Daily MCQ Paper — 6 April 2026

Daily MCQ Paper — 6 April 2026

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

1. Q1. 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
2. Q2. 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)
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. 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
5. Q5. 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
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 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
8. Q8. 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
9. Q9. 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
10. Q10. 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
11. Q11. 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
12. Q12. Curie temperature of iron, above which it loses ferromagnetism, is approximately
    1. 770 K
    2. 1043 K
    3. 1300 K
    4. 1700 K
13. Q13. The speed of EM waves in vacuum is given by
    1. sqrt(mu0/epsilon0)
    2. sqrt(mu0*epsilon0)
    3. 1/sqrt(mu0*epsilon0)
    4. 1/(mu0*epsilon0)
14. Q14. 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
15. Q15. At resonance in a series LCR circuit, the impedance is
    1. Maximum
    2. Equal to R
    3. Equal to XL
    4. Zero
16. Q16. Critical angle for glass-air interface (n=1.5) is approximately
    1. 30 deg
    2. 42 deg
    3. 60 deg
    4. 48 deg
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. 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. 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
21. Q21. 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
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. 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
25. Q25. 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
26. Q26. Mond process refines
    1. Aluminium
    2. Nickel via Ni(CO)_4 vapour formation and decomposition
    3. Iron
    4. Sodium
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. Nernst equation for an electrode reaction at 298 K is E = E° –
    1. (0.0591/n) log Q
    2. (0.0591/n) ln Q
    3. (0.0257/n) log Q
    4. (2.303*RT/F) log Q
29. Q29. The Henderson-Hasselbalch equation for a buffer is
    1. pH = pKa + log([salt]/[acid])
    2. pH = pKa − log([salt]/[acid])
    3. pH = pKa + log([acid]/[salt])
    4. pH = pKw − pKa
30. Q30. Glucose and fructose are linked by which bond in sucrose?
    1. α(1→4) glycosidic
    2. α(1→2)β glycosidic
    3. β(1→4) glycosidic
    4. peptide
31. Q31. The Gattermann reaction differs from Sandmeyer in using
    1. CuCN
    2. Cu/HCl in place of CuCl/HCl
    3. HBF4
    4. HNO2
32. Q32. The solubility product Ksp of AgCl at 25°C is approximately
    1. 1.8 × 10^(−10)
    2. 1.0 × 10^(−14)
    3. 1.0 × 10^(−5)
    4. 1.6 × 10^(−2)
33. Q33. The catalytic activity of d-block metals is attributed to
    1. Inert pair effect
    2. Variable oxidation states + ability to provide adsorption sites
    3. Diamagnetism
    4. Lanthanoid contraction
34. Q34. Peptide bond between amino acids is a
    1. C-N bond formed by condensation
    2. C-O bond
    3. C-C bond
    4. S-S bond
35. Q35. 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
36. Q36. 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
37. Q37. 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
38. Q38. 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
39. Q39. 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
40. Q40. Karl Pearson correlation coefficient r lies in
    1. [0, 1]
    2. [-1, 1]
    3. [0, infinity)
    4. (-infinity, infinity)
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. Standard deviation is the
    1. Square of variance
    2. Square root of variance
    3. Mean of deviations
    4. Range
43. Q43. Coefficient of variation is
    1. sigma
    2. sigma / x_bar
    3. (sigma / x_bar) x 100
    4. x_bar
44. Q44. Power set of a set with n elements has cardinality
    1. n
    2. 2^n
    3. n^2
    4. n!
45. Q45. For a binomial distribution B(n,p), mean and variance are
    1. np, np
    2. np, npq
    3. n²p, npq
    4. np, p²q
46. Q46. 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
47. Q47. The general solution of tan x = tan alpha is
    1. x = n*pi + alpha
    2. x = 2n*pi + alpha
    3. x = (2n+1)*pi/2 + alpha
    4. x = n*pi – alpha
48. Q48. The locus of a point which moves so that its distance from (1,0) equals its distance from the line x = -1 is
    1. y² = 4x
    2. x² = 4y
    3. y² = 2x
    4. x² + y² = 4
49. Q49. Lagrange Mean Value Theorem requires f to be
    1. Continuous on [a,b], differentiable on (a,b)
    2. Only continuous
    3. Only differentiable
    4. Periodic
50. Q50. Bayes theorem expresses P(A|B) as
    1. P(A)P(B)/P(A∩B)
    2. P(B|A)P(A)/P(B)
    3. P(A∪B)/P(B)
    4. P(A)+P(B)-P(A∩B)