Daily MCQ Paper — 27 March 2026

Daily MCQ Paper — 27 March 2026

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

1. Q1. Energy stored in a capacitor of capacitance C charged to voltage V is?
   1. ½CV²
   2. CV
   3. CV²
   4. ½C/V
2. Q2. Time constant of an RC circuit is?
   1. RC
   2. R/C
   3. C/R
   4. R+C
3. Q3. Force per unit area between plates of a parallel plate capacitor is?
   1. σ²/(2ε₀)
   2. σ²/ε₀
   3. σ/ε₀
   4. σ²ε₀
4. Q4. Capacitance of parallel plate capacitor with dielectric of constant K filling the gap is?
   1. Kε₀A/d
   2. ε₀A/(Kd)
   3. ε₀A/d
   4. KA/d
5. Q5. Two capacitors C₁ and C₂ in series have equivalent capacitance?
   1. C₁C₂/(C₁+C₂)
   2. C₁+C₂
   3. (C₁+C₂)/2
   4. C₁+C₂+C₁C₂
6. Q6. Magnifying power of simple microscope (image at near point) is?
   1. 1 + D/f
   2. D/f
   3. f/D
   4. D/f − 1
7. Q7. Capacitors in parallel store same?
   1. Voltage
   2. Charge
   3. Energy
   4. Current
8. Q8. When dielectric is inserted in an isolated charged capacitor, voltage?
   1. Decreases
   2. Increases
   3. Unchanged
   4. Becomes zero
9. Q9. A capacitor discharging through R loses 1/e of charge in time?
   1. τ = RC
   2. 2RC
   3. RC/2
   4. RC²
10. Q10. Astronomical telescope in normal adjustment magnification is?
    1. f_o/f_e
    2. f_e/f_o
    3. f_o + f_e
    4. f_o − f_e
11. Q11. Galilean telescope uses an eye-piece that is?
    1. Concave (diverging)
    2. Convex
    3. Plano-convex
    4. Bi-convex
12. Q12. Newtonian reflecting telescope uses?
    1. Concave primary + plane secondary
    2. Two convex lenses
    3. Concave + concave
    4. Convex + concave
13. Q13. Resolving power of microscope is proportional to?
    1. 1/λ
    2. λ
    3. λ²
    4. independent of λ
14. Q14. The speed of electromagnetic waves in vacuum is given by
    1. c = 1/√(μ₀ε₀)
    2. c = √(μ₀ε₀)
    3. c = μ₀/ε₀
    4. c = ε₀/μ₀
15. Q15. In an isothermal process for an ideal gas, the work done by the gas in expansion from V1 to V2 is
    1. PΔV
    2. nRT ln(V2/V1)
    3. nCvΔT
    4. Zero
16. Q16. 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
17. Q17. 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
18. Q18. Crossed aldol between PhCHO and CH₃CHO gives major?
    1. Cinnamaldehyde
    2. Crotonaldehyde
    3. Acetone
    4. Benzoin
19. Q19. Cannizzaro reaction occurs with aldehydes that?
    1. Lack α-hydrogen
    2. Have α-hydrogen
    3. Are aromatic only
    4. Are aliphatic only
20. Q20. Perkin reaction is condensation of aromatic aldehyde with?
    1. Acid anhydride and Na salt of acid
    2. Ketone
    3. Alcohol
    4. Ester
21. Q21. Aldol condensation requires aldehyde/ketone with?
    1. α-hydrogen
    2. β-hydrogen
    3. γ-hydrogen
    4. no H
22. Q22. Knoevenagel condensation uses?
    1. Active methylene compound + aldehyde + base
    2. Aldehyde + alcohol
    3. Ester + base
    4. Alkyl halide + amine
23. Q23. Reformatsky reaction generates which intermediate?
    1. Zinc enolate of α-bromo ester
    2. Grignard
    3. Enamine
    4. Wittig ylide
24. Q24. Claisen ester condensation requires?
    1. α-hydrogen on ester
    2. no α-H
    3. aromatic ester
    4. tert-butyl ester
25. Q25. Hell-Volhard-Zelinsky reaction halogenates?
    1. α-carbon of carboxylic acid
    2. β-carbon
    3. γ-carbon
    4. aromatic ring
26. Q26. Tyndall effect arises due to?
    1. Scattering of light by colloidal particles
    2. Refraction
    3. Diffraction
    4. Reflection
27. Q27. Freundlich adsorption isotherm equation is?
    1. x/m = k P^(1/n)
    2. x/m = kP
    3. x/m = kP²
    4. x/m = k log P
28. Q28. Langmuir adsorption assumes?
    1. Monolayer adsorption
    2. Multilayer
    3. Cooperative
    4. Random multilayer
29. Q29. Catalyst in Haber process for NH₃ is?
    1. Fe with Mo / K₂O / Al₂O₃ promoter
    2. V₂O₅
    3. Pt-Rh
    4. Ni
30. Q30. Contact process for H₂SO₄ uses catalyst?
    1. V₂O₅
    2. Fe
    3. Pt
    4. Ni
31. Q31. Hardy-Schulze rule states coagulation power is governed by?
    1. Valency of ion of charge opposite to colloid
    2. Same charge ion
    3. Mass of ion
    4. Concentration only
32. Q32. CMC stands for?
    1. Critical Micelle Concentration
    2. Common Molecular Concentration
    3. Centred Mean Concentration
    4. Coagulation Micelle Constant
33. Q33. Lyophilic colloids are?
    1. Solvent-loving and reversible
    2. Solvent-hating and irreversible
    3. Always charged
    4. Coarse
34. Q34. Gabriel's phthalimide synthesis is used to prepare
    1. Tertiary amines
    2. Pure primary amines (without secondary/tertiary contamination)
    3. Secondary amines
    4. Aromatic amines like aniline
35. Q35. Function f(x)=x³−3x is increasing on?
    1. (−∞,−1) ∪ (1,∞)
    2. (−1,1)
    3. (0,∞)
    4. (−∞,0)
36. Q36. At a point of inflection of twice-differentiable f?
    1. f″=0 with sign change
    2. f′=0
    3. f=0
    4. f′″=0
37. Q37. Approximate value of √25.2 using differentials is?
    1. 5.02
    2. 5.04
    3. 5.2
    4. 5.10
38. Q38. If radius of sphere increases at 2 cm/s, rate of volume change at r=5 cm is?
    1. 200π cm³/s
    2. 100π
    3. 50π
    4. 25π
39. Q39. Local maximum of f at x=c by 2nd derivative test requires?
    1. f′(c)=0 and f″(c)<0
    2. f′(c)=0 and f″(c)>0
    3. f′(c)>0
    4. f″(c)=0
40. Q40. Maxima/minima of f on closed [a,b] are attained at?
    1. Critical points or endpoints
    2. Endpoints only
    3. Interior only
    4. Origin
41. Q41. Tangent to y=x² at (1,1) has slope?
    1. 2
    2. 1
    3. ½
    4. 3
42. Q42. A balloon spherical, radius increasing at rate 0.5 cm/s. Surface area rate at r=4 cm?
    1. 16π cm²/s
    2. 32π
    3. 8π
    4. 4π
43. Q43. Normal to curve y=f(x) at (x₀,y₀) has slope?
    1. −1/f′(x₀)
    2. f′(x₀)
    3. 1/f′(x₀)
    4. −f′(x₀)
44. Q44. Of all rectangles with given perimeter, maximum area is?
    1. Square
    2. Long thin rectangle
    3. Half-square
    4. Cannot be determined
45. Q45. If f′(x)<0 on interval, then f is?
    1. Strictly decreasing
    2. Strictly increasing
    3. Constant
    4. Concave
46. Q46. Most economical cylindrical can (no top) of volume V has h:r =?
    1. 1:1
    2. 1:2
    3. 2:1
    4. 3:1
47. Q47. Solution of dy/dx = -y/x is
    1. y = Cx
    2. xy = C
    3. y = C/x
    4. y – x = C
48. Q48. The non-real cube roots of unity are 1, ω, ω² where 1 + ω + ω² equals
    1. 0
    2. 1
    3. 3
    4. ω
49. Q49. 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
50. Q50. 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