Daily MCQ Paper — 22 April 2026

April 22, 2026 ·

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Daily Practice Sheet — 50 Questions

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Daily MCQ Paper — 22 April 2026

50 questions across all sections. Use the practice interface to attempt; review answers and explanations after submission.

Q1. The fundamental frequency of a string of length L fixed at both ends, with wave speed v, is
1. v/L
2. v/2L
3. v/4L
4. 2v/L
Q2. Two tuning forks of frequencies 256 Hz and 260 Hz produce beats at
1. 2 Hz
2. 4 Hz
3. 8 Hz
4. 256 Hz
Q3. For a closed organ pipe of length L (one end closed), the fundamental frequency is
1. v/2L
2. v/4L
3. v/L
4. 3v/4L
Q4. A source of frequency f moves toward a stationary observer at speed vs. The apparent frequency (sound speed v) is
1. f(v + vs)/v
2. f v/(v – vs)
3. f v/(v + vs)
4. f(v – vs)/v
Q5. Stefan-Boltzmann law states the total radiated power per unit area is proportional to
1. T
2. T^2
3. T^4
4. T^(1/2)
Q6. Fourier law of heat conduction is dQ/dt =
1. -kA dT/dx
2. kA dT
3. kA T^4
4. -k dT/dx
Q7. Newton's law of cooling assumes the rate of cooling is proportional to
1. (T – T_ambient)
2. (T – T_ambient)^2
3. T^4
4. log T
Q8. For a thin lens, the lens maker formula in air is
1. 1/f = (n-1)(1/R1 – 1/R2)
2. 1/f = n(1/R1 + 1/R2)
3. f = (R1 + R2)/2
4. f = R/2
Q9. Wien's displacement law states that lambda_max * T equals approximately
1. 2.9 x 10^-3 m K
2. 5.67 x 10^-8 W/m^2K^4
3. 6.63 x 10^-34 J s
4. 9.0 x 10^9 Nm^2/C^2
Q10. The equivalent focal length of two thin lenses in contact is given by
1. 1/f = 1/f1 + 1/f2
2. 1/f = 1/f1 – 1/f2
3. f = f1 + f2
4. f = f1 * f2/(f1 + f2)
Q11. The dimensional formula of Plancks constant is
1. [ML2T-1]
2. [MLT-1]
3. [ML2T-2]
4. [ML-1T]
Q12. Two resistors 6 Ω and 3 Ω in parallel give
1. 9 Ω
2. 2 Ω
3. 3 Ω
4. 4.5 Ω
Q13. A force is conservative if
1. Work done is path-independent
2. Work along closed loop is zero
3. Both A and B
4. It is constant
Q14. For a solid sphere rolling without slipping, the ratio of rotational KE to total KE is
1. 2/5
2. 2/7
3. 5/7
4. 1/2
Q15. The acceleration due to gravity at height h above Earth's surface (h<<R) is approximately
1. g(1 – 2h/R)
2. g(1 + 2h/R)
3. g(1 – h/R)
4. g(1 + h/R)
Q16. The threshold wavelength for photoemission from a metal of work function 2 eV is approximately
1. 620 nm
2. 310 nm
3. 155 nm
4. 1240 nm
Q17. A particle in SHM has amplitude 5 cm and frequency 2 Hz. Maximum velocity is
1. 10*pi cm/s
2. 20*pi cm/s
3. 5*pi cm/s
4. 40*pi cm/s
Q18. A Schottky defect involves
1. Cation vacancy and anion vacancy in equal numbers
2. Cation in interstitial site
3. Extra electron
4. Hole in valence band
Q19. n-type semiconductor is produced by doping silicon with
1. Boron
2. Phosphorus
3. Aluminium
4. Gallium
Q20. A Frenkel defect involves
1. Vacancy only
2. Cation displaced to interstitial site
3. Removal of both ions
4. Substitution of impurity
Q21. F-centres in alkali halide crystals are responsible for
1. Conductivity only
2. Colour due to trapped electron at anion vacancy
3. Magnetism
4. Hardness
Q22. Leaching of gold and silver uses
1. Conc. HCl
2. Dilute NaCN with air
3. Conc. HNO3
4. Dilute H2SO4
Q23. The basicity of H3PO4 (orthophosphoric acid) is
1. 1
2. 2
3. 3
4. 4
Q24. Froth flotation is used for concentration of
1. Oxide ores
2. Sulphide ores
3. Carbonate ores
4. Native metals
Q25. Mond process is used for refining
1. Copper
2. Zinc
3. Nickel
4. Iron
Q26. Hardy-Schulze rule states that the coagulating power of an ion is
1. Independent of charge
2. Greater for higher charge of opposite sign to sol
3. Greater for monovalent ions
4. Inversely proportional to molar mass
Q27. Van Arkel method is used for refining
1. Cu and Ag
2. Zr and Ti (ultra-pure)
3. Pb and Sn
4. Fe and Mn
Q28. Which is a Lewis acid?
1. NH₃
2. BF₃
3. H₂O
4. OH⁻
Q29. Aspirin is chemically
1. Salicylic acid
2. Acetyl salicylic acid
3. Methyl salicylate
4. Phenol
Q30. SN1 reactions proceed via
1. Carbocation intermediate
2. Carbanion
3. Free radical
4. Concerted bimolecular
Q31. Bond order of O₂ from MO theory
1. 1
2. 1.5
3. 2
4. 2.5
Q32. Number of stereoisomers of a molecule with 2 chiral centers (no meso)
1. 2
2. 3
3. 4
4. 8
Q33. Which is most acidic?
1. Phenol
2. Ethanol
3. Methanol
4. Water
Q34. The coordination number of central atom in [Co(NH3)6]3+ is
1. 3
2. 4
3. 5
4. 6
Q35. cos A – cos B = ?
1. -2 sin((A+B)/2) sin((A-B)/2)
2. 2 cos((A+B)/2) cos((A-B)/2)
3. cos(A+B)
4. sin(A – B)
Q36. General solution of sin x = sin alpha is
1. x = n*pi + alpha
2. x = n*pi + (-1)^n * alpha
3. x = 2n*pi + alpha
4. x = 2n*pi – alpha
Q37. Sum of cubes 1^3 + 2^3 + … + n^3 equals
1. n(n+1)/2
2. n(n+1)(2n+1)/6
3. [n(n+1)/2]^2
4. n^4
Q38. sin A + sin B = ?
1. 2 sin((A+B)/2) cos((A-B)/2)
2. 2 cos((A+B)/2) sin((A-B)/2)
3. sin A cos B
4. cos(A – B)
Q39. General solution of cos x = cos alpha is
1. x = n*pi + alpha
2. x = 2n*pi +/- alpha
3. x = (2n+1)*pi + alpha
4. x = n*pi – alpha
Q40. General solution of tan x = tan alpha is
1. x = n*pi + alpha
2. x = 2n*pi + alpha
3. x = n*pi/2 + alpha
4. x = (2n+1)*pi/2
Q41. Principal value of sin^-1(1/2) is
1. pi/3
2. pi/6
3. pi/4
4. pi/2
Q42. tan^-1 x + tan^-1 y = tan^-1((x + y)/(1 – xy)) holds when
1. xy < 1
2. xy > 1
3. xy = 1
4. x + y = 0
Q43. Sum of first n natural numbers 1 + 2 + … + n is
1. n(n+1)/2
2. n^2
3. n(n+1)(2n+1)/6
4. n^2(n+1)^2/4
Q44. Sum of squares 1^2 + 2^2 + … + n^2 equals
1. n(n+1)/2
2. n(n+1)(2n+1)/6
3. [n(n+1)/2]^2
4. n^3
Q45. The eccentricity of hyperbola x²/9 − y²/16 = 1 is
1. 5/4
2. 5/3
3. 4/3
4. 3/5
Q46. The area enclosed by y = x² and y = x is
1. 1/2
2. 1/3
3. 1/6
4. 1
Q47. Shortest distance between two skew lines with vectors a₁, a₂ and directions b₁, b₂ is
1. |(a₂-a₁)·(b₁×b₂)| / |b₁×b₂|
2. |b₁·b₂|
3. |a₂-a₁|
4. 0
Q48. Mean of first 10 natural numbers
1. 5
2. 5.5
3. 6
4. 10
Q49. lim(x→0) sin(x)/x =
1. 0
2. 1
3. ∞
4. undefined
Q50. Coefficient of x^4 in (1 + x)^10 is
1. C(10,3)
2. C(10,4)
3. C(10,5)
4. 10!/4!