Daily MCQ Paper — 7 April 2026

Daily MCQ Paper — 7 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. 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
8. Q8. 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
9. Q9. de Broglie wavelength of a particle of momentum p is
   1. h * p
   2. h / p
   3. p / h
   4. h / (p^2)
10. Q10. 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
11. Q11. Escape velocity from Earth's surface is approximately
    1. 7.9 km/s
    2. 11.2 km/s
    3. 13.6 km/s
    4. 9.8 km/s
12. Q12. A solid sphere and a hollow sphere of same mass and radius rolling without slipping down an incline — which reaches the bottom first
    1. Solid sphere
    2. Hollow sphere
    3. Both together
    4. Depends on incline angle
13. Q13. Gravitational potential energy on Earth surface relative to infinity is
    1. +GMm/R
    2. -GMm/R
    3. -GMm/R²
    4. 0
14. Q14. The motional EMF across a rod of length L moving with velocity v perpendicular to magnetic field B is
    1. BLv
    2. BL/v
    3. B/Lv
    4. BvL^2
15. Q15. Maxwell's equation relating curl of B to current and changing E-field is
    1. Gauss's law
    2. Faraday's law
    3. Ampere-Maxwell law
    4. Gauss's law for magnetism
16. Q16. Kepler's third law states T² is proportional to
    1. a
    2. a²
    3. a³
    4. 1/a
17. Q17. 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
18. Q18. Carboxylic acids on reduction with LiAlH4 yield
    1. Aldehydes
    2. Primary alcohols
    3. Secondary alcohols
    4. Ketones
19. Q19. Decarboxylation of sodium salts of carboxylic acids with sodalime gives
    1. Higher hydrocarbons
    2. Hydrocarbons with one less carbon
    3. Aldehydes
    4. Alcohols
20. Q20. 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
21. Q21. 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
22. Q22. Fischer esterification involves carboxylic acid and alcohol in presence of
    1. NaOH
    2. Conc H2SO4 (acid catalyst)
    3. LiAlH4
    4. Zn dust
23. Q23. Sandmeyer reaction converts an aryl diazonium salt to aryl halide using
    1. CuCl/HCl or CuBr/HBr
    2. HBF4 thermal
    3. H3PO2
    4. NaOH
24. Q24. Schiemann reaction prepares aryl fluorides from diazonium salts via
    1. Direct reaction with KF
    2. HBF4 + thermal decomposition
    3. CuF/HF
    4. HF/peroxide
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. Liebermanns nitroso test is a confirmatory test for
    1. Aldehydes
    2. Phenols
    3. Primary amines
    4. Carboxylic acids
27. Q27. Coupling of diazonium salt with phenol in mildly alkaline medium gives
    1. Methyl orange
    2. para-Hydroxyazobenzene
    3. Aniline yellow
    4. Indigo
28. Q28. 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
29. Q29. The Gattermann reaction differs from Sandmeyer in using
    1. CuCN
    2. Cu/HCl in place of CuCl/HCl
    3. HBF4
    4. HNO2
30. Q30. The bond enthalpy of H-H is approximately (kJ/mol)
    1. 436
    2. 347
    3. 414
    4. 498
31. Q31. A Frenkel defect involves
    1. Vacancy only
    2. Cation displaced to interstitial site
    3. Removal of both ions
    4. Substitution of impurity
32. Q32. The actinide series begins with which element?
    1. Thorium (Z=90)
    2. Actinium (Z=89)
    3. Uranium (Z=92)
    4. Lanthanum (Z=57)
33. Q33. A meso compound is one which
    1. Is optically active
    2. Has chiral centres but an internal plane of symmetry, hence optically inactive
    3. Has no chiral centres
    4. Is a racemic mixture
34. Q34. The most stable allotrope of carbon at standard conditions is
    1. Diamond
    2. Graphite
    3. Fullerene
    4. Amorphous carbon
35. Q35. Principal value branch of sin^-1 x is
    1. [0, pi]
    2. [-pi/2, pi/2]
    3. [-pi, pi]
    4. (0, pi)
36. Q36. 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)
37. Q37. 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
38. Q38. 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
39. Q39. Derivative of log(x) with respect to x (natural logarithm) is
    1. 1/x
    2. x
    3. log x
    4. e^x
40. Q40. Principal value branch of cos^-1 x is
    1. [-pi/2, pi/2]
    2. [0, pi]
    3. (0, pi)
    4. [-pi, 0]
41. Q41. Newtons law of cooling states that dT/dt is proportional to
    1. (T – T0)
    2. (T0 – T)
    3. -(T – T0)
    4. T^2
42. Q42. 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]
43. Q43. 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
44. Q44. 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
45. Q45. The equation of the tangent to the circle x² + y² = 25 at the point (3, 4) is
    1. 3x + 4y = 25
    2. 3x – 4y = 25
    3. 4x + 3y = 25
    4. x + y = 7
46. Q46. Number of arrangements of letters of "BANANA"
    1. 60
    2. 120
    3. 360
    4. 720
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. tan^-1 x + tan^-1 y = tan^-1((x + y)/(1 – xy)) holds when
    1. xy < 1
    2. xy > 1
    3. xy = 1
    4. x + y = 0
49. Q49. The inradius r of a triangle is given by (s = semi-perimeter, Delta = area)
    1. Delta * s
    2. Delta / s
    3. s / Delta
    4. s * Delta
50. Q50. ∫ 1/x dx =
    1. x ln x + C
    2. ln|x| + C
    3. 1/x + C
    4. −1/x^2 + C