Daily MCQ Paper — 23 April 2026

Daily MCQ Paper — 23 April 2026

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

1. Q1. 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
2. Q2. Brewster's angle for a glass of refractive index 1.5 is approximately
   1. 45°
   2. 56.3°
   3. 60°
   4. 33°
3. Q3. Amplitude modulation (AM) involves variation of
   1. Frequency of carrier
   2. Phase of carrier
   3. Amplitude of carrier with signal
   4. Wavelength only
4. Q4. 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
5. Q5. Bohr's quantisation condition for electron angular momentum is
   1. mvr = h/2π
   2. mvr = nh/2π
   3. mvr = nh
   4. E = nhν
6. Q6. Sky-wave propagation uses
   1. Direct line of sight
   2. Reflection from troposphere
   3. Reflection from ionosphere
   4. Surface diffraction
7. Q7. 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
8. Q8. 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
9. Q9. 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
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. Coefficient of restitution e=1 corresponds to
    1. Inelastic
    2. Perfectly elastic
    3. Perfectly inelastic
    4. Cannot say
12. Q12. A body is projected with velocity 20 m/s at 60° to horizontal. Time of flight (g=10):
    1. 2 s
    2. 3.46 s
    3. 4 s
    4. 1.73 s
13. Q13. Two resistors 6 Ω and 3 Ω in parallel give
    1. 9 Ω
    2. 2 Ω
    3. 3 Ω
    4. 4.5 Ω
14. Q14. SI unit of magnetic flux is
    1. Tesla
    2. Weber
    3. Henry
    4. Gauss
15. Q15. Frequency of LC circuit (L=1 mH, C=1 µF) is approximately
    1. 5.03 kHz
    2. 5 kHz
    3. 15.9 kHz
    4. 159 Hz
16. Q16. A wire of resistance R is stretched to double its length. New resistance is
    1. R
    2. 2R
    3. 4R
    4. R/2
17. Q17. A satellite at height h has orbital speed
    1. √(GM/(R+h))
    2. √(GMR)
    3. √(GM/h)
    4. √(2GM/R)
18. Q18. 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
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. Elevation of boiling point ΔT_b is given by
    1. K_b × m
    2. K_f × m
    3. RT/M
    4. PV
21. Q21. van't Hoff factor i for NaCl in dilute solution (full dissociation) is
    1. 1
    2. 2
    3. 3
    4. 0.5
22. Q22. 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(…)
23. Q23. 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
24. Q24. Faraday's first law of electrolysis states
    1. m ∝ Q
    2. m ∝ V
    3. m ∝ I²
    4. m ∝ 1/Q
25. Q25. 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
26. Q26. 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
27. Q27. 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
28. Q28. Number of sigma bonds in ethyne (C2H2) is
    1. 2
    2. 3
    3. 4
    4. 5
29. Q29. The pH of 0.001 M HCl is
    1. 2
    2. 3
    3. 4
    4. 11
30. Q30. The oxidation state of Cr in K2Cr2O7 is
    1. +3
    2. +5
    3. +6
    4. +7
31. Q31. Henderson–Hasselbalch equation for buffer
    1. pH = pKa + log([A⁻]/[HA])
    2. pH = pKa − log([A⁻]/[HA])
    3. pH = pKb + log([B]/[BH⁺])
    4. pH = pKw − pOH
32. Q32. Which is a strong electrolyte?
    1. CH3COOH
    2. NH4OH
    3. H2O
    4. NaCl
33. Q33. Which has the highest first ionisation energy?
    1. Na
    2. Mg
    3. Al
    4. Si
34. Q34. Number of stereoisomers of a molecule with 2 chiral centers (no meso)
    1. 2
    2. 3
    3. 4
    4. 8
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. 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
38. Q38. The locus of a point equidistant from a fixed point and a fixed line is a
    1. Circle
    2. Parabola
    3. Ellipse
    4. Hyperbola
39. Q39. Direction cosines of a line satisfy
    1. l + m + n = 1
    2. l² + m² + n² = 1
    3. lmn = 1
    4. l² + m² + n² = 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. 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
42. Q42. Volume generated by rotating y = √x (0 ≤ x ≤ 4) about x-axis is
    1. 4π
    2. 8π
    3. 16π
    4. 32π
43. Q43. 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
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. The eccentricity of hyperbola x²/9 − y²/16 = 1 is
    1. 5/4
    2. 5/3
    3. 4/3
    4. 3/5
46. Q46. The general solution of dy/dx = y is
    1. y = Cx
    2. y = C e^x
    3. y = ln x + C
    4. y = C/x
47. Q47. Slope of tangent to y = ln x at x = 1 is
    1. 0
    2. 1
    3. e
    4. undefined
48. Q48. Solution of dy/dx = y is
    1. y = e^x + C
    2. y = Ce^x
    3. y = ln x + C
    4. y = x²
49. Q49. Number of ways to arrange letters of the word INDIA is
    1. 60
    2. 120
    3. 24
    4. 30
50. Q50. If sinθ = 3/5 in QI, then cosθ =
    1. 3/5
    2. 4/5
    3. 5/3
    4. 5/4