Daily MCQ Paper — 14 April 2026

Daily MCQ Paper — 14 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. 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)
3. Q3. Time constant of an RC charging circuit is
   1. R/C
   2. RC
   3. R+C
   4. 1/(RC)
4. Q4. 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
5. Q5. Escape velocity from Earth's surface (R, g) is
   1. sqrt(gR)
   2. sqrt(2gR)
   3. sqrt(gR/2)
   4. 2sqrt(gR)
6. Q6. Kepler's third law states T² is proportional to
   1. a
   2. a²
   3. a³
   4. 1/a
7. Q7. 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
8. Q8. 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)
9. Q9. Kirchhoff's junction rule is a consequence of
   1. Conservation of energy
   2. Conservation of charge
   3. Conservation of momentum
   4. Ohm's law
10. Q10. 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
11. Q11. 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
12. Q12. On a p-V diagram, the area under an isothermal expansion equals
    1. Internal energy change
    2. Work done by the gas
    3. Heat absorbed only
    4. Both work and heat (since ΔU=0)
13. Q13. For an ideal gas in an isothermal process
    1. dU = 0
    2. dQ = 0
    3. dW = 0
    4. dS = 0
14. Q14. Magnetic dipole moment of a current loop of N turns, area A and current I is
    1. NIA
    2. I/A
    3. NA/I
    4. N/IA
15. Q15. The self-inductance of a long solenoid (n turns/m, area A, length l) is
    1. mu0*n*A*l
    2. mu0*n^2*A*l
    3. mu0*n^2*A/l
    4. mu0*n*A^2*l
16. Q16. Visible light has wavelength range approximately
    1. 100-400 nm
    2. 400-700 nm
    3. 700-1000 nm
    4. 1-100 nm
17. Q17. The rms speed of gas molecules of molar mass M at temperature T is
    1. sqrt(RT/M)
    2. sqrt(2RT/M)
    3. sqrt(3RT/M)
    4. sqrt(8RT/πM)
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. Borax bead test is based on formation of
    1. Sodium meta-borate
    2. Coloured metaborates of transition metals
    3. Sodium tetraborate
    4. Boric acid
22. Q22. The most stable allotrope of carbon at standard conditions is
    1. Diamond
    2. Graphite
    3. Fullerene
    4. Amorphous carbon
23. Q23. Zeolites belong to the class of
    1. Borosilicates
    2. Aluminosilicates
    3. Carbonates
    4. Phosphates
24. Q24. 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
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. Tyndall effect is shown by
    1. True solutions
    2. Colloidal solutions
    3. Suspensions
    4. Both colloidal and suspensions
29. Q29. The bond enthalpy of H-H is approximately (kJ/mol)
    1. 436
    2. 347
    3. 414
    4. 498
30. Q30. Faraday's first law of electrolysis states
    1. m ∝ Q
    2. m ∝ V
    3. m ∝ I²
    4. m ∝ 1/Q
31. Q31. Van't Hoff factor i for NaCl in water (assuming complete dissociation) is
    1. 1
    2. 2
    3. 3
    4. 4
32. Q32. The osmotic pressure equation is
    1. pi = nRT
    2. pi*V = nRT
    3. pi = nRT/V
    4. pi*V = R/T
33. Q33. The Henderson-Hasselbalch equation for a buffer is
    1. pH = pKa + log([salt]/[acid])
    2. pH = pKa − log([salt]/[acid])
    3. pH = pKa + log([acid]/[salt])
    4. pH = pKw − pKa
34. Q34. For a spontaneous process at constant T and P
    1. ΔG > 0
    2. ΔG = 0
    3. ΔG < 0
    4. ΔS = 0
35. Q35. 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
36. Q36. 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|
37. Q37. 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
38. Q38. 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)|
39. Q39. 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
40. Q40. The scalar triple product [a b c] gives
    1. Area of parallelogram
    2. Volume of parallelepiped
    3. A vector
    4. Zero always
41. Q41. 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)
42. Q42. For a binomial distribution B(n,p), mean and variance are
    1. np, np
    2. np, npq
    3. n²p, npq
    4. np, p²q
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. If y = f(g(x)), then dy/dx equals
    1. f'(g(x))
    2. g'(x)
    3. f'(g(x))·g'(x)
    4. f'(x)·g'(x)
46. Q46. The locus of a point equidistant from a fixed point and a fixed line is a
    1. Circle
    2. Parabola
    3. Ellipse
    4. Hyperbola
47. Q47. The equation of a plane in normal form is
    1. x + y + z = 0
    2. lx + my + nz = p
    3. ax + by + c = 0
    4. x = 0
48. Q48. If A is a 3×3 matrix with |A| = 5, then |adj A| =
    1. 5
    2. 25
    3. 125
    4. 1/5
49. Q49. Equation of parabola with focus (a,0) and directrix x = -a is
    1. y² = 4ax
    2. x² = 4ay
    3. x² = -4ay
    4. y² = -4ax
50. Q50. Sum of squares of first n natural numbers is
    1. n(n+1)/2
    2. n(n+1)(2n+1)/6
    3. [n(n+1)/2]²
    4. n²