Daily MCQ Paper — 18 April 2026

Daily MCQ Paper — 18 April 2026

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

1. Q1. 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
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. Lenz's law is a consequence of conservation of
   1. Charge
   2. Energy
   3. Momentum
   4. Mass
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. 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
6. Q6. 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)
7. Q7. Visible light has wavelength range approximately
   1. 100-400 nm
   2. 400-700 nm
   3. 700-1000 nm
   4. 1-100 nm
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. Magnetic dipole moment of a current loop of N turns, area A and current I is
    1. NIA
    2. I/A
    3. NA/I
    4. N/IA
12. Q12. A wire of resistance R is stretched to double its length. New resistance is
    1. R
    2. 2R
    3. 4R
    4. R/2
13. Q13. The maximum line-of-sight distance for a transmitting antenna of height h on a smooth earth (radius R) is approximately
    1. √(2Rh)
    2. √(Rh)
    3. 2√(Rh)
    4. Rh
14. Q14. 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
15. Q15. Young's modulus has units of
    1. N
    2. N·m
    3. Pa
    4. J
16. Q16. 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
17. Q17. The Rydberg formula for hydrogen spectral lines gives wavenumber 1/λ =
    1. R(1/n₁² – 1/n₂²)
    2. R(1/n₂² – 1/n₁²)
    3. Rn₁n₂
    4. R/n
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. 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
22. Q22. Henry's law constant has units of
    1. Pressure
    2. Pressure/concentration or pressure/mole-fraction
    3. Concentration
    4. Dimensionless
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. Standard hydrogen electrode (SHE) potential is taken as
    1. 0.00 V
    2. 1.00 V
    3. -1.00 V
    4. 0.34 V
26. Q26. 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
27. Q27. 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
28. Q28. Carboxylic acids are more acidic than alcohols because
    1. -COOH has a less stable conjugate base
    2. Resonance stabilisation of carboxylate ion
    3. Sigma effect only
    4. -OH is non-acidic
29. Q29. Bond order of O2 from MO theory is
    1. 1
    2. 1.5
    3. 2
    4. 3
30. Q30. Froth flotation is used for concentration of
    1. Oxide ores
    2. Sulphide ores
    3. Carbonate ores
    4. Native metals
31. Q31. Mole fraction of solute x_A in a solution is defined as
    1. n_A / n_B
    2. n_A / (n_A + n_B)
    3. n_B / (n_A + n_B)
    4. m / V
32. Q32. Half-life of a zero-order reaction is
    1. t = [A]₀/(2k)
    2. t = ln2/k
    3. t = 1/(k[A]₀)
    4. t = [A]₀/k
33. Q33. n-type semiconductor is produced by doping silicon with
    1. Boron
    2. Phosphorus
    3. Aluminium
    4. Gallium
34. Q34. Wurtz reaction couples two alkyl halides using
    1. Na/dry ether
    2. Zn/HCl
    3. Fe/H2O
    4. LiAlH4
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. For positive numbers AM-GM inequality states AM
    1. >= GM
    2. <= GM
    3. = GM always
    4. > GM strictly always
38. Q38. lim_{x->0} (sin x)/x equals
    1. 0
    2. 1
    3. infinity
    4. undefined
39. Q39. lim_{x->0} (1-cos x)/x^2 equals
    1. 0
    2. 1/2
    3. 1
    4. infinity
40. Q40. By L'Hospital's rule, lim_{x->0} (e^x – 1)/x =
    1. 0
    2. 1
    3. e
    4. infinity
41. Q41. 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
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. det of identity matrix of order n is
    1. 0
    2. 1
    3. n
    4. n!
46. Q46. The general solution of dy/dx = y is
    1. y = Cx
    2. y = C e^x
    3. y = ln x + C
    4. y = C/x
47. Q47. Principal value of sin^-1(1/2) is
    1. pi/3
    2. pi/6
    3. pi/4
    4. pi/2
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. Maximum value of y = sin x + cos x is
    1. 1
    2. √2
    3. 2
    4. √3
50. Q50. ∫(0 to π/2) sin x dx equals
    1. 0
    2. 1
    3. π/2
    4. 2