Daily MCQ Paper — 2 April 2026

Daily MCQ Paper — 2 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. 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
3. Q3. 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
4. Q4. 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
5. Q5. 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
6. Q6. 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
7. Q7. 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
8. Q8. 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
9. Q9. 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
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. In Youngs double slit experiment with slit separation d and screen distance D, fringe width is
    1. lambda * D / d
    2. lambda * d / D
    3. D / (lambda * d)
    4. d / (lambda * D)
12. Q12. The efficiency of a Carnot engine operating between source 400 K and sink 300 K is
    1. 100%
    2. 25%
    3. 75%
    4. 33.3%
13. Q13. At resonance in a series LCR circuit, the current is
    1. Zero
    2. Maximum, with impedance Z=R and circuit purely resistive
    3. Half of source current
    4. Imaginary
14. Q14. 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
15. Q15. In Youngs double slit experiment if the intensity from each slit is I0, the maximum intensity at the screen is
    1. I0
    2. 2 I0
    3. 4 I0
    4. sqrt(2) I0
16. Q16. Einsteins photoelectric equation is
    1. h nu = phi + (1/2) m vmax^2
    2. h nu = phi – (1/2) m vmax^2
    3. h nu = phi + m vmax^2
    4. h nu = (1/2) m vmax^2
17. Q17. On the magnetic axial line of a short bar magnet of moment m at distance r, the magnetic field is
    1. μ0m/(4πr3)
    2. 2μ0m/(4πr3)
    3. μ0m/(4πr2)
    4. Zero
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. 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
21. Q21. The Wurtz reaction synthesises higher alkanes from alkyl halides by treatment with
    1. Na/dry ether
    2. Zn/HCl
    3. KMnO4
    4. LiAlH4
22. Q22. 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
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. 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
25. Q25. 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
26. Q26. 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
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. Hinsberg reagent (benzenesulphonyl chloride) is used to distinguish
    1. Alkyl halides
    2. 1°, 2°, 3° amines
    3. Alcohols
    4. Aldehydes from ketones
29. Q29. The most stable allotrope of carbon at standard conditions is
    1. Diamond
    2. Graphite
    3. Fullerene
    4. Amorphous carbon
30. Q30. Hybridisation of carbon in methane is
    1. sp
    2. sp2
    3. sp3
    4. sp3d
31. Q31. Which is a Lewis acid?
    1. NH₃
    2. BF₃
    3. H₂O
    4. OH⁻
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. Henry's law constant has units of
    1. Pressure
    2. Pressure/concentration or pressure/mole-fraction
    3. Concentration
    4. Dimensionless
34. Q34. Vitamin C (ascorbic acid) deficiency causes
    1. Beriberi
    2. Scurvy — bleeding gums, poor wound healing, weakness
    3. Pellagra
    4. Rickets
35. Q35. The principal argument of z = -1 + i is
    1. π/4
    2. 3π/4
    3. -π/4
    4. -3π/4
36. Q36. For complex numbers, |z1·z2| equals
    1. |z1| + |z2|
    2. |z1| · |z2|
    3. |z1|/|z2|
    4. |z1|² + |z2|²
37. Q37. The non-real cube roots of unity are 1, ω, ω² where 1 + ω + ω² equals
    1. 0
    2. 1
    3. 3
    4. ω
38. Q38. 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
39. Q39. 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
40. Q40. 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
41. Q41. 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)
42. Q42. 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
43. Q43. 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
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. The shortest distance between two skew lines r=a1+λb1 and r=a2+μb2 is
    1. |(a2-a1)·(b1×b2)|/|b1×b2|
    2. Always zero
    3. |a1-a2|
    4. |b1-b2|
46. Q46. Negation of “For all x, p(x)” is
    1. For all x, not p(x)
    2. There exists x such that not p(x)
    3. There exists x such that p(x)
    4. None
47. Q47. The integrating factor of dy/dx + Py = Q is
    1. e^∫P dx
    2. e^∫Q dx
    3. e^−∫P dx
    4. ∫P dx
48. Q48. 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
49. Q49. If f'(x0)=0 and f''(x0)<0, then x0 is a
    1. Point of inflection
    2. Local maximum
    3. Local minimum
    4. Saddle point
50. Q50. Lagrange Mean Value Theorem states that for f continuous on [a,b] and differentiable on (a,b), there exists c in (a,b) such that
    1. f'(c)=0
    2. f(b)-f(a)=f'(c)(b-a)
    3. f(b)+f(a)=2f'(c)
    4. f(c)=0