Daily MCQ Paper — 24 April 2026 - JEE Gurukul
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Daily MCQ Paper — 24 April 2026

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Daily Practice Sheet — 50 Questions

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Daily MCQ Paper — 24 April 2026

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

  1. Q1. Brewster's angle for a glass of refractive index 1.5 is approximately
    1. 45°
    2. 56.3°
    3. 60°
    4. 33°
  2. Q2. Amplitude modulation (AM) involves variation of
    1. Frequency of carrier
    2. Phase of carrier
    3. Amplitude of carrier with signal
    4. Wavelength only
  3. Q3. In single-slit diffraction, the first minimum occurs at
    1. a sinθ = λ/2
    2. a sinθ = λ
    3. a sinθ = 2λ
    4. a sinθ = nλ where n = 0
  4. Q4. In Young's double slit experiment, fringe width β is given by (λ wavelength, d slit separation, D screen distance)
    1. λD/d
    2. λd/D
    3. λD/(2d)
    4. 2λD/d
  5. Q5. Sky-wave propagation uses
    1. Direct line of sight
    2. Reflection from troposphere
    3. Reflection from ionosphere
    4. Surface diffraction
  6. Q6. The maximum line-of-sight distance for a transmitting antenna of height h on a smooth earth (radius R) is approximately
    1. √(2Rh)
    2. √(Rh)
    3. 2√(Rh)
    4. Rh
  7. Q7. A MOSFET differs from a JFET in that the gate is
    1. Connected directly to channel
    2. Insulated by an oxide layer
    3. Made of metal only
    4. Reverse-biased always
  8. Q8. The energy of the n-th hydrogen orbit is given by
    1. -13.6/n² eV
    2. -13.6n² eV
    3. 13.6/n eV
    4. -3.4n eV
  9. Q9. Bohr's quantisation condition for electron angular momentum is
    1. mvr = h/2π
    2. mvr = nh/2π
    3. mvr = nh
    4. E = nhν
  10. Q10. The Rydberg formula for hydrogen spectral lines gives wavenumber 1/λ =
    1. R(1/n₁² – 1/n₂²)
    2. R(1/n₂² – 1/n₁²)
    3. Rn₁n₂
    4. R/n
  11. Q11. Two resistors 6 Ω and 3 Ω in parallel give
    1. 9 Ω
    2. 2 Ω
    3. 3 Ω
    4. 4.5 Ω
  12. Q12. Young's modulus has dimensions of
    1. Force
    2. Pressure
    3. Energy
    4. Power
  13. Q13. A 2 kg block slides down a frictionless incline of 30°. Acceleration is
    1. 5 m/s²
    2. 9.8 m/s²
    3. 4.9 m/s²
    4. 7 m/s²
  14. Q14. Lenz's law is a consequence of conservation of
    1. Charge
    2. Momentum
    3. Energy
    4. Mass
  15. Q15. de Broglie wavelength of an electron with KE 100 eV is approximately
    1. 0.123 nm
    2. 1.23 nm
    3. 12.3 nm
    4. 0.0123 nm
  16. Q16. In a step-up transformer
    1. Ns < Np
    2. Ns = Np
    3. Ns > Np
    4. Independent of N
  17. Q17. A satellite at height h has orbital speed
    1. √(GM/(R+h))
    2. √(GMR)
    3. √(GM/h)
    4. √(2GM/R)
  18. Q18. Elevation of boiling point ΔT_b is given by
    1. K_b × m
    2. K_f × m
    3. RT/M
    4. PV
  19. Q19. Mole fraction of solute x_A in a solution is defined as
    1. n_A / n_B
    2. n_A / (n_A + n_B)
    3. n_B / (n_A + n_B)
    4. m / V
  20. Q20. van't Hoff factor i for NaCl in dilute solution (full dissociation) is
    1. 1
    2. 2
    3. 3
    4. 0.5
  21. Q21. Raoult's law for an ideal solution states
    1. P_total = x_A P°_A + x_B P°_B
    2. P = nRT/V
    3. PV = nRT
    4. P_A = x_B P°_A
  22. Q22. The Nernst equation for cell EMF at 298 K (in volts) is
    1. E = E° – (0.0591/n) log Q
    2. E = E° + (0.0591/n) log Q
    3. E = E°
    4. E = (RT/F) ln Q
  23. Q23. Faraday's first law of electrolysis states
    1. m ∝ Q
    2. m ∝ V
    3. m ∝ I²
    4. m ∝ 1/Q
  24. Q24. The integrated rate equation for a first-order reaction is
    1. k = (1/t) ln([A]₀/[A])
    2. k = (1/t)([A]₀-[A])
    3. k = ln([A]₀-[A])
    4. k = (1/t²) ln(…)
  25. Q25. Half-life of a zero-order reaction is
    1. t = [A]₀/(2k)
    2. t = ln2/k
    3. t = 1/(k[A]₀)
    4. t = [A]₀/k
  26. Q26. Adsorption is exothermic because
    1. Surface area increases
    2. ΔS is positive
    3. Entropy of adsorbed species decreases (so ΔH must be negative for ΔG < 0)
    4. Bond formation absorbs heat
  27. Q27. Catalytic activity of transition metals is best explained by
    1. Their colour
    2. Variable oxidation states and ability to form intermediates
    3. Low atomic radius
    4. High lattice energy
  28. Q28. Nylon 6,6 is a
    1. Addition polymer
    2. Condensation polymer of hexamethylenediamine and adipic acid
    3. Natural polymer
    4. Vulcanised rubber
  29. Q29. Equilibrium constant Kp for a reaction with Δn=0
    1. Kc
    2. Kc·RT
    3. Kc/(RT)
    4. 0
  30. Q30. SN1 reactions proceed via
    1. Carbocation intermediate
    2. Carbanion
    3. Free radical
    4. Concerted bimolecular
  31. Q31. The oxidation state of Cr in K2Cr2O7 is
    1. +3
    2. +5
    3. +6
    4. +7
  32. Q32. Aspirin is chemically
    1. Salicylic acid
    2. Acetyl salicylic acid
    3. Methyl salicylate
    4. Phenol
  33. Q33. Wurtz reaction couples two alkyl halides using
    1. Na/dry ether
    2. Zn/HCl
    3. Fe/H2O
    4. LiAlH4
  34. Q34. IUPAC name of CH₃COCH₃
    1. Acetone
    2. Propanal
    3. Propan-2-one
    4. Propanoic acid
  35. Q35. Equation of parabola with focus (a,0) and directrix x = -a is
    1. y² = 4ax
    2. x² = 4ay
    3. x² = -4ay
    4. y² = -4ax
  36. Q36. Length of latus rectum of y² = 16x is
    1. 4
    2. 8
    3. 16
    4. 32
  37. Q37. The locus of a point equidistant from a fixed point and a fixed line is a
    1. Circle
    2. Parabola
    3. Ellipse
    4. Hyperbola
  38. Q38. Direction cosines of a line satisfy
    1. l + m + n = 1
    2. l² + m² + n² = 1
    3. lmn = 1
    4. l² + m² + n² = 0
  39. Q39. The equation of a plane in normal form is
    1. x + y + z = 0
    2. lx + my + nz = p
    3. ax + by + c = 0
    4. x = 0
  40. Q40. The angle between two lines with direction ratios (a₁,b₁,c₁) and (a₂,b₂,c₂) satisfies
    1. cosθ = (a₁a₂+b₁b₂+c₁c₂)/(√Σa₁²·√Σa₂²)
    2. sinθ = …
    3. tanθ = a₁/a₂
    4. cosθ = 1
  41. Q41. Shortest distance between two skew lines with vectors a₁, a₂ and directions b₁, b₂ is
    1. |(a₂-a₁)·(b₁×b₂)| / |b₁×b₂|
    2. |b₁·b₂|
    3. |a₂-a₁|
    4. 0
  42. Q42. Area bounded by y = x² and y = x between x = 0 and x = 1 is
    1. 1/6
    2. 1/3
    3. 1/2
    4. 1/12
  43. Q43. Volume generated by rotating y = √x (0 ≤ x ≤ 4) about x-axis is
    1. 4π
    2. 8π
    3. 16π
    4. 32π
  44. Q44. Area enclosed by the parabola y² = 4ax and its latus rectum is
    1. (8/3)a²
    2. (4/3)a²
    3. (2/3)a²
    4. (16/3)a²
  45. Q45. By Bayes' theorem, P(A|B) equals
    1. P(B|A)P(A)/P(B)
    2. P(A)P(B)
    3. P(A∩B)/P(A)
    4. P(B|A)
  46. Q46. Derivative of x³ is
    1. 3x²
    2. x²
    3. 3x
    4. x⁴/4
  47. Q47. If A is a 3×3 matrix with det A=2, det(2A) =
    1. 4
    2. 8
    3. 16
    4. 32
  48. Q48. 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)
  49. Q49. The area enclosed by y = x² and y = x is
    1. 1/2
    2. 1/3
    3. 1/6
    4. 1
  50. Q50. The locus of |z – 2| = |z + 2| in the complex plane is
    1. Circle
    2. Real axis
    3. Imaginary axis
    4. Parabola

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