Daily MCQ Paper — 15 April 2026

Daily MCQ Paper — 15 April 2026

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

1. Q1. The first law of thermodynamics is a statement of
   1. Conservation of mass
   2. Conservation of energy
   3. Conservation of momentum
   4. Conservation of charge
2. Q2. In an adiabatic process for an ideal gas
   1. PV = constant
   2. PV^γ = constant
   3. TV = constant
   4. P/T = constant
3. Q3. For an ideal gas in an isothermal process
   1. dU = 0
   2. dQ = 0
   3. dW = 0
   4. dS = 0
4. Q4. 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)
5. Q5. 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
6. Q6. The number of degrees of freedom of a diatomic molecule at room temperature is
   1. 3
   2. 5
   3. 6
   4. 7
7. Q7. The time period of a simple pendulum of length L (small angle) is
   1. 2π√(g/L)
   2. 2π√(L/g)
   3. π√(L/g)
   4. (1/2π)√(L/g)
8. Q8. By the equipartition theorem, energy per degree of freedom per molecule is
   1. kT
   2. (1/2)kT
   3. (3/2)kT
   4. (5/2)kT
9. Q9. Two springs of constants k1 and k2 connected in parallel give effective k =
   1. k1 + k2
   2. k1k2/(k1+k2)
   3. (k1+k2)/2
   4. sqrt(k1k2)
10. Q10. In SHM, at the mean position the energy is
    1. Entirely potential
    2. Entirely kinetic
    3. Equally divided
    4. Zero
11. Q11. 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
12. Q12. Visible light has wavelength range approximately
    1. 100-400 nm
    2. 400-700 nm
    3. 700-1000 nm
    4. 1-100 nm
13. Q13. Two capacitors of 4 µF and 6 µF are connected in series. The equivalent capacitance is
    1. 10 µF
    2. 2.4 µF
    3. 24 µF
    4. 5 µF
14. Q14. When a dielectric of constant K is fully inserted between plates of an isolated charged parallel-plate capacitor, the energy
    1. Increases K times
    2. Decreases K times
    3. Remains same
    4. Becomes K² times
15. Q15. In single-slit diffraction, the first minimum occurs at
    1. a sinθ = λ/2
    2. a sinθ = λ
    3. a sinθ = 2λ
    4. a sinθ = nλ where n = 0
16. Q16. Lenz's law is a consequence of conservation of
    1. Charge
    2. Energy
    3. Momentum
    4. Mass
17. Q17. 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
18. Q18. For a first-order reaction, the half-life is
    1. Independent of initial concentration
    2. Proportional to [A]0
    3. Inversely proportional to [A]0
    4. Proportional to [A]0^2
19. Q19. The Arrhenius equation is
    1. k = A·e^(−Ea/RT)
    2. k = A·e^(Ea/RT)
    3. k = A/RT
    4. k = ln(A) − Ea/RT
20. Q20. The order of a reaction can be
    1. Zero
    2. Fractional
    3. Negative
    4. All of these
21. Q21. For the reaction N2 + 3H2 ⇌ 2NH3, the relation between Kp and Kc is
    1. Kp = Kc
    2. Kp = Kc(RT)
    3. Kp = Kc(RT)^(−2)
    4. Kp = Kc(RT)^2
22. Q22. According to Le Chatelier's principle, increasing pressure on N2+3H2⇌2NH3 will
    1. Shift equilibrium left
    2. Shift equilibrium right (towards NH3)
    3. Have no effect
    4. Decompose NH3
23. Q23. 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
24. Q24. The solubility product Ksp of AgCl at 25°C is approximately
    1. 1.8 × 10^(−10)
    2. 1.0 × 10^(−14)
    3. 1.0 × 10^(−5)
    4. 1.6 × 10^(−2)
25. Q25. For a spontaneous process at constant T and P
    1. ΔG > 0
    2. ΔG = 0
    3. ΔG < 0
    4. ΔS = 0
26. Q26. Hess's law of constant heat summation is a consequence of
    1. First law
    2. Second law
    3. Third law
    4. Zeroth law
27. Q27. The bond enthalpy of H-H is approximately (kJ/mol)
    1. 436
    2. 347
    3. 414
    4. 498
28. Q28. van't Hoff factor i for NaCl in dilute solution (full dissociation) is
    1. 1
    2. 2
    3. 3
    4. 0.5
29. Q29. Leaching of gold and silver uses
    1. Conc. HCl
    2. Dilute NaCN with air
    3. Conc. HNO3
    4. Dilute H2SO4
30. Q30. The magnitude of crystal field splitting in tetrahedral vs octahedral (with same metal/ligand) is
    1. Equal
    2. Δt = (4/9)Δo
    3. Δt = (9/4)Δo
    4. Δt = 2Δo
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. Which actinide shows the maximum oxidation state of +7?
    1. U
    2. Np
    3. Pu
    4. Am
33. Q33. The spin-only magnetic moment formula is
    1. µ = √(n(n+2)) BM
    2. µ = n BM
    3. µ = √n BM
    4. µ = n² BM
34. Q34. Catalytic activity of transition metals is best explained by
    1. Their colour
    2. Variable oxidation states and ability to form intermediates
    3. Low atomic radius
    4. High lattice energy
35. Q35. ∫ 1/x dx =
    1. x ln x + C
    2. ln|x| + C
    3. 1/x + C
    4. −1/x^2 + C
36. Q36. ∫ e^x dx =
    1. e^x + C
    2. e^x/x + C
    3. x·e^x + C
    4. e^(x+1)/(x+1) + C
37. Q37. ∫ x·e^x dx (by parts) =
    1. xe^x + e^x + C
    2. xe^x − e^x + C
    3. x^2·e^x/2 + C
    4. e^x/x + C
38. Q38. ∫(0 to π) sin x dx =
    1. 0
    2. 1
    3. 2
    4. π
39. Q39. By the Newton-Leibniz theorem, d/dx ∫(a to x) f(t) dt =
    1. f(a)
    2. f(x)
    3. f(x) − f(a)
    4. F(x) − F(a)
40. Q40. The differential equation dy/dx = ky has solution
    1. y = kx + C
    2. y = Ce^(kx)
    3. y = C·sin(kx)
    4. y = k/x + C
41. Q41. The order of the differential equation (d^2y/dx^2)^3 + (dy/dx)^4 = sin x is
    1. 1
    2. 2
    3. 3
    4. 4
42. Q42. The area enclosed between y = x^2 and y = x from x=0 to x=1 is
    1. 1/6
    2. 1/3
    3. 1/2
    4. 1
43. Q43. The integrating factor of dy/dx + Py = Q is
    1. e^∫P dx
    2. e^∫Q dx
    3. e^−∫P dx
    4. ∫P dx
44. Q44. The differential equation modelling Newton's law of cooling is
    1. dT/dt = −k(T − Ts)
    2. dT/dt = k·T
    3. dT/dt = −kT^2
    4. dT/dt = k(T + Ts)
45. Q45. 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
46. Q46. Direction cosines of a line satisfy
    1. l + m + n = 1
    2. l² + m² + n² = 1
    3. lmn = 1
    4. l² + m² + n² = 0
47. Q47. A function is increasing on an interval if
    1. f'(x) >= 0 on that interval
    2. f'(x) <= 0
    3. f''(x) > 0
    4. f(x) > 0
48. Q48. The middle term in the expansion of (1 + x)¹⁰ is
    1. T5
    2. T6 (i.e., 6th term, r=5)
    3. T7
    4. T11
49. Q49. 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)
50. Q50. Solution of dy/dx = y is
    1. y = e^x + C
    2. y = Ce^x
    3. y = ln x + C
    4. y = x²