Daily MCQ Paper — 30 March 2026

Daily MCQ Paper — 30 March 2026

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

1. Q1. X-rays were discovered by
   1. Roentgen
   2. Marie Curie
   3. Henri Becquerel
   4. J J Thomson
2. Q2. 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
3. Q3. 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
4. Q4. Energy stored in an inductor carrying current I is
   1. ½ LI
   2. ½ LI²
   3. LI²
   4. LI
5. Q5. Eddy currents are utilised in
   1. Electric brakes and induction furnaces
   2. Galvanometer suspension wires
   3. Capacitors
   4. Diodes
6. Q6. 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)
7. Q7. 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
8. Q8. 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
9. Q9. The time constant of an RC circuit is
   1. RC
   2. R/C
   3. C/R
   4. 1/(RC)
10. Q10. Maxwell's correction to Ampere's law introduced the concept of
    1. Magnetic monopoles
    2. Displacement current
    3. Electromagnetic flux
    4. Vector potential
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. 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
13. Q13. In an electromagnetic wave, the ratio of E to B amplitudes equals
    1. c (speed of light)
    2. 1/c
    3. c²
    4. 1
14. Q14. 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
15. Q15. 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
16. Q16. 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
17. Q17. 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
18. Q18. 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
19. Q19. 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
20. Q20. Coupling of diazonium salt with phenol in alkaline medium gives
    1. Para-hydroxyazobenzene (orange dye)
    2. Aniline
    3. Cyclohexane
    4. Benzaldehyde
21. Q21. 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
22. Q22. 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
23. Q23. 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
24. Q24. 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
25. Q25. 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
26. Q26. Diazonium salts (ArN₂⁺X⁻) are typically prepared at temperature
    1. 0-5°C
    2. 25°C
    3. 100°C
    4. -78°C
27. Q27. 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
28. Q28. 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
29. Q29. The Clemmensen reduction reduces R-C=O to R-CH₂- using
    1. Zn-Hg / HCl
    2. LiAlH₄
    3. NaBH₄
    4. H₂/Pt
30. Q30. In a face-centred cubic (FCC) unit cell, the number of atoms per unit cell is
    1. 1
    2. 2
    3. 4
    4. 8
31. Q31. In a body-centred cubic (BCC) unit cell, the number of atoms is
    1. 1
    2. 2
    3. 4
    4. 8
32. Q32. The packing efficiency in a hexagonal close-packed (hcp) lattice is
    1. 52%
    2. 68%
    3. 74%
    4. 100%
33. Q33. Hinsberg test distinguishes 1°, 2°, 3° amines using
    1. Benzenesulfonyl chloride (C₆H₅SO₂Cl)
    2. Acetyl chloride
    3. Hydrochloric acid
    4. Sodium nitrite
34. Q34. 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
35. Q35. Rolle's theorem requires f to be
    1. Continuous on (a,b) only
    2. Continuous on [a,b], differentiable on (a,b), and f(a)=f(b) — guarantees ∃c∈(a,b) with f'(c)=0
    3. Differentiable everywhere
    4. Linear
36. Q36. lim_{x->0} (1-cos x)/x^2 equals
    1. 0
    2. 1/2
    3. 1
    4. infinity
37. Q37. The "king property" of definite integrals states ∫_a^b f(x)dx equals
    1. ∫_a^b f(a+b-x) dx
    2. ∫_a^b f(b-x) dx
    3. ∫_a^b f(x+a) dx
    4. -∫_a^b f(x) dx
38. Q38. Rolles theorem requires the function to be
    1. Continuous on [a,b], differentiable on (a,b) and f(a) = f(b)
    2. Only continuous on [a,b]
    3. Only differentiable on (a,b)
    4. Monotonic on [a,b]
39. Q39. 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
40. Q40. 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
41. Q41. 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)
42. Q42. The equation of the tangent to the circle x² + y² = 25 at the point (3, 4) is
    1. 3x + 4y = 25
    2. 3x – 4y = 25
    3. 4x + 3y = 25
    4. x + y = 7
43. Q43. For a binomial distribution B(n,p), mean and variance are
    1. np, np
    2. np, npq
    3. n²p, npq
    4. np, p²q
44. Q44. The length of the latus rectum of the parabola y² = 16x is
    1. 4
    2. 8
    3. 16
    4. 32
45. Q45. The eccentricity of the ellipse x²/25 + y²/9 = 1 is
    1. 3/5
    2. 4/5
    3. 5/3
    4. 5/4
46. Q46. For complex numbers, |z1·z2| equals
    1. |z1| + |z2|
    2. |z1| · |z2|
    3. |z1|/|z2|
    4. |z1|² + |z2|²
47. Q47. If f'(x0)=0 and f''(x0)<0, then x0 is a
    1. Point of inflection
    2. Local maximum
    3. Local minimum
    4. Saddle point
48. Q48. If two rows (or columns) of a determinant are interchanged, the determinant
    1. Remains same
    2. Becomes zero
    3. Changes sign
    4. Doubles
49. Q49. The greatest coefficient in the expansion of (1 + x)²ⁿ is
    1. nCn
    2. 2nCn
    3. 2nCn-1
    4. 2nC1
50. Q50. The shortest distance between two skew lines r=a1+λb1 and r=a2+μb2 is
    1. |(a2-a1)·(b1×b2)|/|b1×b2|
    2. Always zero
    3. |a1-a2|
    4. |b1-b2|