Daily MCQ Paper — 1 April 2026

Daily MCQ Paper — 1 April 2026

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

1. Q1. The dimensional formula of Young's modulus is the same as that of
   1. [ML^-1 T^-2] (same as pressure / stress)
   2. [MLT^-2]
   3. [ML^2 T^-2]
   4. [M^0 L^0 T^0]
2. Q2. The Poisson ratio σ = (lateral strain)/(longitudinal strain) for an isotropic material lies in the theoretical range
   1. -1 to 0.5
   2. 0 to 1
   3. -1 to 1
   4. -0.5 to 0.5
3. Q3. By Bernoulli's theorem along a streamline, P + ½ρv² + ρgh remains constant for a fluid that is
   1. Compressible and viscous
   2. Incompressible, non-viscous, and in steady streamline flow
   3. Compressible only
   4. Turbulent
4. Q4. The elastic potential energy stored per unit volume in a stretched wire is
   1. ½ × stress × strain
   2. stress × strain
   3. stress / strain
   4. ½ × Y × strain
5. Q5. Torricelli's law gives the efflux speed from an orifice in a tank of liquid of height h as
   1. v = √(gh)
   2. v = √(2gh)
   3. v = 2√(gh)
   4. v = gh
6. Q6. Stokes' law gives the terminal velocity of a sphere of radius r and density ρ falling in a fluid of viscosity η and density σ as
   1. v = 2(ρ-σ)gr² / (9η)
   2. v = (ρ-σ)g/η
   3. v = √(ρgr/η)
   4. v = ρgr/η
7. Q7. For a thin lens, the lens-maker's formula is
   1. 1/f = (n-1)(1/R1 – 1/R2)
   2. 1/f = (n+1)(1/R1 + 1/R2)
   3. f = (n-1)(R1 + R2)
   4. f = (n-1)R1
8. Q8. The capillary rise of a liquid in a tube is given by Jurin's law h = 2T cosθ/(ρgr); water rises in glass because
   1. θ > 90° and density is low
   2. The angle of contact θ < 90° for water-glass (acute) so cosθ is positive, producing capillary rise
   3. Mercury and water behave alike
   4. Surface tension is zero
9. Q9. The Reynolds number Re = ρvD/η; flow becomes turbulent typically when
   1. Re < 2000
   2. Re > 4000 (laminar for Re < 2000, transition between)
   3. Re = 0
   4. Re < 100
10. Q10. For a prism in minimum deviation position (δm), the refractive index is
    1. μ = sin((A+δm)/2) / sin(A/2)
    2. μ = sin A / sin δm
    3. μ = δm / A
    4. μ = (A-δm)/A
11. Q11. The minimum speed at the top of a vertical circular loop of radius R for a body to maintain contact is
    1. sqrt(gR)
    2. sqrt(2gR)
    3. sqrt(5gR)
    4. 0
12. Q12. In a pure inductor connected to AC source, the current
    1. Leads voltage by 90°
    2. Lags voltage by 90°
    3. Is in phase with voltage
    4. Lags by 45°
13. Q13. The Coefficient of Performance (COP) of a refrigerator working between T1 (hot) and T2 (cold) is
    1. T1/T2
    2. T2/(T1-T2)
    3. T1-T2
    4. (T1-T2)/T1
14. Q14. The escape velocity from Earth’s surface is approximately
    1. 7.9 km/s
    2. 11.2 km/s
    3. 3 km/s
    4. 30 km/s
15. Q15. In a perfectly elastic 1-D head-on collision between equal masses with one initially at rest, the velocities after collision are
    1. Both stop
    2. The moving particle stops and the stationary one moves with the original velocity
    3. They stick together
    4. Both move with v/2
16. Q16. Lenz's law is a consequence of conservation of
    1. Charge
    2. Energy
    3. Momentum
    4. Mass
17. Q17. The orbital speed of a satellite at radius r from Earth’s centre is
    1. sqrt(GM/r)
    2. sqrt(2GM/r)
    3. sqrt(GM r)
    4. GMr
18. Q18. In the laboratory, hydrogen gas is conveniently prepared by the reaction of
    1. Concentrated HCl with copper
    2. Granulated zinc with dilute H2SO4 → ZnSO4 + H2
    3. Sodium with water
    4. Iron with NaOH
19. Q19. The water-gas shift reaction used industrially to enrich hydrogen is
    1. CH4 + H2O → CO + 3H2
    2. CO + H2O → CO2 + H2 (catalysed by Fe2O3/Cr2O3 at ~673 K)
    3. C + 2H2O → CO2 + 2H2
    4. 2H2O → 2H2 + O2
20. Q20. Calgon, used as a water softener, is chemically
    1. Sodium aluminate
    2. Sodium hexametaphosphate (NaPO3)6 — sequesters Ca²⁺/Mg²⁺ into soluble complex
    3. Sodium carbonate
    4. Sodium silicate
21. Q21. Hydrogen peroxide is industrially manufactured by the
    1. Bosch process
    2. Auto-oxidation of 2-ethylanthraquinol (cyclic process with H2 reduction)
    3. Haber process
    4. Solvay process
22. Q22. In Group 1 alkali metals, the order of hydration enthalpy of M⁺ ions (most negative first) is
    1. Cs⁺ > Rb⁺ > K⁺ > Na⁺ > Li⁺
    2. Li⁺ > Na⁺ > K⁺ > Rb⁺ > Cs⁺ (smallest cation has highest charge density, most hydrated)
    3. K⁺ > Na⁺ > Cs⁺ > Li⁺
    4. All equal
23. Q23. Kharasch peroxide effect (anti-Markovnikov addition) is observed only for
    1. HCl
    2. HBr in presence of peroxides via free-radical chain mechanism
    3. HI
    4. HF
24. Q24. The Wurtz reaction synthesises higher alkanes from alkyl halides by treatment with
    1. Na/dry ether
    2. Zn/HCl
    3. KMnO4
    4. LiAlH4
25. Q25. Hückel's rule for aromaticity requires a planar, cyclic, fully conjugated system with
    1. 4n π electrons
    2. (4n+2) π electrons (n = 0,1,2,…)
    3. Any number of π electrons
    4. Only 6 σ electrons
26. Q26. When alkali metals are dissolved in liquid ammonia, a deep blue colour is produced due to
    1. Free ammonium
    2. Ammoniated electrons (solvated free electrons) absorbing in the visible region
    3. Sodium amide
    4. Hydrogen evolution
27. Q27. Markovnikov's rule for HX addition to an unsymmetrical alkene states the H atom adds to the
    1. Carbon with more hydrogens (the more substituted carbon gets X)
    2. Carbon with fewer hydrogens
    3. Either carbon equally
    4. Carbon at the chain end always
28. Q28. The Nernst equation for an electrode reaction at 298 K is
    1. E = E° – (0.0591/n) log Q
    2. E = E° + RT log Q
    3. E = E° – 2.303 RT/F
    4. E = nFE°
29. Q29. Kohlrausch’s law of independent migration of ions states that
    1. Conductivity is independent of concentration
    2. Limiting molar conductivity is the sum of independent contributions of cation and anion
    3. Conductivity is zero at infinite dilution
    4. None
30. Q30. Sandmeyer reaction converts an aryl diazonium salt to aryl halide using
    1. CuCl/HCl or CuBr/HBr
    2. HBF4 thermal
    3. H3PO2
    4. NaOH
31. Q31. Reaction of arenediazonium salt with hypophosphorous acid (H3PO2) results in
    1. Replacement of N2+ by H
    2. Replacement of N2+ by OH
    3. Coupling
    4. Reduction to phenylhydrazine
32. Q32. The Rosenmund reduction converts an acyl chloride to an aldehyde using
    1. LiAlH4
    2. NaBH4
    3. H2 / Pd-BaSO4 (poisoned)
    4. Zn-Hg/HCl
33. Q33. Anti-Markovnikov addition of HBr to an alkene occurs in the presence of
    1. Pure HBr in dark
    2. Peroxides (Kharasch effect) — proceeds via free radical mechanism
    3. Sunlight only
    4. Acid catalyst
34. Q34. Arrhenius equation links rate constant and temperature as
    1. k = A exp(-E_a/RT)
    2. k = A T
    3. k = A/T^2
    4. k = 1/A
35. Q35. The non-real cube roots of unity are 1, ω, ω² where 1 + ω + ω² equals
    1. 0
    2. 1
    3. 3
    4. ω
36. Q36. By De Moivre's theorem, (cos θ + i sin θ)ⁿ equals
    1. cos(nθ) + i sin(nθ) for integer n
    2. cos(θⁿ) + i sin(θⁿ)
    3. n cosθ + n i sinθ
    4. cos θ – i sin θ
37. Q37. For complex numbers, |z1·z2| equals
    1. |z1| + |z2|
    2. |z1| · |z2|
    3. |z1|/|z2|
    4. |z1|² + |z2|²
38. Q38. The number of permutations of n distinct objects taken r at a time is
    1. n!
    2. n!/(n-r)!
    3. n!/r!
    4. C(n,r)
39. Q39. The principal argument of z = -1 + i is
    1. π/4
    2. 3π/4
    3. -π/4
    4. -3π/4
40. Q40. For ax² + bx + c = 0 with real coefficients, the discriminant Δ = b² – 4ac. Roots are real and distinct iff
    1. Δ < 0
    2. Δ > 0
    3. Δ = 0
    4. Δ ≥ 0
41. Q41. The locus of z satisfying |z – z1| = |z – z2| is
    1. A circle
    2. The perpendicular bisector of the segment joining z1 and z2
    3. An ellipse
    4. A parabola
42. Q42. If α and β are roots of ax² + bx + c = 0, then α + β and αβ are
    1. -c/a, b/a
    2. -b/a, c/a
    3. b/a, -c/a
    4. b/a, c/a
43. Q43. The number of ways to arrange n distinct objects around a circular table (rotations equivalent) is
    1. n!
    2. (n-1)!
    3. n!/2
    4. (n-1)!/2
44. Q44. The number of ways to distribute n distinct objects into k distinct boxes such that no box is empty (surjections) is given by the formula
    1. k!·S(n,k) where S(n,k) is the Stirling number of the second kind
    2. n!
    3. C(n,k)
    4. k^n
45. Q45. A relation R on a set A which is reflexive, symmetric and transitive is called
    1. Partial order
    2. Equivalence relation
    3. Function
    4. Identity
46. Q46. A function f: A -> B is bijective if and only if
    1. It is injective only
    2. It is surjective only
    3. It is both injective and surjective
    4. It is constant
47. Q47. The eccentricity of the ellipse x²/25 + y²/9 = 1 is
    1. 3/5
    2. 4/5
    3. 5/3
    4. 5/4
48. Q48. 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
49. Q49. The contrapositive of “If p then q” is
    1. If q then p
    2. If not q then not p
    3. If not p then not q
    4. p and q
50. Q50. The general solution of tan x = tan alpha is
    1. x = n*pi + alpha
    2. x = 2n*pi + alpha
    3. x = (2n+1)*pi/2 + alpha
    4. x = n*pi – alpha