Daily MCQ Paper — 26 March 2026

Daily MCQ Paper — 26 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. Force per unit area between plates of a parallel plate capacitor is?
   1. σ²/(2ε₀)
   2. σ²/ε₀
   3. σ/ε₀
   4. σ²ε₀
3. Q3. 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
4. Q4. Time constant of an RC circuit is?
   1. RC
   2. R/C
   3. C/R
   4. R+C
5. Q5. 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
6. Q6. Capacitors in parallel store same?
   1. Voltage
   2. Charge
   3. Energy
   4. Current
7. Q7. When dielectric is inserted in an isolated charged capacitor, voltage?
   1. Decreases
   2. Increases
   3. Unchanged
   4. Becomes zero
8. Q8. Magnifying power of simple microscope (image at near point) is?
   1. 1 + D/f
   2. D/f
   3. f/D
   4. D/f − 1
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. In a stationary wave on a string fixed at both ends, the fundamental mode has
    1. One node and one antinode
    2. Two nodes and one antinode
    3. Two antinodes and one node
    4. Three nodes
15. Q15. 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
16. Q16. 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%
17. Q17. 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
18. Q18. Aldol condensation requires aldehyde/ketone with?
    1. α-hydrogen
    2. β-hydrogen
    3. γ-hydrogen
    4. no H
19. Q19. Crossed aldol between PhCHO and CH₃CHO gives major?
    1. Cinnamaldehyde
    2. Crotonaldehyde
    3. Acetone
    4. Benzoin
20. Q20. Cannizzaro reaction occurs with aldehydes that?
    1. Lack α-hydrogen
    2. Have α-hydrogen
    3. Are aromatic only
    4. Are aliphatic only
21. Q21. Knoevenagel condensation uses?
    1. Active methylene compound + aldehyde + base
    2. Aldehyde + alcohol
    3. Ester + base
    4. Alkyl halide + amine
22. Q22. Perkin reaction is condensation of aromatic aldehyde with?
    1. Acid anhydride and Na salt of acid
    2. Ketone
    3. Alcohol
    4. Ester
23. Q23. Reformatsky reaction generates which intermediate?
    1. Zinc enolate of α-bromo ester
    2. Grignard
    3. Enamine
    4. Wittig ylide
24. Q24. Hell-Volhard-Zelinsky reaction halogenates?
    1. α-carbon of carboxylic acid
    2. β-carbon
    3. γ-carbon
    4. aromatic ring
25. Q25. Claisen ester condensation requires?
    1. α-hydrogen on ester
    2. no α-H
    3. aromatic ester
    4. tert-butyl ester
26. Q26. 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
27. Q27. Langmuir adsorption assumes?
    1. Monolayer adsorption
    2. Multilayer
    3. Cooperative
    4. Random multilayer
28. Q28. Catalyst in Haber process for NH₃ is?
    1. Fe with Mo / K₂O / Al₂O₃ promoter
    2. V₂O₅
    3. Pt-Rh
    4. Ni
29. Q29. Contact process for H₂SO₄ uses catalyst?
    1. V₂O₅
    2. Fe
    3. Pt
    4. Ni
30. Q30. Lyophilic colloids are?
    1. Solvent-loving and reversible
    2. Solvent-hating and irreversible
    3. Always charged
    4. Coarse
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. Tyndall effect arises due to?
    1. Scattering of light by colloidal particles
    2. Refraction
    3. Diffraction
    4. Reflection
33. Q33. CMC stands for?
    1. Critical Micelle Concentration
    2. Common Molecular Concentration
    3. Centred Mean Concentration
    4. Coagulation Micelle Constant
34. Q34. 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
35. Q35. 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
36. Q36. 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
37. Q37. Function f(x)=x³−3x is increasing on?
    1. (−∞,−1) ∪ (1,∞)
    2. (−1,1)
    3. (0,∞)
    4. (−∞,0)
38. Q38. 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)
39. Q39. At a point of inflection of twice-differentiable f?
    1. f″=0 with sign change
    2. f′=0
    3. f=0
    4. f′″=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. If f′(x)<0 on interval, then f is?
    1. Strictly decreasing
    2. Strictly increasing
    3. Constant
    4. Concave
42. Q42. Approximate value of √25.2 using differentials is?
    1. 5.02
    2. 5.04
    3. 5.2
    4. 5.10
43. Q43. Most economical cylindrical can (no top) of volume V has h:r =?
    1. 1:1
    2. 1:2
    3. 2:1
    4. 3:1
44. Q44. Tangent to y=x² at (1,1) has slope?
    1. 2
    2. 1
    3. ½
    4. 3
45. Q45. Of all rectangles with given perimeter, maximum area is?
    1. Square
    2. Long thin rectangle
    3. Half-square
    4. Cannot be determined
46. Q46. 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
47. Q47. 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
48. Q48. Four points P1, P2, P3, P4 in 3D are coplanar iff
    1. They lie on x-axis
    2. Scalar triple product [P2-P1, P3-P1, P4-P1]=0
    3. They are equidistant
    4. They form a parallelogram
49. Q49. Volume generated by rotating y = √x (0 ≤ x ≤ 4) about x-axis is
    1. 4π
    2. 8π
    3. 16π
    4. 32π
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