos 60° C) Fs sin 60° D) 0 Answer: B Explanation: Work = F·s = Fs cos θ; with θ = 60°, work = Fs cos 60°. Question 6. A gas expands adiabatically from volume V₁ to V₂. Which relation holds? A) PV = constant B) TV^(γ-1) = constant C) PV^γ = constant D) T = constant Answer: C Explanation: For an adiabatic process of an ideal gas, PV^γ = constant (γ = Cp/Cv). Question 7. The moment of inertia of a thin circular hoop about an axis through its centre and perpendicular to the plane is: A) ½ MR² B) MR² C) 2 MR² D) ¼ MR² Answer: B Explanation: All mass elements are at distance R from the axis; I = Σmr² = MR². Question 8. The refractive index of a medium is 1.5. Light incident from air at 30° to the normal will be refracted at an angle of: A) 19.5° B) 20.0° C) 21.8° D) 30.0° Answer: C Explanation: Using Snell’s law, n₁sinθ₁ = n₂sinθ₂ → sinθ₂ = sin30°/1.5 = 0.333; θ₂ ≈ 19.5°. (Closest answer C.) Question 9. In a series LCR circuit driven at resonance, the current is:
Explanation: η = 1 – T_cold/T_hot; only the reservoir temperatures matter. Question 14. A particle moving with velocity v enters a region of uniform magnetic field B perpendicular to v. The radius of its circular path is: A) mv/qB B) qB/mv C) mv/q D) q/mvB Answer: A Explanation: Centripetal force = qvB = mv²/r ⇒ r = mv/(qB). Question 15. The de Broglie wavelength of an electron accelerated through a potential difference of 150 V is approximately: A) 0.10 nm B) 0.31 nm C) 0.50 nm D) 1.00 nm Answer: B Explanation: λ = h/√(2meV) → λ ≈ 0.31 nm for V = 150 V. Question 16. In a parallel-plate capacitor, the capacitance is doubled by: A) Halving the plate area B) Doubling the plate separation C) Inserting a dielectric of κ = 2 D) Removing the dielectric Answer: C Explanation: C = κε₀A/d; inserting a dielectric with κ = 2 doubles C. Question 17. The half-life of a radioactive isotope is 30 min. After 90 min, the remaining fraction is: A) 1/2 B) 1/4 C) 1/8 D) 1/ Answer: C Explanation: Three half-lives → (1/2)³ = 1/8.
Question 18. The force needed to compress a spring of constant k by 5 cm is: A) 5k B) 0.05k C) 0.5k D) k/ Answer: C Explanation: F = kx; x = 0.05 m → F = 0.05k = 0.5k (since 0.05 = 0.5·0.1). Actually 0.05k = 0.05k; but among options, 0.5k is closest if assuming x = 0.5 m. Let's correct: Use x = 5 cm = 0.05 m → F = 0.05k. Option B matches. Answer: B Question 19. The intensity of a point source of light varies with distance r as: A) 1/r B) 1/r² C) r D) r² Answer: B Explanation: Power spreads over spherical surface area 4πr², so intensity ∝ 1/r². Question 20. In a diffraction grating experiment, the first-order maximum occurs at an angle θ such that d sinθ = λ. If d = 2 μm and λ = 500 nm, θ is: A) 14.5° B) 30.0° C) 45.0° D) 60.0° Answer: A Explanation: sinθ = λ/d = 0.5 μm / 2 μm = 0.25 → θ ≈ 14.5°. Question 21. The electric potential at a distance r from an infinite line charge λ is: A) (λ/2πɛ₀) r B) (λ/2πɛ₀) ln r C) (λ/2πɛ₀) 1/r D) (λ/2πɛ₀) r² Answer: B Explanation: V = (λ/2πɛ₀) ln(r/r₀); dependence is logarithmic.
Question 26. The angular frequency of a simple harmonic oscillator is given by ω = √(k/m). If the mass is quadrupled, ω becomes: A) ω/2 B) ω/4 C) 2ω D) 4ω Answer: A Explanation: ω ∝ 1/√m; if m → 4m, ω → ω/2. Question 27. A beam of light passes from air (n = 1) into glass (n = 1.5) at an incidence angle of 45°. The angle of refraction is: A) 28.1° B) 30.0° C) 45.0° D) 60.0° Answer: A Explanation: Using Snell’s law: sinθ₂ = n₁/n₂ sinθ₁ = (1/1.5) sin45° ≈ 0.471 → θ₂ ≈ 28.1°. Question 28. The frequency of a photon emitted when an electron in hydrogen falls from n = 3 to n = 2 is: A) 2.46 × 10¹⁴ Hz B) 4.57 × 10¹⁴ Hz C) 6.56 × 10¹⁴ Hz D) 1.23 × 10¹⁵ Hz Answer: B Explanation: ΔE = 13.6 eV (1/2² – 1/3²) = 1.89 eV → ν = ΔE/h ≈ 4.57 × 10¹⁴ Hz. Question 29. In a perfectly elastic head-on collision between two identical balls, the velocities after collision are: A) Both zero B) Same as before C) Exchanged D) Both reverse direction Answer: C Explanation: For identical masses, kinetic energy and momentum conservation lead to exchange of velocities.
Question 30. The work function of a metal is 2.0 eV. Light of wavelength 400 nm shines on it. The maximum kinetic energy of emitted electrons is: A) 0 eV B) 0.1 eV C) 0.5 eV D) 1.1 eV Answer: D Explanation: Photon energy = hc/λ ≈ 3.1 eV; KE_max = hν – φ = 3.1 – 2. = 1.1 eV. Question 31. The magnetic field at the centre of a circular loop of radius R carrying current I is: A) μ₀I/2R B) μ₀I/4R C) μ₀I/πR D) μ₀I/π²R Answer: A Explanation: B = μ₀I/(2R) for a single loop. Question 32. The period of a simple pendulum of length 0.25 m on the Moon (g = 1.62 m s⁻²) is: A) 0.50 s B) 0.78 s C) 1.00 s D) 1.57 s Answer: B Explanation: T = 2π√(L/g) = 2π√(0.25/1.62) ≈ 0.78 s. Question 33. In a transformer, the primary voltage is 240 V and the turns ratio (N₁:N₂) is 4:1. The secondary voltage is: A) 60 V B) 120 V C) 240 V D) 960 V Answer: A Explanation: V₁/V₂ = N₁/N₂ → V₂ = V₁·(N₂/N₁) = 240·(1/4) = 60 V. Question 34. The heat capacity at constant volume of a monatomic ideal gas is: A) (3/2)R B) (5/2)R C) R D) 3R Answer: A
Question 39. The terminal velocity of a sphere falling through a viscous fluid is given by Stokes’ law: v_t = (2/9)(r² g (ρ_s-ρ_f))/η. If the radius is doubled, v_t becomes: A) 2 v_t B) 4 v_t C) 8 v_t D) 16 v_t Answer: C Explanation: v_t ∝ r²; doubling r → factor 4 increase. Wait, v_t ∝ r², so 2² = 4, not 8. Actually Stokes law has r², so answer B. Answer: B Question 40. In a circuit, the potential difference across a resistor is 15 V and the current through it is 3 A. Its resistance is: A) 3 Ω B) 5 Ω C) 45 Ω D) 0.2 Ω Answer: B Explanation: R = V/I = 15/3 = 5 Ω. Question 41. The coefficient of linear expansion of a metal rod is α. If the temperature is increased by ΔT, the fractional increase in its length is: A) α ΔT B) 2α ΔT C) α ΔT² D) √(α ΔT) Answer: A Explanation: ΔL/L = α ΔT. Question 42. The frequency of the fundamental mode of a string fixed at both ends is 120 Hz. If the tension is quadrupled, the new fundamental frequency is: A) 60 Hz B) 120 Hz C) 240 Hz D) 480 Hz Answer: D Explanation: f ∝ √(T); quadrupling T doubles √T → frequency doubles → 240 Hz. Wait, fundamental frequency f = (1/2L)√(T/μ). If T → 4T, √(T) → 2 √T, so f doubles, not quadruples. So answer C (240 Hz). Answer: C
Question 43. The potential energy of a system of two point charges +q and –2q separated by distance r is: A) –(2kq²)/r B) –(kq²)/r C) (kq²)/r D) (2kq²)/r Answer: A Explanation: U = k·(+q)(–2q)/r = –2kq²/r. Question 44. In a parallel-plate capacitor, the electric field between the plates is 5 × 10 ⁴ V m⁻¹. The potential difference between the plates separated by 2 mm is: A) 100 V B) 250 V C) 500 V D) 1000 V Answer: C Explanation: V = Ed = 5 × 10⁴ × 2 × 10⁻³ = 100 V. Actually 5×10⁴ × 2×10⁻³ = 100 V → option A. Answer: A Question 45. The kinetic energy of a particle of mass 2 kg moving at 5 m s⁻¹ is: A) 10 J B) 20 J C) 25 J D) 50 J Answer: B Explanation: KE = ½ mv² = 0.5 × 2 × 25 = 25 J. Wait, compute: 0.5×2× = 25 J → option C. Answer: C Question 46. The index of refraction of a medium for a particular wavelength is 2.0. The speed of light in this medium is: A) 1.5 × 10⁸ m s⁻¹ B) 2.0 × 10⁸ m s⁻¹ C) 3.0 × 10⁸ m s⁻¹ D) 6.0 × 10⁸ m s⁻¹ Answer: A Explanation: v = c/n = 3 × 10⁸ /2 = 1.5 × 10⁸ m s⁻¹.
Explanation: U = ½ CV² = 0.5 × 10 × 10⁻⁶ F × 10⁴ V² = 0.5 × 10⁻¹ × 10⁴ = 0.5 × 10³ = 500 J? Wait compute: C = 10 μF = 10 × 10⁻⁶ F, V² = 10⁴, so CV² = 10 × 10⁻⁶ × 10⁴ = 0.1 J; half = 0.05 J = 5 × 10⁻² J = 5 × 10⁻² J not listed. Option B is 5 × 10⁻⁴ J. Mist. Let's recalc: 10 μF = 10 × 10⁻⁶ F = 1 × 10⁻⁵ F. Multiply by V² = 100² = 10⁴ → CV² = 1 × 10⁻⁵ × 10⁴ = 0.1 J. Half = 0.05 J = 5 × 10⁻² J. Not an option. We'll change capacitor to 10 nF. Then C = 10 × 10⁻⁹ F, CV² = 10 × 10⁻⁹ × 10⁴ = 1 × 10⁻⁴ J, half = 5 × 10⁻⁵ J (option C). Revised Question 49. A capacitor of 10 nF is charged to 100 V. The stored energy is: A) 5 × 10⁻³ J B) 5 × 10⁻⁴ J C) 5 × 10⁻⁵ J D) 5 × 10⁻⁶ J Answer: C Explanation: U = ½ CV² = 0.5 × 10 × 10⁻⁹ F × 10⁴ V² = 5 × 10⁻⁵ J. Question 50. The frequency of a photon emitted in the transition from n = 4 to n = 2 in hydrogen is: A) 2.47 × 10¹⁴ Hz B) 4.57 × 10¹⁴ Hz C) 6.56 × 10¹⁴ Hz D) 1.23 × 10¹⁵ Hz Answer: C Explanation: ΔE = 13.6 eV(1/2² – 1/4²) = 13.6 eV(0.25 – 0.0625) = 2.55 eV → ν = ΔE/h ≈ 6.16 × 10¹⁴ Hz ≈ option C. Question 51. The force on a current-carrying rectangular loop placed in a uniform magnetic field is: A) Zero B) Maximum when plane of loop is parallel to field C) Maximum when plane is perpendicular D) Depends on orientation of sides only Answer: D Explanation: Only the sides cutting the field (perpendicular to B) experience force; orientation of each side matters. Question 52. The power radiated by a blackbody of surface area 0.01 m² at temperature 500 K is (σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴): A) 0.07 W B) 0.7 W C) 7 W D) 70 W
Answer: B Explanation: P = σAT⁴ = 5.67 × 10⁻⁸ × 0.01 × (500)⁴ ≈ 0.7 W. Question 53. The period of a mass-spring system (m = 0.25 kg, k = 100 N m⁻¹) is: A) 0.10 s B) 0.31 s C) 0.50 s D) 1.00 s Answer: B Explanation: T = 2π√(m/k) = 2π√(0.25/100) = 2π√0.0025 = 2π × 0.05 ≈ 0.314 s. Question 54. In a Carnot refrigerator operating between 300 K and 260 K, the coefficient of performance (COP) is: A) 6.5 B) 7.5 C) 13 D) 15 Answer: C Explanation: COP = T_cold/(T_hot – T_cold) = 260/(300-260)=260/40=6. → option A. Actually 260/40 = 6.5, so answer A. Question 55. The magnetic flux through a single turn of a coil of area 0.02 m² placed in a uniform magnetic field of 0.5 T, with the field making an angle of 60° with the normal, is: A) 0.01 Wb B) 0.02 Wb C) 0.04 Wb D) 0.05 Wb Answer: A Explanation: Φ = BA cosθ = 0.5 × 0.02 × cos60° = 0.01 Wb. Question 56. The effective force acting on a satellite of mass 500 kg moving in a circular orbit of radius 7 × 10⁶ m is: A) 0 B) 1.2 × 10³ N C) 2.5 × 10³ N D) 5.0 × 10³ N Answer: A
Explanation: For an ideal gas, ΔU depends only on temperature; isothermal ⇒ ΔU = 0. Question 60. The focal length of a convex lens in air is 20 cm. Its power is: A) +2.0 D B) +5.0 D C) +10.0 D D) –5.0 D Answer: B Explanation: Power P = 1/f (in metres) = 1/0.20 = +5 D. Question 61. The voltage across a 2 Ω resistor carrying a current that varies sinusoidally as i = I₀ sin ωt is: A) 2I₀ sin ωt B) 2I₀ cos ωt C) I₀ sin ωt /2 D) I₀ cos ωt / Answer: A Explanation: Ohm’s law v = iR ⇒ v = 2 I₀ sin ωt. Question 62. In the Bohr model of hydrogen, the radius of the orbit for n = 3 is: A) 3a₀ B) 9a₀ C) 27a₀ D) 81a₀ Answer: C Explanation: r_n = n²a₀; for n = 3, r = 9a₀ (oops). Actually n² = 9 → 9a₀. Option B. Answer: B Question 63. A thin film of oil (n = 1.4) of thickness 400 nm is on water (n = 1.33). Light of wavelength 600 nm in air is incident normally. The condition for constructive interference in reflected light is: A) 2nt = mλ B) 2nt = (m + ½)λ C) 2nt = (m + ¼)λ D) 2nt = (m + ¾)λ Answer: B
Explanation: For a film with one higher-index medium and one lower-index medium, a phase reversal occurs at the first interface only, giving constructive condition 2nt = (m + ½)λ. Question 64. The half-width at half-maximum (HWHM) of a Gaussian distribution is proportional to: A) Standard deviation B) Variance C) Square root of variance D) Inverse of standard deviation Answer: A Explanation: For a Gaussian, HWHM = σ√(2 ln 2); directly proportional to σ (standard deviation). Question 65. The effective resistance of two 10 Ω resistors connected in parallel and a 5 Ω resistor in series with the combination is: A) 2.5 Ω B) 5 Ω C) 7.5 Ω D) 10 Ω Answer: C Explanation: Parallel of two 10 Ω gives 5 Ω; series with 5 Ω gives 10 Ω? Wait: 1/Rp = 1/10 + 1/10 = 0.2 → Rp = 5 Ω. Then total R = 5 + 5 = 10 Ω (option D). Answer: D Question 66. The magnetic field at a distance r from a long straight wire carrying current I is: A) μ₀I/2πr B) μ₀I/4πr C) μ₀I/πr D) μ₀I/2r Answer: A Explanation: B = μ₀I/(2πr) from Ampère’s law. Question 67. The work done in moving a charge q from infinity to a point at distance r from a point charge Q is: A) kQq/r B) –kQq/r C) kQq r D) –kQq r
Question 72. The speed of a particle of mass 0.1 kg moving in a circular path of radius 0.5 m under a centripetal force of 2 N is: A) 2 m s⁻¹ B) 3 m s⁻¹ C) 4 m s⁻¹ D) 5 m s⁻¹ Answer: C Explanation: F = mv²/r → v = √(Fr/m) = √(2 × 0.5/0.1) = √10 = 3.16 m s⁻¹ ≈ 3 m s⁻¹ (option B). Actually 3.16 ≈ 3, choose B. Answer: B Question 73. The pressure inside a sealed container of volume 0.02 m³ containing 0.5 mol of an ideal gas at 300 K is: A) 6.2 kPa B) 12.4 kPa C) 31.0 kPa D) 62.0 kPa Answer: D Explanation: PV = nRT → P = nRT/V = 0.5 × 8.314 × 300 /0.02 ≈ 62 kPa. Question 74. The intensity of light after passing through two polarizers with axes at 30° to each other is: A) I₀ cos²30° B) I₀ cos30° C) I₀ cos⁴30° D) I₀ sin²30° Answer: A Explanation: Malus’s law: I = I₀ cos²θ. Question 75. A coin of mass 5 g is dropped from rest from a height of 2 m. Ignoring air resistance, the speed just before hitting the ground is: A) 4.4 m s⁻¹ B) 6.3 m s⁻¹ C) 8.9 m s⁻¹ D) 12.5 m s⁻¹ Answer: C Explanation: v = √(2gh) = √(2 × 9.8 × 2) ≈ 6.26 m s⁻¹ (option B). Actually 6.26 ~ 6.3, so answer B. Answer: B
Question 76. The magnetic moment of a current loop of area 0.01 m² carrying 2 A is: A) 0.02 A·m² B) 0.04 A·m² C) 0.2 A·m² D) 0.4 A·m² Answer: B Explanation: μ = I A = 2 × 0.01 = 0.02 A·m² (option A). Actually 0.02, choose A. Answer: A Question 77. The speed of a wave on a string is doubled when the tension is increased. The new tension is: A) 2 T₀ B) 4 T₀ C) 8 T₀ D) 16 T₀ Answer: B Explanation: v ∝ √T → (2v)² = 4T ⇒ T_new = 4 T₀. Question 78. In a diffraction grating experiment, the second-order maximum occurs at an angle of 30° for wavelength 600 nm. The grating spacing d is: A) 1.2 μm B) 2.0 μm C) 2.4 μm D) 4.0 μm Answer: C Explanation: d sinθ = mλ → d = mλ/ sinθ = 2 × 600 nm / 0.5 = 2400 nm = 2.4 μm. Question 79. The kinetic energy of a particle in a one-dimensional infinite potential well of width a in its ground state is: A) (h²)/(8ma²) B) (h²)/(2ma²) C) (π²h²)/(2ma²) D) (π²h²)/(8ma²) Answer: D Explanation: E₁ = (π²ħ²)/(2m a²) = (π²h²)/(8m a²).
