Daily MCQ Paper — 28 March 2026

Daily MCQ Paper — 28 March 2026

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

1. Q1. 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
2. Q2. 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
3. Q3. 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
4. Q4. 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
5. Q5. 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
6. Q6. 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
7. Q7. 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
8. Q8. 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
9. Q9. Eddy currents are utilised in
   1. Electric brakes and induction furnaces
   2. Galvanometer suspension wires
   3. Capacitors
   4. Diodes
10. Q10. 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
11. Q11. A geostationary satellite has orbital period T = 24h and approximate radius from Earth’s centre
    1. 42,000 km
    2. 6,400 km
    3. 3,84,000 km
    4. 1,000 km
12. Q12. The quality factor Q of a series LCR resonant circuit is
    1. R/L
    2. (1/R)√(L/C) = ωrL/R
    3. RC
    4. LC
13. Q13. A liquid of total column length L oscillates in a U-tube. The time period of small oscillations is
    1. 2π√(L/g)
    2. 2π√(L/2g)
    3. 2π√(2L/g)
    4. 2π√(L/g) /2
14. Q14. 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
15. Q15. In a Wheatstone bridge balanced at P/Q = R/S, the current through the galvanometer is
    1. Zero
    2. I/2
    3. I
    4. Maximum
16. Q16. The mass defect Delta m and binding energy E of a nucleus are related by
    1. E = Delta m * c
    2. E = Delta m * c^2
    3. E = Delta m / c^2
    4. E = Delta m * c^3
17. Q17. An open organ pipe and a closed organ pipe of the same length will have fundamental frequencies in ratio
    1. 1:1
    2. 2:1
    3. 1:2
    4. 4:1
18. Q18. Werner's coordination theory introduced
    1. Primary and secondary valencies
    2. Hybridisation
    3. Atomic orbitals
    4. Resonance
19. Q19. 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
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. The strongest oxidising halogen is
    1. F2
    2. Cl2
    3. Br2
    4. I2
23. Q23. 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
24. Q24. The interhalogen ICl3 has structure
    1. Linear
    2. T-shape
    3. Trigonal pyramidal
    4. Square planar
25. Q25. Strongest oxoacid of chlorine is
    1. HOCl
    2. HClO2
    3. HClO3
    4. HClO4
26. Q26. The Wurtz reaction synthesises higher alkanes from alkyl halides by treatment with
    1. Na/dry ether
    2. Zn/HCl
    3. KMnO4
    4. LiAlH4
27. Q27. The element with strongest reducing nature in the first transition series in aqueous solution (E°) is
    1. Sc
    2. Cr
    3. Mn
    4. Cu
28. Q28. The Clemmensen reduction reduces R-C=O to R-CH₂- using
    1. Zn-Hg / HCl
    2. LiAlH₄
    3. NaBH₄
    4. H₂/Pt
29. Q29. Lyophobic colloids are stabilised by
    1. Hydration
    2. Charge on dispersed particles
    3. Solvent affinity
    4. Salting out
30. Q30. The order of a reaction can be
    1. Zero
    2. Fractional
    3. Negative
    4. All of these
31. Q31. Sucrose is a non-reducing sugar because
    1. It has no anomeric carbon
    2. Both anomeric carbons of glucose and fructose are involved in the glycosidic α,β-1,2 linkage
    3. It is a polysaccharide
    4. It cannot dissolve
32. Q32. 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
33. Q33. 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
34. Q34. 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
35. Q35. Order of (d^2y/dx^2)^3 + (dy/dx)^2 + y = 0 is
    1. 1
    2. 2
    3. 3
    4. 5
36. Q36. Degree 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. 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
42. Q42. ∫ 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
43. Q43. The non-real cube roots of unity are 1, ω, ω² where 1 + ω + ω² equals
    1. 0
    2. 1
    3. 3
    4. ω
44. Q44. Rolle's theorem requires f to be
    1. Continuous on (a,b) only
    2. Continuous on [a,b], differentiable on (a,b), and f(a)=f(b) — guarantees ∃c∈(a,b) with f'(c)=0
    3. Differentiable everywhere
    4. Linear
45. Q45. The dot product a·b of two vectors a and b is
    1. |a||b|sinθ
    2. |a||b|cosθ
    3. |a×b|
    4. |a|+|b|
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. Lagranges Mean Value Theorem guarantees existence of c in (a,b) such that
    1. f(c) = (f(b)-f(a))/(b-a)
    2. f(c) = 0
    3. f(c) = (f(b)+f(a))/2
    4. f(c) = 1
48. Q48. In any triangle ABC, by the sine rule a/sin A equals
    1. R
    2. 2R
    3. 3R
    4. R/2
49. Q49. The asymptotes of the hyperbola x²/16 – y²/9 = 1 are
    1. y = ±(3/4)x
    2. y = ±(4/3)x
    3. y = ±(16/9)x
    4. y = ±x
50. Q50. The form 0/0 is an
    1. Indeterminate form
    2. Defined as 0
    3. Defined as 1
    4. Defined as ∞