Daily MCQ Paper — 16 April 2026

April 16, 2026 ·

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Daily Practice Sheet — 50 Questions

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Daily MCQ Paper — 16 April 2026

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

Q1. In an adiabatic process for an ideal gas
1. PV = constant
2. PV^γ = constant
3. TV = constant
4. P/T = constant
Q2. 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
Q3. For an ideal gas in an isothermal process
1. dU = 0
2. dQ = 0
3. dW = 0
4. dS = 0
Q4. 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
Q5. 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)
Q6. 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
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)
Q8. The number of degrees of freedom of a diatomic molecule at room temperature is
1. 3
2. 5
3. 6
4. 7
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)
Q10. In SHM, at the mean position the energy is
1. Entirely potential
2. Entirely kinetic
3. Equally divided
4. Zero
Q11. The resonance frequency of a series LCR circuit with L = 2 H and C = 8 µF is approximately
1. 40 Hz
2. 25 Hz
3. 100 Hz
4. 400 Hz
Q12. 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
Q13. In a stationary wave, distance between two consecutive nodes is
1. λ
2. λ/2
3. λ/4
4. 2λ
Q14. In a perfectly elastic 1-D collision between equal masses, the velocities
1. Are exchanged
2. Both become zero
3. Both become equal
4. Reverse signs
Q15. In a step-up transformer
1. Ns < Np
2. Ns = Np
3. Ns > Np
4. Independent of N
Q16. Escape velocity from Earth's surface is approximately
1. 7.9 km/s
2. 11.2 km/s
3. 13.6 km/s
4. 9.8 km/s
Q17. Sky-wave propagation uses
1. Direct line of sight
2. Reflection from troposphere
3. Reflection from ionosphere
4. Surface diffraction
Q18. 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
Q19. 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
Q20. 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
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
Q22. 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
Q23. For a spontaneous process at constant T and P
1. ΔG > 0
2. ΔG = 0
3. ΔG < 0
4. ΔS = 0
Q24. The order of a reaction can be
1. Zero
2. Fractional
3. Negative
4. All of these
Q25. 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)
Q26. The bond enthalpy of H-H is approximately (kJ/mol)
1. 436
2. 347
3. 414
4. 498
Q27. Hess's law of constant heat summation is a consequence of
1. First law
2. Second law
3. Third law
4. Zeroth law
Q28. 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
Q29. Which actinide shows the maximum oxidation state of +7?
1. U
2. Np
3. Pu
4. Am
Q30. Nernst equation for an electrode reaction at 298 K is E = E° –
1. (0.0591/n) log Q
2. (0.0591/n) ln Q
3. (0.0257/n) log Q
4. (2.303*RT/F) log Q
Q31. Faraday's first law of electrolysis states
1. m ∝ Q
2. m ∝ V
3. m ∝ I²
4. m ∝ 1/Q
Q32. Boyle's law states
1. PV = constant at constant T
2. V/T = constant
3. P/T = constant
4. PV/T = constant
Q33. One major consequence of lanthanide contraction is
1. Zr and Hf have similar atomic radii
2. Increase in metallic character
3. Higher reactivity of 5d elements
4. None
Q34. Brown ring test confirms
1. NO2-
2. NO3-
3. Cl-
4. SO4^2-
Q35. ∫ 1/x dx =
1. x ln x + C
2. ln|x| + C
3. 1/x + C
4. −1/x^2 + C
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
Q37. ∫(0 to π) sin x dx =
1. 0
2. 1
3. 2
4. π
Q38. 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
Q39. ∫ 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
Q40. 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
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
Q42. 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)
Q43. 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)
Q44. The integrating factor of dy/dx + Py = Q is
1. e^∫P dx
2. e^∫Q dx
3. e^−∫P dx
4. ∫P dx
Q45. A statement that is always true is called
1. Contradiction
2. Tautology
3. Contingency
4. Disjunction
Q46. By multinomial theorem, the number of terms in (x + y + z)^n is
1. n + 1
2. n+2 choose 2
3. n+1 choose 2
4. n^2
Q47. Length of latus rectum of y² = 16x is
1. 4
2. 8
3. 16
4. 32
Q48. tan^-1 x + tan^-1 y = tan^-1((x + y)/(1 – xy)) holds when
1. xy < 1
2. xy > 1
3. xy = 1
4. x + y = 0
Q49. In linear regression Y = a + bX, the slope b equals
1. Cov(X,Y)/Var(Y)
2. Cov(X,Y)/Var(X)
3. Var(X)/Cov(X,Y)
4. r
Q50. log₂ 32 =
1. 4
2. 5
3. 6
4. 8