Daily MCQ Paper — 29 March 2026

Daily MCQ Paper — 29 March 2026

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

1. Q1. By the parallel-axis theorem, moment of inertia about an axis parallel to and at distance d from a centroidal axis is
   1. I_cm + Md^2
   2. I_cm – Md^2
   3. I_cm + Md
   4. I_cm * d^2
2. Q2. The perpendicular-axis theorem (planar laminae) states
   1. I_z = I_x + I_y
   2. I_z = I_x – I_y
   3. I_z = I_x * I_y
   4. I_z = (I_x + I_y)/2
3. Q3. A solid sphere of mass M and radius R has moment of inertia about a diameter equal to
   1. (2/5)MR^2
   2. (2/3)MR^2
   3. (1/2)MR^2
   4. MR^2
4. Q4. When a body rolls without slipping on a horizontal surface, the velocity of the contact point is
   1. v_cm
   2. 2v_cm
   3. 0
   4. v_cm/2
5. Q5. Moment of inertia of a uniform thin rod of mass M and length L about an axis through its centre and perpendicular to its length is
   1. ML^2/3
   2. ML^2/12
   3. ML^2/2
   4. ML^2
6. Q6. For a solid cylinder rolling without slipping down an incline, fraction of total KE that is rotational is
   1. 1/2
   2. 1/3
   3. 2/3
   4. 1/4
7. Q7. Angular momentum of a rigid body rotating about a fixed axis is
   1. L = mvr
   2. L = Iω
   3. L = Iα
   4. L = (1/2)Iω^2
8. Q8. A solid sphere and a hollow sphere of equal mass and radius roll down the same incline. The first to reach bottom is
   1. Solid sphere
   2. Hollow sphere
   3. Both reach together
   4. Depends on incline angle
9. Q9. 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
10. Q10. Maxwell's correction to Ampere's law introduced the concept of
    1. Magnetic monopoles
    2. Displacement current
    3. Electromagnetic flux
    4. Vector potential
11. Q11. 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
12. Q12. 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
13. Q13. Curie's law for paramagnetic susceptibility states that χ varies with temperature T as
    1. χ ∝ T
    2. χ = C/T (inversely proportional to absolute temperature)
    3. χ ∝ T^2
    4. χ independent of T
14. Q14. In an adiabatic process for an ideal gas
    1. PV = constant
    2. PV^γ = constant
    3. TV = constant
    4. P/T = constant
15. Q15. The time constant of an RC circuit is
    1. RC
    2. R/C
    3. C/R
    4. 1/(RC)
16. Q16. 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
17. Q17. The acceleration due to gravity at height h above Earth's surface (h<<R) is approximately
    1. g(1 – 2h/R)
    2. g(1 + 2h/R)
    3. g(1 – h/R)
    4. g(1 + h/R)
18. Q18. According to Crystal Field Theory, in an octahedral complex the d-orbitals split into
    1. Two t2g + three eg
    2. Three t2g + two eg
    3. Five degenerate orbitals
    4. Three eg + two t2g
19. Q19. Werner's coordination theory introduced
    1. Primary and secondary valencies
    2. Hybridisation
    3. Atomic orbitals
    4. Resonance
20. Q20. In [Co(NH3)6]Cl3, the coordination number of Co is
    1. 3
    2. 4
    3. 6
    4. 9
21. Q21. Geometrical (cis-trans) isomerism is exhibited by
    1. [Co(NH3)6]^3+
    2. [Co(NH3)5Cl]^2+
    3. [Co(NH3)4Cl2]^+
    4. [Ni(CN)4]^2-
22. Q22. Strongest oxoacid of chlorine is
    1. HOCl
    2. HClO2
    3. HClO3
    4. HClO4
23. Q23. The strongest oxidising halogen is
    1. F2
    2. Cl2
    3. Br2
    4. I2
24. Q24. The interhalogen ICl3 has structure
    1. Linear
    2. T-shape
    3. Trigonal pyramidal
    4. Square planar
25. Q25. Bleaching powder Ca(OCl)Cl is made by passing
    1. Cl2 over slaked lime
    2. HCl over CaO
    3. Cl2 over CaO
    4. HOCl over Ca
26. Q26. Hinsberg test distinguishes 1°, 2°, 3° amines using
    1. Benzenesulfonyl chloride (C₆H₅SO₂Cl)
    2. Acetyl chloride
    3. Hydrochloric acid
    4. Sodium nitrite
27. Q27. Hell-Volhard-Zelinsky reaction effects which transformation
    1. Alpha-halogenation of carboxylic acids
    2. Beta-halogenation of alcohols
    3. Aromatic ring nitration
    4. Reduction of esters
28. Q28. The Gattermann reaction differs from Sandmeyer in using
    1. CuCN
    2. Cu/HCl in place of CuCl/HCl
    3. HBF4
    4. HNO2
29. Q29. SN2 reaction is favoured by
    1. Tertiary alkyl halide
    2. Primary alkyl halide with strong nucleophile in polar aprotic solvent (DMSO, DMF, acetone)
    3. Bulky substrates
    4. Weak nucleophile
30. Q30. Galvanic cell converts
    1. Electrical → chemical
    2. Chemical → electrical
    3. Heat → electrical
    4. Light → electrical
31. Q31. Elevation of boiling point ΔT_b is given by
    1. K_b × m
    2. K_f × m
    3. RT/M
    4. PV
32. Q32. Markovnikov's rule for HX addition to an unsymmetrical alkene states that the H atom attaches to
    1. The carbon with fewer H atoms
    2. The carbon with more H atoms (giving the more stable carbocation intermediate)
    3. The terminal carbon always
    4. The carbon with double bond
33. Q33. Lucas reagent (anhydrous ZnCl2 + concentrated HCl) distinguishes alcohols. Tertiary alcohols give turbidity
    1. Immediately
    2. In about 5 minutes
    3. Only on warming
    4. Never
34. Q34. In cyclohexane, the chair conformation is preferred over the boat because
    1. Boat has more torsional strain (eclipsing) and flagpole interactions
    2. Chair has bond angles of exactly 120°
    3. Boat is planar
    4. Chair has more torsional strain
35. Q35. Degree of (d^2y/dx^2)^3 + (dy/dx)^2 + y = 0 is
    1. 1
    2. 2
    3. 3
    4. 5
36. Q36. Order of (d^2y/dx^2)^3 + (dy/dx)^2 + y = 0 is
    1. 1
    2. 2
    3. 3
    4. 5
37. Q37. The general solution of dy/dx = y is
    1. y = Cx
    2. y = Ce^x
    3. y = ln x + C
    4. y = x + C
38. Q38. Solution of dy/dx = -y/x is
    1. y = Cx
    2. xy = C
    3. y = C/x
    4. y – x = C
39. Q39. A first-order linear DE dy/dx + Py = Q has integrating factor
    1. e^(∫P dx)
    2. e^(∫Q dx)
    3. e^(P+Q)
    4. P/Q
40. Q40. Bernoulli equation dy/dx + Py = Qy^n is solved by substitution
    1. v = y^(1-n)
    2. v = y^n
    3. v = 1/y
    4. v = ln y
41. Q41. ∫ e^x sin x dx is
    1. (e^x/2)(sin x – cos x) + C
    2. e^x sin x + C
    3. e^x cos x + C
    4. (e^x/2)(sin x + cos x) + C
42. Q42. An exact differential equation M dx + N dy = 0 satisfies
    1. ∂M/∂y = ∂N/∂x
    2. ∂M/∂x = ∂N/∂y
    3. M = N
    4. M + N = 0
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. 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
45. Q45. 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
46. Q46. The vector triple product a×(b×c) equals
    1. (a·c)b – (a·b)c
    2. (a·b)c – (a·c)b
    3. a·(b×c)
    4. b×(a×c)
47. Q47. ∫ 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
48. Q48. The locus of a point equidistant from a fixed point and a fixed line is a
    1. Circle
    2. Parabola
    3. Ellipse
    4. Hyperbola
49. Q49. By De Moivre's theorem, (cos θ + i sin θ)^n =
    1. cos nθ + i sin nθ
    2. cos θ + i sin nθ
    3. cos nθ – i sin nθ
    4. n(cos θ + i sin θ)
50. Q50. The derivative of sin^2 x is
    1. 2 sin x
    2. 2 sin x cos x
    3. cos^2 x
    4. -sin 2x