Daily MCQ Paper — 8 April 2026

Daily MCQ Paper — 8 April 2026

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

1. Q1. In Youngs double slit experiment with slit separation d and screen distance D, fringe width is
   1. lambda * D / d
   2. lambda * d / D
   3. D / (lambda * d)
   4. d / (lambda * D)
2. Q2. In Youngs double slit experiment if the intensity from each slit is I0, the maximum intensity at the screen is
   1. I0
   2. 2 I0
   3. 4 I0
   4. sqrt(2) I0
3. Q3. In single slit Fraunhofer diffraction, the first minimum occurs at angle satisfying
   1. b sin theta = lambda
   2. b sin theta = lambda / 2
   3. b sin theta = 2 lambda
   4. b cos theta = lambda
4. Q4. Brewsters law states that at the polarising angle iB
   1. tan iB = mu
   2. sin iB = mu
   3. cos iB = mu
   4. cot iB = mu
5. Q5. Maluss law gives the intensity transmitted through a polariser as I = I0 cos^2 theta where theta is angle between
   1. Light direction and polariser axis
   2. Polariser and analyser transmission axes
   3. Electric and magnetic field vectors
   4. Two coherent sources
6. Q6. Einsteins photoelectric equation is
   1. h nu = phi + (1/2) m vmax^2
   2. h nu = phi – (1/2) m vmax^2
   3. h nu = phi + m vmax^2
   4. h nu = (1/2) m vmax^2
7. Q7. de Broglie wavelength of a particle of momentum p is
   1. h * p
   2. h / p
   3. p / h
   4. h / (p^2)
8. Q8. The mass defect Delta m and binding energy E of a nucleus are related by
   1. E = Delta m * c
   2. E = Delta m * c^2
   3. E = Delta m / c^2
   4. E = Delta m * c^3
9. Q9. The radioactive decay law N = N0 e^(-lambda t) gives half-life t1/2 equal to
   1. 1 / lambda
   2. ln 2 / lambda
   3. lambda / 2
   4. 2 lambda
10. Q10. Stable nuclei in the binding-energy-per-nucleon curve peak around mass number
    1. A = 8
    2. A = 28
    3. A = 56
    4. A = 200
11. Q11. The fundamental frequency of an organ pipe closed at one end of length L and sound speed v is
    1. v/(2L)
    2. v/(4L)
    3. v/L
    4. 2v/L
12. Q12. Total mechanical energy of a satellite in circular orbit of radius r is
    1. -GMm/r
    2. -GMm/(2r)
    3. +GMm/(2r)
    4. -GMm/(4r)
13. Q13. Brewster's angle for a glass of refractive index 1.5 is approximately
    1. 45°
    2. 56.3°
    3. 60°
    4. 33°
14. Q14. The efficiency of a Carnot engine working between T1 (hot) and T2 (cold) is
    1. 1 − T2/T1
    2. T1/T2 − 1
    3. T2/T1
    4. (T1−T2)/T2
15. Q15. For a rigid body rotating about a fixed axis, angular momentum L and angular velocity ω are related by
    1. L = Iω
    2. L = mvω
    3. L = ω/I
    4. L = I²ω
16. Q16. The time period of a simple pendulum of length L (small angle) is
    1. 2π√(g/L)
    2. 2π√(L/g)
    3. π√(L/g)
    4. (1/2π)√(L/g)
17. Q17. The horizontal component of Earths magnetic field at the equator is
    1. Maximum
    2. Zero
    3. Equal to vertical component
    4. Negative
18. Q18. Hell-Volhard-Zelinsky reaction effects which transformation
    1. Alpha-halogenation of carboxylic acids
    2. Beta-halogenation of alcohols
    3. Aromatic ring nitration
    4. Reduction of esters
19. Q19. Fischer esterification involves carboxylic acid and alcohol in presence of
    1. NaOH
    2. Conc H2SO4 (acid catalyst)
    3. LiAlH4
    4. Zn dust
20. Q20. Carboxylic acids on reduction with LiAlH4 yield
    1. Aldehydes
    2. Primary alcohols
    3. Secondary alcohols
    4. Ketones
21. Q21. Decarboxylation of sodium salts of carboxylic acids with sodalime gives
    1. Higher hydrocarbons
    2. Hydrocarbons with one less carbon
    3. Aldehydes
    4. Alcohols
22. Q22. Schiemann reaction prepares aryl fluorides from diazonium salts via
    1. Direct reaction with KF
    2. HBF4 + thermal decomposition
    3. CuF/HF
    4. HF/peroxide
23. Q23. Kolbe-Schmitt reaction is the carboxylation of sodium phenoxide with CO2 yielding primarily
    1. Benzoic acid
    2. Salicylic acid
    3. Phthalic acid
    4. Acetic acid
24. Q24. Sandmeyer reaction converts an aryl diazonium salt to aryl halide using
    1. CuCl/HCl or CuBr/HBr
    2. HBF4 thermal
    3. H3PO2
    4. NaOH
25. Q25. Reaction of arenediazonium salt with hypophosphorous acid (H3PO2) results in
    1. Replacement of N2+ by H
    2. Replacement of N2+ by OH
    3. Coupling
    4. Reduction to phenylhydrazine
26. Q26. Coupling of diazonium salt with phenol in mildly alkaline medium gives
    1. Methyl orange
    2. para-Hydroxyazobenzene
    3. Aniline yellow
    4. Indigo
27. Q27. Liebermanns nitroso test is a confirmatory test for
    1. Aldehydes
    2. Phenols
    3. Primary amines
    4. Carboxylic acids
28. Q28. The Kolbe-Schmitt reaction converts sodium phenoxide and CO2 (under pressure) to
    1. Salicylaldehyde
    2. Salicylic acid
    3. Picric acid
    4. Phthalic acid
29. Q29. Which test gives a silver mirror with aldehydes but not ketones
    1. Fehlings test
    2. Tollens test
    3. Lucas test
    4. Iodoform test
30. Q30. In Friedel-Crafts alkylation, a major limitation is
    1. Failure with deactivated arenes (e.g., nitrobenzene)
    2. Polyalkylation due to product being more activated
    3. Carbocation rearrangements
    4. All of the above
31. Q31. In the aldol condensation, the alpha-hydrogen of a carbonyl compound is removed by a
    1. Strong acid (H₂SO₄)
    2. Mild base (OH⁻ or alkoxide)
    3. Free radical initiator
    4. Lewis acid AlCl₃
32. Q32. According to VSEPR, the shape of XeF4 is
    1. Tetrahedral
    2. Square planar
    3. See-saw
    4. T-shape
33. Q33. Henry's law constant has units of
    1. Pressure
    2. Pressure/concentration or pressure/mole-fraction
    3. Concentration
    4. Dimensionless
34. Q34. LiCl is more covalent than NaCl primarily due to
    1. Smaller size of Li+
    2. Higher electronegativity of Li
    3. Polarising power of Li+ (Fajans rules)
    4. Li being lighter
35. Q35. Principal value branch of cos^-1 x is
    1. [-pi/2, pi/2]
    2. [0, pi]
    3. (0, pi)
    4. [-pi, 0]
36. Q36. Principal value branch of sin^-1 x is
    1. [0, pi]
    2. [-pi/2, pi/2]
    3. [-pi, pi]
    4. (0, pi)
37. Q37. 2 tan^-1 x equals (for |x| < 1)
    1. tan^-1 (2x / (1 – x^2))
    2. tan^-1 (2x / (1 + x^2))
    3. sin^-1 (1 – x^2)
    4. cos^-1 (2x)
38. Q38. Rolles theorem requires the function to be
    1. Continuous on [a,b], differentiable on (a,b) and f(a) = f(b)
    2. Only continuous on [a,b]
    3. Only differentiable on (a,b)
    4. Monotonic on [a,b]
39. Q39. Lagranges Mean Value Theorem guarantees existence of c in (a,b) such that
    1. f(c) = (f(b)-f(a))/(b-a)
    2. f(c) = 0
    3. f(c) = (f(b)+f(a))/2
    4. f(c) = 1
40. Q40. Derivative of log(x) with respect to x (natural logarithm) is
    1. 1/x
    2. x
    3. log x
    4. e^x
41. Q41. If x = a cos t and y = a sin t, then dy/dx equals
    1. -cot t
    2. -tan t
    3. tan t
    4. cot t
42. Q42. Order and degree of differential equation (d^2 y/dx^2)^3 + (dy/dx)^2 + y = 0 are
    1. 2 and 3
    2. 3 and 2
    3. 2 and 1
    4. 3 and 3
43. Q43. Newtons law of cooling states that dT/dt is proportional to
    1. (T – T0)
    2. (T0 – T)
    3. -(T – T0)
    4. T^2
44. Q44. Solution of differential equation dy/dx + y = 0 is
    1. y = C e^x
    2. y = C e^(-x)
    3. y = Cx
    4. y = C/x
45. Q45. The length of the latus rectum of the parabola y² = 16x is
    1. 4
    2. 8
    3. 16
    4. 32
46. Q46. Sum of binomial coefficients in expansion of (1 + x)ⁿ is
    1. 2ⁿ
    2. 3ⁿ
    3. n²
    4. n!
47. Q47. 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!
48. Q48. Length of latus rectum of y² = 16x is
    1. 4
    2. 8
    3. 16
    4. 32
49. Q49. The eccentricity of the ellipse x²/25 + y²/9 = 1 is
    1. 3/5
    2. 4/5
    3. 5/3
    4. 5/4
50. Q50. Sum of squares 1^2 + 2^2 + … + n^2 equals
    1. n(n+1)/2
    2. n(n+1)(2n+1)/6
    3. [n(n+1)/2]^2
    4. n^3