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Daily MCQ Paper — 20 April 2026

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Daily Practice Sheet — 50 Questions

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Daily MCQ Paper — 20 April 2026

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

  1. Q1. Two capacitors of 4 µF and 6 µF are connected in series. The equivalent capacitance is
    1. 10 µF
    2. 2.4 µF
    3. 24 µF
    4. 5 µF
  2. Q2. A parallel-plate capacitor with plate area A and separation d has capacitance C. If d is halved, C becomes
    1. C/2
    2. C
    3. 2C
    4. 4C
  3. Q3. Energy stored in a capacitor of capacitance C charged to voltage V is
    1. CV
    2. CV²
    3. ½ CV²
    4. ½ C/V
  4. Q4. Torque on a magnetic dipole of moment m in a uniform field B making angle θ is
    1. mB cos θ
    2. mB sin θ
    3. mB tan θ
    4. mB
  5. Q5. When a dielectric of constant K is fully inserted between plates of an isolated charged parallel-plate capacitor, the energy
    1. Increases K times
    2. Decreases K times
    3. Remains same
    4. Becomes K² times
  6. Q6. Two identical capacitors, charged to potentials V1 and V2, are connected in parallel. Common potential is
    1. (V1+V2)/2
    2. V1V2/(V1+V2)
    3. (V1V2)/2
    4. (V1-V2)/2
  7. Q7. Magnetic dipole moment of a current loop of N turns, area A and current I is
    1. NIA
    2. I/A
    3. NA/I
    4. N/IA
  8. Q8. A magnetic dipole in a uniform field B has potential energy U = -m·B. It is in stable equilibrium when
    1. m parallel to B
    2. m antiparallel to B
    3. m perpendicular to B
    4. m at 45° to B
  9. Q9. The resonance frequency of a series LCR circuit with L = 2 H and C = 8 µF is approximately
    1. 40 Hz
    2. 25 Hz
    3. 100 Hz
    4. 400 Hz
  10. Q10. At resonance in a series LCR circuit, the impedance is
    1. Maximum
    2. Equal to R
    3. Equal to XL
    4. Zero
  11. Q11. The Quality factor (Q) of a series LCR circuit at resonance is
    1. ω₀L/R
    2. R/ω₀L
    3. RC
    4. ω₀/R
  12. Q12. A particle moves with v(t)=4t² m/s. Acceleration at t=2 s is
    1. 8 m/s²
    2. 12 m/s²
    3. 16 m/s²
    4. 4 m/s²
  13. Q13. Coefficient of restitution e=1 corresponds to
    1. Inelastic
    2. Perfectly elastic
    3. Perfectly inelastic
    4. Cannot say
  14. Q14. Two resistors 6 ohm and 3 ohm are in parallel. Equivalent resistance is
    1. 9 ohm
    2. 2 ohm
    3. 4.5 ohm
    4. 1.5 ohm
  15. Q15. A force is conservative if
    1. Work done is path-independent
    2. Work along closed loop is zero
    3. Both A and B
    4. It is constant
  16. Q16. Gravitational potential energy on Earth surface relative to infinity is
    1. +GMm/R
    2. -GMm/R
    3. -GMm/R²
    4. 0
  17. Q17. In SHM, when displacement is half the amplitude, the ratio KE:PE is
    1. 1:1
    2. 3:1
    3. 1:3
    4. 2:1
  18. Q18. According to Crystal Field Theory, in an octahedral complex, the d-orbitals split into
    1. t2g (lower) and eg (higher)
    2. eg (lower) and t2g (higher)
    3. Three sets
    4. Two equal sets
  19. Q19. The magnitude of crystal field splitting in tetrahedral vs octahedral (with same metal/ligand) is
    1. Equal
    2. Δt = (4/9)Δo
    3. Δt = (9/4)Δo
    4. Δt = 2Δo
  20. Q20. In a tetrahedral crystal field, the d-orbitals split into
    1. e (lower) and t2 (higher)
    2. t2 (lower) and e (higher)
    3. t2g and eg
    4. No splitting
  21. Q21. Magnetic moment of [Fe(CN)6]³⁻ (low-spin d⁵, 1 unpaired) is approximately
    1. √3 BM
    2. √5 BM
    3. √15 BM
    4. 5.92 BM
  22. Q22. The spin-only magnetic moment formula is
    1. µ = √(n(n+2)) BM
    2. µ = n BM
    3. µ = √n BM
    4. µ = n² BM
  23. Q23. Lanthanide contraction refers to the
    1. Increase in atomic radii across the series
    2. Decrease in atomic and ionic radii across La to Lu
    3. Constancy of radii
    4. Random variation
  24. Q24. The most common oxidation state of lanthanides is
    1. +2
    2. +3
    3. +4
    4. +5
  25. Q25. One major consequence of lanthanide contraction is
    1. Zr and Hf have similar atomic radii
    2. Increase in metallic character
    3. Higher reactivity of 5d elements
    4. None
  26. Q26. Which actinide shows the maximum oxidation state of +7?
    1. U
    2. Np
    3. Pu
    4. Am
  27. Q27. The actinide series begins with which element?
    1. Thorium (Z=90)
    2. Actinium (Z=89)
    3. Uranium (Z=92)
    4. Lanthanum (Z=57)
  28. Q28. Compared to lanthanides, actinide contraction is
    1. Smaller
    2. Greater (5f shielding poorer)
    3. Same
    4. Reverse
  29. Q29. Bond order of O₂ from MO theory
    1. 1
    2. 1.5
    3. 2
    4. 2.5
  30. Q30. The reagent that converts an amide to amine with one less carbon is
    1. LiAlH4
    2. Br2/KOH (Hofmann bromamide)
    3. SOCl2
    4. LDA
  31. Q31. Galvanic cell converts
    1. Electrical → chemical
    2. Chemical → electrical
    3. Heat → electrical
    4. Light → electrical
  32. Q32. Among HClO, HClO2, HClO3, HClO4, the strongest acid is
    1. HClO
    2. HClO2
    3. HClO3
    4. HClO4
  33. Q33. First law of thermodynamics for an isolated system
    1. ΔU = q + w
    2. ΔU = 0
    3. ΔH = 0
    4. ΔS = 0
  34. Q34. Number of sigma bonds in ethyne (C2H2) is
    1. 2
    2. 3
    3. 4
    4. 5
  35. Q35. The number of ways to arrange the letters of MISSISSIPPI is
    1. 11!/(4! 4! 2!)
    2. 11!
    3. 11!/(4! 2!)
    4. 11!/2!
  36. Q36. Number of ways to choose a committee of 5 from 12 people is
    1. 12P5
    2. 12C5 = 792
    3. 12!/5!
    4. 12 × 11 × 10
  37. Q37. The middle term in the expansion of (1 + x)¹⁰ is
    1. T5
    2. T6 (i.e., 6th term, r=5)
    3. T7
    4. T11
  38. Q38. The number of 5-digit numbers with all distinct digits using {0..9} is
    1. 9 × 9P4
    2. 10P5
    3. 9 × 10P4
    4. 9P5
  39. Q39. The general term in the expansion of (x + a)ⁿ is Tr+1 =
    1. nCr xⁿ⁻ʳ aʳ
    2. nCr xʳ aⁿ⁻ʳ
    3. nCr (-x)ʳ
    4. xⁿ⁻ʳ aʳ
  40. Q40. In the expansion of (1+x)¹¹, the two middle terms are
    1. T6 and T7
    2. T5 and T6
    3. T6 and T8
    4. T11 and T12
  41. Q41. The greatest coefficient in the expansion of (1 + x)²ⁿ is
    1. nCn
    2. 2nCn
    3. 2nCn-1
    4. 2nC1
  42. Q42. Sum of binomial coefficients in expansion of (1 + x)ⁿ is
    1. 2ⁿ
    2. 3ⁿ
    3. n²
    4. n!
  43. Q43. Area of triangle with vertices (0,0),(4,0),(0,3)
    1. 6
    2. 12
    3. 7
    4. 5
  44. Q44. log₂ 32 =
    1. 4
    2. 5
    3. 6
    4. 8
  45. Q45. If A is a 3×3 matrix with |A| = 5, then |adj A| =
    1. 5
    2. 25
    3. 125
    4. 1/5
  46. Q46. Derivative of x³ is
    1. 3x²
    2. x²
    3. 3x
    4. x⁴/4
  47. Q47. Slope of tangent to y = ln x at x = 1 is
    1. 0
    2. 1
    3. e
    4. undefined
  48. Q48. Rolle's Theorem requires additionally that
    1. f(a) = f(b)
    2. f(a) > f(b)
    3. f is monotone
    4. f is bounded
  49. Q49. General solution of sin x = sin alpha is
    1. x = n*pi + alpha
    2. x = n*pi + (-1)^n * alpha
    3. x = 2n*pi + alpha
    4. x = 2n*pi – alpha
  50. Q50. Sum of cubes of first n natural numbers equals
    1. n(n+1)/2
    2. n(n+1)(2n+1)/6
    3. [n(n+1)/2]²
    4. n²(n+1)

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