Daily MCQ Paper — 21 April 2026

April 21, 2026 ·

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Daily Practice Sheet — 50 Questions

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Daily MCQ Paper — 21 April 2026

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

Q1. 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
Q2. 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
Q3. 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
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. 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
Q7. 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
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. Fourier law of heat conduction is dQ/dt =
1. -kA dT/dx
2. kA dT
3. kA T^4
4. -k dT/dx
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. A particle moves with v(t)=4t² m/s. Acceleration at t=2 s is
1. 8 m/s²
2. 12 m/s²
3. 16 m/s²
4. 4 m/s²
Q12. The work done in moving a charge in equipotential surface is
1. Maximum
2. Zero
3. Negative
4. Depends on path
Q13. A satellite at height h has orbital speed
1. √(GM/(R+h))
2. √(GMR)
3. √(GM/h)
4. √(2GM/R)
Q14. A 2 kg block slides down a frictionless incline of 30°. Acceleration is
1. 5 m/s²
2. 9.8 m/s²
3. 4.9 m/s²
4. 7 m/s²
Q15. Two resistors 6 ohm and 3 ohm are in parallel. Equivalent resistance is
1. 9 ohm
2. 2 ohm
3. 4.5 ohm
4. 1.5 ohm
Q16. A capacitor of 4 µF charged to 100 V stores energy of
1. 0.02 J
2. 0.04 J
3. 0.2 J
4. 0.4 J
Q17. Young's modulus has dimensions of
1. Force
2. Pressure
3. Energy
4. Power
Q18. A Frenkel defect involves
1. Vacancy only
2. Cation displaced to interstitial site
3. Removal of both ions
4. Substitution of impurity
Q19. 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
Q20. Froth flotation is used for concentration of
1. Oxide ores
2. Sulphide ores
3. Carbonate ores
4. Native metals
Q21. n-type semiconductor is produced by doping silicon with
1. Boron
2. Phosphorus
3. Aluminium
4. Gallium
Q22. 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
Q23. The basicity of H3PO4 (orthophosphoric acid) is
1. 1
2. 2
3. 3
4. 4
Q24. Mond process is used for refining
1. Copper
2. Zinc
3. Nickel
4. Iron
Q25. Leaching of gold and silver uses
1. Conc. HCl
2. Dilute NaCN with air
3. Conc. HNO3
4. Dilute H2SO4
Q26. 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
Q27. 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
Q28. Half-life of a zero-order reaction is
1. t = [A]₀/(2k)
2. t = ln2/k
3. t = 1/(k[A]₀)
4. t = [A]₀/k
Q29. Number of stereoisomers possible for 2-bromobutane is
1. 1
2. 2
3. 3
4. 4
Q30. Lanthanide contraction refers to
1. Increase in atomic radius across La-Lu
2. Decrease in atomic radius across La-Lu
3. Constant radius
4. Random variation
Q31. EMF of a Daniell cell (Zn|Zn2+ || Cu2+|Cu) under standard conditions is approximately
1. +0.34 V
2. +0.76 V
3. +1.10 V
4. +1.50 V
Q32. The pH of 0.001 M HCl is
1. 2
2. 3
3. 4
4. 11
Q33. Molality is defined as
1. Moles solute per litre solution
2. Moles solute per kg solvent
3. Mass solute per litre
4. Moles solute per mole solvent
Q34. Glucose and fructose are linked by which bond in sucrose?
1. α(1→4) glycosidic
2. α(1→2)β glycosidic
3. β(1→4) glycosidic
4. peptide
Q35. 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
Q36. 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)
Q37. 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)
Q38. 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
Q39. 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
Q40. Principal value of sin^-1(1/2) is
1. pi/3
2. pi/6
3. pi/4
4. pi/2
Q41. 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
Q42. 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
Q43. 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
Q44. 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
Q45. Maximum value of y = sin x + cos x is
1. 1
2. √2
3. 2
4. √3
Q46. log₂ 32 =
1. 4
2. 5
3. 6
4. 8
Q47. lim x->0 (sin x)/x =
1. 0
2. 1
3. infinity
4. Undefined
Q48. The general solution of dy/dx = y is
1. y = Cx
2. y = C e^x
3. y = ln x + C
4. y = C/x
Q49. The eccentricity of ellipse x²/25 + y²/16 = 1 is
1. 3/5
2. 4/5
3. 3/4
4. 5/4
Q50. Cramer's rule applies when
1. |A| = 0
2. |A| ≠ 0
3. A is singular
4. A is rectangular