Daily MCQ Paper — 5 April 2026

Daily MCQ Paper — 5 April 2026

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

1. Q1. On a banked road of angle theta with friction neglected, the maximum speed for a curve of radius r is
   1. sqrt(rg tan theta)
   2. sqrt(rg/tan theta)
   3. rg tan theta
   4. 0
2. Q2. In an Atwood machine with masses m1 and m2 (m1>m2) connected by a light inextensible string over a frictionless pulley, the acceleration of the system is
   1. g
   2. (m1-m2)g/(m1+m2)
   3. (m1+m2)g/(m1-m2)
   4. 0
3. Q3. In a perfectly elastic 1-D head-on collision between equal masses with one initially at rest, the velocities after collision are
   1. Both stop
   2. The moving particle stops and the stationary one moves with the original velocity
   3. They stick together
   4. Both move with v/2
4. Q4. For a conical pendulum with string length L making angle theta with vertical, the period of revolution is
   1. 2 pi sqrt(L cos theta / g)
   2. 2 pi sqrt(L / g)
   3. 2 pi sqrt(L sin theta / g)
   4. sqrt(g/L)
5. Q5. The minimum speed at the top of a vertical circular loop of radius R for a body to maintain contact is
   1. sqrt(gR)
   2. sqrt(2gR)
   3. sqrt(5gR)
   4. 0
6. Q6. The escape velocity from Earth’s surface is approximately
   1. 7.9 km/s
   2. 11.2 km/s
   3. 3 km/s
   4. 30 km/s
7. Q7. The orbital speed of a satellite at radius r from Earth’s centre is
   1. sqrt(GM/r)
   2. sqrt(2GM/r)
   3. sqrt(GM r)
   4. GMr
8. Q8. A geostationary satellite has orbital period T = 24h and approximate radius from Earth’s centre
   1. 42,000 km
   2. 6,400 km
   3. 3,84,000 km
   4. 1,000 km
9. Q9. Total mechanical energy of a satellite of mass m in a circular orbit of radius r is
   1. -GMm/(2r)
   2. -GMm/r
   3. +GMm/(2r)
   4. 0
10. Q10. Coefficient of static friction (mu_s) and kinetic friction (mu_k) for the same surfaces typically obey
    1. mu_s = mu_k
    2. mu_s > mu_k
    3. mu_s < mu_k
    4. mu_s = 0
11. Q11. 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
12. Q12. The wave equation for a transverse wave on a string is given by y = A sin(kx – omega*t). Wave speed equals
    1. A*omega
    2. omega/k
    3. k*omega
    4. A/k
13. Q13. 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
14. Q14. 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
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. Curies law states that magnetic susceptibility of a paramagnetic material is
    1. Directly proportional to absolute temperature
    2. Inversely proportional to absolute temperature
    3. Independent of temperature
    4. Proportional to T squared
17. Q17. 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
18. Q18. The Nernst equation for an electrode reaction at 298 K is
    1. E = E° – (0.0591/n) log Q
    2. E = E° + RT log Q
    3. E = E° – 2.303 RT/F
    4. E = nFE°
19. Q19. The relationship between standard cell EMF and equilibrium constant is
    1. E°_cell = (0.0591/n) log K
    2. E°_cell = nFK
    3. E°_cell = K/n
    4. E°_cell = -log K
20. Q20. Mond process refines
    1. Aluminium
    2. Nickel via Ni(CO)_4 vapour formation and decomposition
    3. Iron
    4. Sodium
21. Q21. Faraday’s first law of electrolysis is
    1. m = ZIt where Z is electrochemical equivalent
    2. m = nFI
    3. m = It/n
    4. m = E^2
22. Q22. Order of a reaction is
    1. Sum of stoichiometric coefficients
    2. Sum of exponents of concentrations in the experimental rate law
    3. Always equal to molecularity
    4. Always 1
23. Q23. Half-life of a first-order reaction depends on
    1. Initial concentration only
    2. Rate constant only and is t_{1/2} = 0.693/k
    3. Both concentration and k
    4. Neither
24. Q24. Kohlrausch’s law of independent migration of ions states that
    1. Conductivity is independent of concentration
    2. Limiting molar conductivity is the sum of independent contributions of cation and anion
    3. Conductivity is zero at infinite dilution
    4. None
25. Q25. Arrhenius equation links rate constant and temperature as
    1. k = A exp(-E_a/RT)
    2. k = A T
    3. k = A/T^2
    4. k = 1/A
26. Q26. Froth flotation is principally used for concentrating which type of ores
    1. Iron oxide
    2. Sulphide ores like galena, sphalerite, chalcopyrite
    3. Bauxite
    4. Rock salt
27. Q27. Van Arkel method is used to obtain ultra-pure
    1. Iron
    2. Zirconium and titanium via thermal decomposition of their iodides
    3. Sodium
    4. Aluminium
28. Q28. Hinsberg reagent (benzenesulphonyl chloride) is used to distinguish
    1. Alkyl halides
    2. 1°, 2°, 3° amines
    3. Alcohols
    4. Aldehydes from ketones
29. Q29. The intense colour of transition-metal complexes is due to
    1. s-s transitions
    2. p-p transitions
    3. d-d transitions
    4. f-f transitions
30. Q30. The most stable conformation of n-butane is
    1. Gauche
    2. Eclipsed
    3. Anti (180°)
    4. Skew
31. Q31. Which gas is liberated at the anode during electrolysis of dilute H2SO4?
    1. H2
    2. O2
    3. SO2
    4. Cl2
32. Q32. The bond enthalpy of H-H is approximately (kJ/mol)
    1. 436
    2. 347
    3. 414
    4. 498
33. Q33. A racemic mixture is
    1. Equimolar mixture of two enantiomers, optically inactive due to external compensation
    2. A meso compound
    3. A diastereomer mixture
    4. Optically active
34. Q34. Zeolites belong to the class of
    1. Borosilicates
    2. Aluminosilicates
    3. Carbonates
    4. Phosphates
35. Q35. Coefficient of variation is
    1. sigma
    2. sigma / x_bar
    3. (sigma / x_bar) x 100
    4. x_bar
36. Q36. If A and B are two sets, A intersect B = phi means
    1. A and B are equal
    2. A and B are disjoint
    3. A is subset of B
    4. B is subset of A
37. Q37. A relation R on a set A which is reflexive, symmetric and transitive is called
    1. Partial order
    2. Equivalence relation
    3. Function
    4. Identity
38. Q38. Standard deviation is the
    1. Square of variance
    2. Square root of variance
    3. Mean of deviations
    4. Range
39. Q39. A function f: A -> B is bijective if and only if
    1. It is injective only
    2. It is surjective only
    3. It is both injective and surjective
    4. It is constant
40. Q40. The contrapositive of “If p then q” is
    1. If q then p
    2. If not q then not p
    3. If not p then not q
    4. p and q
41. Q41. Mean deviation about mean is computed as
    1. sigma (x_i – x_bar)^2 / n
    2. sigma |x_i – x_bar| / n
    3. sigma x_i / n
    4. x_max – x_min
42. Q42. Negation of “For all x, p(x)” is
    1. For all x, not p(x)
    2. There exists x such that not p(x)
    3. There exists x such that p(x)
    4. None
43. Q43. Karl Pearson correlation coefficient r lies in
    1. [0, 1]
    2. [-1, 1]
    3. [0, infinity)
    4. (-infinity, infinity)
44. Q44. Power set of a set with n elements has cardinality
    1. n
    2. 2^n
    3. n^2
    4. n!
45. Q45. Equation of parabola with focus (a,0) and directrix x = -a is
    1. y² = 4ax
    2. x² = 4ay
    3. x² = -4ay
    4. y² = -4ax
46. Q46. 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
47. Q47. If A is a 3×3 matrix with |A| ≠ 0, then A⁻¹ equals
    1. adj(A)/|A|
    2. |A|·adj(A)
    3. adj(A)·|A|²
    4. (adj A)⁻¹
48. Q48. Principal value branch of cos^-1 x is
    1. [-pi/2, pi/2]
    2. [0, pi]
    3. (0, pi)
    4. [-pi, 0]
49. Q49. 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
50. Q50. The general equation x² + y² + 2gx + 2fy + c = 0 represents a real circle iff
    1. g² + f² – c > 0
    2. g² + f² – c = 0
    3. g² + f² – c < 0
    4. g + f + c > 0