Daily MCQ Paper — 31 March 2026

Daily MCQ Paper — 31 March 2026

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

1. Q1. In an electromagnetic wave, the ratio of E to B amplitudes equals
   1. c (speed of light)
   2. 1/c
   3. c²
   4. 1
2. Q2. A liquid of total column length L oscillates in a U-tube. The time period of small oscillations is
   1. 2π√(L/g)
   2. 2π√(L/2g)
   3. 2π√(2L/g)
   4. 2π√(L/g) /2
3. Q3. In a Wheatstone bridge balanced at P/Q = R/S, the current through the galvanometer is
   1. Zero
   2. I/2
   3. I
   4. Maximum
4. Q4. At resonance in a forced oscillator, the driving frequency equals the
   1. Damped frequency
   2. Natural frequency of the oscillator
   3. Half the natural frequency
   4. Twice the natural frequency
5. Q5. The drift velocity v_d of electrons in a conductor of cross-section A carrying current I, with electron density n, is
   1. v_d = I/(nAe)
   2. v_d = nAe/I
   3. v_d = IA/(ne)
   4. v_d = nIe/A
6. Q6. In an ideal step-down transformer, if N_p > N_s, then
   1. V_s < V_p, I_s > I_p
   2. V_s > V_p, I_s < I_p
   3. V_s = V_p
   4. Both V and I decrease
7. Q7. In a damped oscillator, the amplitude decays as
   1. A₀ e^(-bt/2m)
   2. A₀ e^(-bt/m)
   3. A₀ cos(ωt)
   4. A₀ (1-bt)
8. Q8. The speed of electromagnetic waves in vacuum is given by
   1. c = 1/√(μ₀ε₀)
   2. c = √(μ₀ε₀)
   3. c = μ₀/ε₀
   4. c = ε₀/μ₀
9. Q9. A rod of length L moves with velocity v perpendicular to a uniform magnetic field B. The motional EMF induced across its ends is
   1. BLv
   2. BL/v
   3. Bv/L
   4. B²Lv
10. Q10. X-rays were discovered by
    1. Roentgen
    2. Marie Curie
    3. Henri Becquerel
    4. J J Thomson
11. Q11. A solenoid of length l, area A, with N turns has self-inductance
    1. μ₀N²A/l
    2. μ₀NA/l
    3. μ₀N²Al
    4. μ₀NA·l
12. Q12. Maxwell's correction to Ampere's law introduced the concept of
    1. Magnetic monopoles
    2. Displacement current
    3. Electromagnetic flux
    4. Vector potential
13. Q13. Two springs of force constants k₁ and k₂ in series have an equivalent spring constant
    1. k₁ + k₂
    2. k₁k₂/(k₁+k₂)
    3. k₁/k₂
    4. (k₁+k₂)/k₁k₂
14. Q14. Energy stored in an inductor carrying current I is
    1. ½ LI
    2. ½ LI²
    3. LI²
    4. LI
15. Q15. According to Lenz's law, the induced current opposes
    1. The cause that produced it
    2. The direction of magnetic field
    3. The motion of the conductor only
    4. The flux through the loop only
16. Q16. Eddy currents are utilised in
    1. Electric brakes and induction furnaces
    2. Galvanometer suspension wires
    3. Capacitors
    4. Diodes
17. Q17. The time constant of an RC circuit is
    1. RC
    2. R/C
    3. C/R
    4. 1/(RC)
18. Q18. The Hofmann bromamide rearrangement converts
    1. RCONH₂ to RNH₂ (with loss of CO₂)
    2. RNH₂ to RCONH₂
    3. RCN to RCH₂NH₂
    4. RNO₂ to RNH₂
19. Q19. Aniline is less basic than ammonia because
    1. The lone pair on N is delocalised into the benzene ring
    2. Steric hindrance
    3. High electronegativity of phenyl
    4. Hydrogen bonding
20. Q20. Gabriel's phthalimide synthesis is used to prepare
    1. Tertiary amines
    2. Pure primary amines (without secondary/tertiary contamination)
    3. Secondary amines
    4. Aromatic amines like aniline
21. Q21. In a body-centred cubic (BCC) unit cell, the number of atoms is
    1. 1
    2. 2
    3. 4
    4. 8
22. Q22. Hinsberg test distinguishes 1°, 2°, 3° amines using
    1. Benzenesulfonyl chloride (C₆H₅SO₂Cl)
    2. Acetyl chloride
    3. Hydrochloric acid
    4. Sodium nitrite
23. Q23. Diazonium salts (ArN₂⁺X⁻) are typically prepared at temperature
    1. 0-5°C
    2. 25°C
    3. 100°C
    4. -78°C
24. Q24. The iodoform test (CHI₃ yellow ppt with I₂/NaOH) is positive for
    1. Methyl ketones (CH₃CO-R), CH₃CH(OH)R, CH₃CHO and ethanol
    2. All ketones
    3. All aldehydes
    4. Carboxylic acids
25. Q25. The Clemmensen reduction reduces R-C=O to R-CH₂- using
    1. Zn-Hg / HCl
    2. LiAlH₄
    3. NaBH₄
    4. H₂/Pt
26. Q26. Aldol condensation of two molecules of acetaldehyde in dilute NaOH gives
    1. Acetone
    2. 3-Hydroxybutanal (β-hydroxybutyraldehyde) → on heating → crotonaldehyde
    3. Acetic acid
    4. Ethanol
27. Q27. Carbylamine reaction (1° amine + CHCl₃ + KOH → RNC) is a test for
    1. Tertiary amines
    2. Primary amines (gives foul-smelling isocyanide)
    3. Secondary amines
    4. Quaternary salts
28. Q28. NaCl crystal structure has Cl⁻ ions in fcc arrangement with Na⁺ ions occupying
    1. All tetrahedral voids
    2. All octahedral voids
    3. Half of tetrahedral voids
    4. Body-centre only
29. Q29. The Sandmeyer reaction replaces the diazo group with halide using
    1. Cu/HCl
    2. CuCl/HCl, CuBr/HBr, or CuCN/KCN
    3. Pd/H₂
    4. Zn/HCl
30. Q30. Coupling of diazonium salt with phenol in alkaline medium gives
    1. Para-hydroxyazobenzene (orange dye)
    2. Aniline
    3. Cyclohexane
    4. Benzaldehyde
31. Q31. The Cannizzaro reaction occurs with aldehydes that have
    1. α-hydrogen atoms
    2. No α-hydrogen atoms (e.g., HCHO, C₆H₅CHO, (CH₃)₃CCHO)
    3. Hydroxyl groups
    4. Halogen substituents
32. Q32. The packing efficiency in a hexagonal close-packed (hcp) lattice is
    1. 52%
    2. 68%
    3. 74%
    4. 100%
33. Q33. A Schottky defect in an ionic solid is a
    1. Pair of cation and anion vacancies (preserves stoichiometry)
    2. Misplaced atom
    3. Cation in interstitial site
    4. Foreign impurity
34. Q34. In a face-centred cubic (FCC) unit cell, the number of atoms per unit cell is
    1. 1
    2. 2
    3. 4
    4. 8
35. Q35. Principal value branch of cos^-1 x is
    1. [-pi/2, pi/2]
    2. [0, pi]
    3. (0, pi)
    4. [-pi, 0]
36. Q36. The inradius r of a triangle is given by (s = semi-perimeter, Delta = area)
    1. Delta * s
    2. Delta / s
    3. s / Delta
    4. s * Delta
37. Q37. The non-real cube roots of unity are 1, ω, ω² where 1 + ω + ω² equals
    1. 0
    2. 1
    3. 3
    4. ω
38. Q38. If x = a cos t and y = a sin t, then dy/dx equals
    1. -cot t
    2. -tan t
    3. tan t
    4. cot t
39. Q39. By De Moivre's theorem, (cos θ + i sin θ)ⁿ equals
    1. cos(nθ) + i sin(nθ) for integer n
    2. cos(θⁿ) + i sin(θⁿ)
    3. n cosθ + n i sinθ
    4. cos θ – i sin θ
40. Q40. Order and degree of differential equation (d^2 y/dx^2)^3 + (dy/dx)^2 + y = 0 are
    1. 2 and 3
    2. 3 and 2
    3. 2 and 1
    4. 3 and 3
41. Q41. The principal argument of z = -1 + i is
    1. π/4
    2. 3π/4
    3. -π/4
    4. -3π/4
42. Q42. Maximum value of y = sin x + cos x is
    1. 1
    2. √2
    3. 2
    4. √3
43. Q43. A function f: A -> B is bijective if and only if
    1. It is injective only
    2. It is surjective only
    3. It is both injective and surjective
    4. It is constant
44. Q44. Four points P1, P2, P3, P4 in 3D are coplanar iff
    1. They lie on x-axis
    2. Scalar triple product [P2-P1, P3-P1, P4-P1]=0
    3. They are equidistant
    4. They form a parallelogram
45. Q45. Negation of “For all x, p(x)” is
    1. For all x, not p(x)
    2. There exists x such that not p(x)
    3. There exists x such that p(x)
    4. None
46. Q46. If α and β are roots of ax² + bx + c = 0, then α + β and αβ are
    1. -c/a, b/a
    2. -b/a, c/a
    3. b/a, -c/a
    4. b/a, c/a
47. Q47. Lagrange Mean Value Theorem states that for f continuous on [a,b] and differentiable on (a,b), there exists c in (a,b) such that
    1. f'(c)=0
    2. f(b)-f(a)=f'(c)(b-a)
    3. f(b)+f(a)=2f'(c)
    4. f(c)=0
48. Q48. Coefficient of variation is
    1. sigma
    2. sigma / x_bar
    3. (sigma / x_bar) x 100
    4. x_bar
49. Q49. The scalar triple product [a b c] gives
    1. Area of parallelogram
    2. Volume of parallelepiped
    3. A vector
    4. Zero always
50. Q50. The vector triple product a×(b×c) equals
    1. (a·c)b – (a·b)c
    2. (a·b)c – (a·c)b
    3. a·(b×c)
    4. b×(a×c)