Daily MCQ Paper — 13 April 2026

Daily MCQ Paper — 13 April 2026

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

1. Q1. A spring of force constant k is compressed by x. The elastic PE stored is
   1. kx
   2. (1/2)kx
   3. (1/2)kx²
   4. kx²
2. Q2. The work-energy theorem states that the net work done on a particle equals
   1. Change in its momentum
   2. Change in its kinetic energy
   3. Change in its potential energy
   4. Change in its total energy
3. Q3. Power delivered by a constant force F to a body moving with velocity v is
   1. Fv
   2. Fv²
   3. F·v (dot product)
   4. F/v
4. Q4. For a satellite in circular orbit of radius r around Earth (mass M), orbital velocity is
   1. sqrt(GM/r)
   2. sqrt(2GM/r)
   3. GM/r
   4. sqrt(GMr)
5. Q5. Kepler's third law states T² is proportional to
   1. a
   2. a²
   3. a³
   4. 1/a
6. Q6. Escape velocity from Earth's surface (R, g) is
   1. sqrt(gR)
   2. sqrt(2gR)
   3. sqrt(gR/2)
   4. 2sqrt(gR)
7. Q7. Total mechanical energy of a satellite in circular orbit of radius r is
   1. -GMm/r
   2. -GMm/(2r)
   3. +GMm/(2r)
   4. -GMm/(4r)
8. Q8. Kirchhoff's junction rule is a consequence of
   1. Conservation of energy
   2. Conservation of charge
   3. Conservation of momentum
   4. Ohm's law
9. Q9. In a balanced Wheatstone bridge (P,Q,R,S), the condition is
   1. P/Q = R/S
   2. P/R = Q/S
   3. P·Q = R·S
   4. PQRS = 1
10. Q10. Time constant of an RC charging circuit is
    1. R/C
    2. RC
    3. R+C
    4. 1/(RC)
11. Q11. The maximum line-of-sight distance for a transmitting antenna of height h on a smooth earth (radius R) is approximately
    1. √(2Rh)
    2. √(Rh)
    3. 2√(Rh)
    4. Rh
12. Q12. de Broglie wavelength of an electron with KE 100 eV is approximately
    1. 0.123 nm
    2. 1.23 nm
    3. 12.3 nm
    4. 0.0123 nm
13. Q13. A magnetic dipole in a uniform field B has potential energy U = -m·B. It is in stable equilibrium when
    1. m parallel to B
    2. m antiparallel to B
    3. m perpendicular to B
    4. m at 45° to B
14. Q14. Maxwell's equation relating curl of B to current and changing E-field is
    1. Gauss's law
    2. Faraday's law
    3. Ampere-Maxwell law
    4. Gauss's law for magnetism
15. Q15. Fourier law of heat conduction is dQ/dt =
    1. -kA dT/dx
    2. kA dT
    3. kA T^4
    4. -k dT/dx
16. Q16. In photoelectric effect, stopping potential depends on
    1. Intensity only
    2. Frequency only
    3. Both
    4. Neither
17. Q17. The efficiency of a Carnot engine working between T1 (hot) and T2 (cold) is
    1. 1 − T2/T1
    2. T1/T2 − 1
    3. T2/T1
    4. (T1−T2)/T2
18. Q18. The diagonal relationship in periodic table is between
    1. Li-Be
    2. Li-Mg
    3. Be-B
    4. Na-Mg
19. Q19. LiCl is more covalent than NaCl primarily due to
    1. Smaller size of Li+
    2. Higher electronegativity of Li
    3. Polarising power of Li+ (Fajans rules)
    4. Li being lighter
20. Q20. Diborane (B₂H₆) has bonding involving
    1. Only 2c-2e bonds
    2. Two 3c-2e (banana) bonds + four 2c-2e bonds
    3. Only 3c-2e bonds
    4. Hydrogen bonds only
21. Q21. Zeolites belong to the class of
    1. Borosilicates
    2. Aluminosilicates
    3. Carbonates
    4. Phosphates
22. Q22. First transition series elements typically show
    1. Only +2 oxidation state
    2. Variable oxidation states due to participation of (n-1)d electrons
    3. Only +3
    4. +1 only
23. Q23. Borax bead test is based on formation of
    1. Sodium meta-borate
    2. Coloured metaborates of transition metals
    3. Sodium tetraborate
    4. Boric acid
24. Q24. The most stable allotrope of carbon at standard conditions is
    1. Diamond
    2. Graphite
    3. Fullerene
    4. Amorphous carbon
25. Q25. The intense colour of transition-metal complexes is due to
    1. s-s transitions
    2. p-p transitions
    3. d-d transitions
    4. f-f transitions
26. Q26. The catalytic activity of d-block metals is attributed to
    1. Inert pair effect
    2. Variable oxidation states + ability to provide adsorption sites
    3. Diamagnetism
    4. Lanthanoid contraction
27. Q27. The element with strongest reducing nature in the first transition series in aqueous solution (E°) is
    1. Sc
    2. Cr
    3. Mn
    4. Cu
28. Q28. Compared to lanthanides, actinide contraction is
    1. Smaller
    2. Greater (5f shielding poorer)
    3. Same
    4. Reverse
29. Q29. 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
30. Q30. Bakelite is a polymer of
    1. Phenol + formaldehyde
    2. Urea + formaldehyde
    3. Vinyl chloride
    4. Styrene + butadiene
31. Q31. Magnetic moment of [Fe(CN)6]³⁻ (low-spin d⁵, 1 unpaired) is approximately
    1. √3 BM
    2. √5 BM
    3. √15 BM
    4. 5.92 BM
32. Q32. Nylon 6,6 is a
    1. Addition polymer
    2. Condensation polymer of hexamethylenediamine and adipic acid
    3. Natural polymer
    4. Vulcanised rubber
33. Q33. Peptide bond between amino acids is a
    1. C-N bond formed by condensation
    2. C-O bond
    3. C-C bond
    4. S-S bond
34. Q34. 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
35. Q35. The dot product a·b of two vectors a and b is
    1. |a||b|sinθ
    2. |a||b|cosθ
    3. |a×b|
    4. |a|+|b|
36. Q36. The scalar triple product [a b c] gives
    1. Area of parallelogram
    2. Volume of parallelepiped
    3. A vector
    4. Zero always
37. Q37. The cross product a×b yields a vector
    1. Parallel to a
    2. Parallel to b
    3. Perpendicular to both a and b
    4. In the plane of a and b
38. Q38. The equation of a line through point A(a) parallel to vector b in vector form is
    1. r = a
    2. r = a + λb
    3. r·b = 0
    4. r×b = a
39. Q39. The shortest distance between two skew lines r = a₁+λb₁ and r = a₂+μb₂ is
    1. |(a₂-a₁)·(b₁×b₂)| / |b₁×b₂|
    2. |a₂-a₁|
    3. |b₁×b₂|
    4. |(a₂-a₁)×(b₁×b₂)|
40. Q40. Bayes theorem expresses P(A|B) as
    1. P(A)P(B)/P(A∩B)
    2. P(B|A)P(A)/P(B)
    3. P(A∪B)/P(B)
    4. P(A)+P(B)-P(A∩B)
41. Q41. For a binomial distribution B(n,p), mean and variance are
    1. np, np
    2. np, npq
    3. n²p, npq
    4. np, p²q
42. Q42. If A is a 3×3 matrix with |A| ≠ 0, then A⁻¹ equals
    1. adj(A)/|A|
    2. |A|·adj(A)
    3. adj(A)·|A|²
    4. (adj A)⁻¹
43. Q43. The system AX = B has a unique solution if
    1. |A| = 0
    2. |A| ≠ 0
    3. rank(A) < n
    4. A is singular
44. Q44. If two rows (or columns) of a determinant are interchanged, the determinant
    1. Remains same
    2. Becomes zero
    3. Changes sign
    4. Doubles
45. Q45. 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
46. Q46. lim(x→0) sin(x)/x =
    1. 0
    2. 1
    3. ∞
    4. undefined
47. Q47. The angle between two lines with direction ratios (a₁,b₁,c₁) and (a₂,b₂,c₂) satisfies
    1. cosθ = (a₁a₂+b₁b₂+c₁c₂)/(√Σa₁²·√Σa₂²)
    2. sinθ = …
    3. tanθ = a₁/a₂
    4. cosθ = 1
48. Q48. ∫(0 to π) sin x dx =
    1. 0
    2. 1
    3. 2
    4. π
49. Q49. Sum of binomial coefficients in expansion of (1 + x)ⁿ is
    1. 2ⁿ
    2. 3ⁿ
    3. n²
    4. n!
50. Q50. The locus of |z – 2| = |z + 2| in the complex plane is
    1. Circle
    2. Real axis
    3. Imaginary axis
    4. Parabola