Daily MCQ Paper — 17 April 2026

Daily MCQ Paper — 17 April 2026

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

1. Q1. Lenz's law is a consequence of conservation of
   1. Charge
   2. Energy
   3. Momentum
   4. Mass
2. Q2. The induced EMF in a coil of N turns when flux changes from phi1 to phi2 in time t is
   1. N(phi1-phi2)/t
   2. -N(phi2-phi1)/t
   3. -(phi2-phi1)/Nt
   4. N(phi2-phi1)t
3. Q3. The self-inductance of a long solenoid (n turns/m, area A, length l) is
   1. mu0*n*A*l
   2. mu0*n^2*A*l
   3. mu0*n^2*A/l
   4. mu0*n*A^2*l
4. Q4. 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
5. Q5. Visible light has wavelength range approximately
   1. 100-400 nm
   2. 400-700 nm
   3. 700-1000 nm
   4. 1-100 nm
6. Q6. 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
7. Q7. 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)
8. Q8. The photoelectric work function of a metal corresponds to
   1. KE of fastest electron
   2. Minimum energy to eject an electron
   3. Energy of incident photon
   4. Stopping potential
9. Q9. de Broglie wavelength of a particle of momentum p is
   1. h*p
   2. h/p
   3. p/h
   4. hp/c
10. Q10. The Davisson-Germer experiment confirmed
    1. Particle nature of light
    2. Wave nature of electrons
    3. Quantization of charge
    4. Existence of neutron
11. Q11. The resonance frequency of a series LCR circuit with L = 2 H and C = 8 µF is approximately
    1. 40 Hz
    2. 25 Hz
    3. 100 Hz
    4. 400 Hz
12. Q12. A source of frequency f moves toward a stationary observer at speed vs. The apparent frequency (sound speed v) is
    1. f(v + vs)/v
    2. f v/(v – vs)
    3. f v/(v + vs)
    4. f(v – vs)/v
13. Q13. Wien's displacement law states that lambda_max * T equals approximately
    1. 2.9 x 10^-3 m K
    2. 5.67 x 10^-8 W/m^2K^4
    3. 6.63 x 10^-34 J s
    4. 9.0 x 10^9 Nm^2/C^2
14. Q14. Energy stored in a capacitor of capacitance C charged to voltage V is
    1. CV
    2. CV²
    3. ½ CV²
    4. ½ C/V
15. Q15. A magnetic dipole in a uniform field B has potential energy U = -m·B. It is in stable equilibrium when
    1. m parallel to B
    2. m antiparallel to B
    3. m perpendicular to B
    4. m at 45° to B
16. Q16. The work-energy theorem states that net work done equals
    1. Change in momentum
    2. Change in kinetic energy
    3. Change in potential energy
    4. Change in mechanical energy
17. Q17. The Quality factor (Q) of a series LCR circuit at resonance is
    1. ω₀L/R
    2. R/ω₀L
    3. RC
    4. ω₀/R
18. Q18. Physisorption is characterized by
    1. High enthalpy of adsorption
    2. Van der Waals forces
    3. Specific to adsorbate-adsorbent
    4. Activation energy required
19. Q19. The Freundlich adsorption isotherm is x/m =
    1. k*P^(1/n)
    2. k*P/(1+aP)
    3. k+P/n
    4. k*log(P)
20. Q20. Tyndall effect is shown by
    1. True solutions
    2. Colloidal solutions
    3. Suspensions
    4. Both colloidal and suspensions
21. Q21. Henry's law constant has units of
    1. Pressure
    2. Pressure/concentration or pressure/mole-fraction
    3. Concentration
    4. Dimensionless
22. Q22. Raoult's law states that for an ideal solution, partial vapour pressure equals
    1. x_solvent * p0_solvent
    2. p0/x
    3. x*p0_solute
    4. x^2 * p0
23. Q23. The osmotic pressure equation is
    1. pi = nRT
    2. pi*V = nRT
    3. pi = nRT/V
    4. pi*V = R/T
24. Q24. Van't Hoff factor i for NaCl in water (assuming complete dissociation) is
    1. 1
    2. 2
    3. 3
    4. 4
25. Q25. Kohlrausch's law of independent migration of ions states that
    1. Lambda_m at infinite dilution = sum of ionic conductances
    2. Ionic mobility = constant
    3. Conductance increases with concentration
    4. None
26. Q26. Standard hydrogen electrode (SHE) potential is taken as
    1. 0.00 V
    2. 1.00 V
    3. -1.00 V
    4. 0.34 V
27. Q27. 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
28. Q28. Compared to lanthanides, actinide contraction is
    1. Smaller
    2. Greater (5f shielding poorer)
    3. Same
    4. Reverse
29. Q29. A Schottky defect involves
    1. Cation vacancy and anion vacancy in equal numbers
    2. Cation in interstitial site
    3. Extra electron
    4. Hole in valence band
30. Q30. A Frenkel defect involves
    1. Vacancy only
    2. Cation displaced to interstitial site
    3. Removal of both ions
    4. Substitution of impurity
31. Q31. Mond process is used for refining
    1. Copper
    2. Zinc
    3. Nickel
    4. Iron
32. Q32. Markovnikov's rule applies to addition of
    1. Symmetric reagent to symmetric alkene
    2. HX to unsymmetric alkene
    3. Halogen to alkyne
    4. Diazonium decomposition
33. Q33. Van Arkel method is used for refining
    1. Cu and Ag
    2. Zr and Ti (ultra-pure)
    3. Pb and Sn
    4. Fe and Mn
34. Q34. The pH of 0.001 M HCl is
    1. 2
    2. 3
    3. 4
    4. 11
35. Q35. Sum of first n natural numbers is
    1. n(n+1)/2
    2. n(n-1)/2
    3. n(n+1)(2n+1)/6
    4. n^2
36. Q36. Sum of first n 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^2(n+1)^2/4
37. Q37. lim_{x->0} (1-cos x)/x^2 equals
    1. 0
    2. 1/2
    3. 1
    4. infinity
38. Q38. For positive numbers AM-GM inequality states AM
    1. >= GM
    2. <= GM
    3. = GM always
    4. > GM strictly always
39. Q39. lim_{x->0} (sin x)/x equals
    1. 0
    2. 1
    3. infinity
    4. undefined
40. Q40. Rolle's Theorem requires the function to be
    1. Continuous on [a,b], differentiable on (a,b), and f(a)=f(b)
    2. Continuous on (a,b) only
    3. Differentiable everywhere
    4. Monotonic
41. Q41. By L'Hospital's rule, lim_{x->0} (e^x – 1)/x =
    1. 0
    2. 1
    3. e
    4. infinity
42. Q42. A function is increasing on an interval if
    1. f'(x) >= 0 on that interval
    2. f'(x) <= 0
    3. f''(x) > 0
    4. f(x) > 0
43. Q43. Lagrange's Mean Value Theorem states that for continuous f on [a,b], differentiable on (a,b), there exists c with
    1. f'(c) = f(b)-f(a)
    2. f'(c) = (f(b)-f(a))/(b-a)
    3. f(c) = (f(b)-f(a))/(b-a)
    4. f'(c) = (b-a)/(f(b)-f(a))
44. Q44. At a local maximum of a twice-differentiable function f, we have
    1. f'(x)=0 and f''(x)>0
    2. f'(x)=0 and f''(x)<0
    3. f'(x)>0 and f''(x)=0
    4. f''(x)=0
45. Q45. The number of 5-digit numbers with all distinct digits using {0..9} is
    1. 9 × 9P4
    2. 10P5
    3. 9 × 10P4
    4. 9P5
46. Q46. Volume generated by rotating y = √x (0 ≤ x ≤ 4) about x-axis is
    1. 4π
    2. 8π
    3. 16π
    4. 32π
47. Q47. The general term in the expansion of (x + a)ⁿ is Tr+1 =
    1. nCr xⁿ⁻ʳ aʳ
    2. nCr xʳ aⁿ⁻ʳ
    3. nCr (-x)ʳ
    4. xⁿ⁻ʳ aʳ
48. Q48. Variance of n observations equals
    1. Mean of squares – square of mean
    2. Square of mean – mean of squares
    3. Mean of squares only
    4. Always 0
49. Q49. The locus of a point equidistant from a fixed point and a fixed line is a
    1. Circle
    2. Parabola
    3. Ellipse
    4. Hyperbola
50. Q50. Sum of cubes 1^3 + 2^3 + … + n^3 equals
    1. n(n+1)/2
    2. n(n+1)(2n+1)/6
    3. [n(n+1)/2]^2
    4. n^4