Daily MCQ Paper — 12 April 2026

Daily MCQ Paper — 12 April 2026

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

1. Q1. Electric field inside a uniformly charged solid conducting sphere of radius R, at point r<R, is
   1. kQr/R³
   2. kQ/r²
   3. kQ/R²
   4. zero
2. Q2. A point charge q at the centre of a cube — total electric flux through the cube is
   1. q/ε₀
   2. q/(6ε₀)
   3. zero
   4. q/(8ε₀)
3. Q3. Two point charges +q and -q form a dipole of length 2a; electric field on the axial line at distance r (r>>a) is
   1. kp/r³
   2. 2kp/r³
   3. kp/r²
   4. 3kp/r³
4. Q4. The minimum deviation through a prism of refractive index μ and angle A occurs when
   1. Light enters and exits symmetrically
   2. i = e (angles of incidence and emergence equal)
   3. Both A and B
   4. Light is incident normally
5. Q5. 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
6. Q6. A combination of two thin lenses of focal lengths f₁ and f₂ in contact has equivalent focal length F given by
   1. F = f₁ + f₂
   2. 1/F = 1/f₁ + 1/f₂
   3. F = f₁f₂/(f₁+f₂)
   4. Both B and C
7. Q7. Moment of inertia of a uniform thin rod of length L and mass M about an axis through one end perpendicular to length is
   1. ML²/12
   2. ML²/3
   3. ML²/4
   4. 2ML²/3
8. Q8. For a rigid body rotating about a fixed axis, angular momentum L and angular velocity ω are related by
   1. L = Iω
   2. L = mvω
   3. L = ω/I
   4. L = I²ω
9. Q9. The kinetic energy of a body of mass M and radius R rolling without slipping with linear speed v is
   1. ½Mv²
   2. ½Mv²(1 + I/MR²)
   3. Mv²
   4. Mv²(1 + I/MR²)
10. Q10. A simple astronomical telescope in normal adjustment has objective focal length f_o and eyepiece f_e; its magnifying power is
    1. f_o + f_e
    2. f_o/f_e
    3. f_e/f_o
    4. f_o·f_e
11. Q11. 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)
12. Q12. Amplitude modulation (AM) involves variation of
    1. Frequency of carrier
    2. Phase of carrier
    3. Amplitude of carrier with signal
    4. Wavelength only
13. Q13. In SHM, at the mean position the energy is
    1. Entirely potential
    2. Entirely kinetic
    3. Equally divided
    4. Zero
14. Q14. 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
15. Q15. de Broglie wavelength of an electron accelerated through 150 V is approximately
    1. 1 angstrom
    2. 0.5 angstrom
    3. 2 angstrom
    4. 12 angstrom
16. Q16. 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
17. Q17. In SHM, when displacement is half the amplitude, the ratio KE:PE is
    1. 1:1
    2. 3:1
    3. 1:3
    4. 2:1
18. Q18. The Cannizzaro reaction is undergone by aldehydes that have
    1. At least one alpha-hydrogen
    2. No alpha-hydrogen (e.g., HCHO, PhCHO)
    3. A double bond
    4. Two carbonyls
19. Q19. In the aldol condensation, the alpha-hydrogen of a carbonyl compound is removed by a
    1. Strong acid (H₂SO₄)
    2. Mild base (OH⁻ or alkoxide)
    3. Free radical initiator
    4. Lewis acid AlCl₃
20. Q20. In electrophilic aromatic substitution, –OCH₃ on benzene acts as a
    1. Strong deactivator, meta director
    2. Strong activator, ortho/para director
    3. Weak deactivator, meta director
    4. Activator, meta director
21. Q21. In a crossed-Cannizzaro reaction with HCHO and PhCHO in concentrated NaOH, the products are
    1. PhCHO is reduced; HCHO is oxidised
    2. HCHO is reduced; PhCHO is oxidised
    3. Both oxidised
    4. Both reduced
22. Q22. In Friedel-Crafts alkylation, a major limitation is
    1. Failure with deactivated arenes (e.g., nitrobenzene)
    2. Polyalkylation due to product being more activated
    3. Carbocation rearrangements
    4. All of the above
23. Q23. 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
24. Q24. The R/S configuration is assigned by the Cahn-Ingold-Prelog rules; priority is decided by
    1. Atomic number at the chiral centre
    2. Atomic mass only
    3. Bond length
    4. Polarity of substituent
25. Q25. The most stable conformation of n-butane is
    1. Gauche
    2. Eclipsed
    3. Anti (180°)
    4. Skew
26. Q26. In cyclohexane, the chair conformation is preferred over the boat because
    1. Boat has more torsional strain (eclipsing) and flagpole interactions
    2. Chair has bond angles of exactly 120°
    3. Boat is planar
    4. Chair has more torsional strain
27. Q27. 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
28. Q28. For the reaction N2 + 3H2 ⇌ 2NH3, the relation between Kp and Kc is
    1. Kp = Kc
    2. Kp = Kc(RT)
    3. Kp = Kc(RT)^(−2)
    4. Kp = Kc(RT)^2
29. Q29. Standard hydrogen electrode (SHE) potential is taken as
    1. 0.00 V
    2. 1.00 V
    3. -1.00 V
    4. 0.34 V
30. Q30. First transition series elements typically show
    1. Only +2 oxidation state
    2. Variable oxidation states due to participation of (n-1)d electrons
    3. Only +3
    4. +1 only
31. Q31. One major consequence of lanthanide contraction is
    1. Zr and Hf have similar atomic radii
    2. Increase in metallic character
    3. Higher reactivity of 5d elements
    4. None
32. Q32. 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
33. Q33. The spin-only magnetic moment formula is
    1. µ = √(n(n+2)) BM
    2. µ = n BM
    3. µ = √n BM
    4. µ = n² BM
34. Q34. Markovnikov's rule applies to
    1. Free-radical addition
    2. Electrophilic addition to alkenes
    3. Nucleophilic substitution
    4. Elimination
35. Q35. The asymptotes of the hyperbola x²/16 – y²/9 = 1 are
    1. y = ±(3/4)x
    2. y = ±(4/3)x
    3. y = ±(16/9)x
    4. y = ±x
36. Q36. The eccentricity of the ellipse x²/25 + y²/9 = 1 is
    1. 3/5
    2. 4/5
    3. 5/3
    4. 5/4
37. Q37. The length of the latus rectum of the parabola y² = 16x is
    1. 4
    2. 8
    3. 16
    4. 32
38. Q38. The directrix of the parabola y² = 12x is
    1. x = -3
    2. x = 3
    3. y = -3
    4. y = 3
39. Q39. 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
40. Q40. 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
41. Q41. Two circles x²+y²+2g₁x+2f₁y+c₁=0 and x²+y²+2g₂x+2f₂y+c₂=0 cut orthogonally iff
    1. 2g₁g₂ + 2f₁f₂ = c₁ + c₂
    2. g₁g₂ + f₁f₂ = c₁c₂
    3. g₁+g₂ = f₁+f₂
    4. c₁+c₂ = 0
42. Q42. The angle between the lines y = 2x + 3 and y = -3x + 1 is given by
    1. tan⁻¹(1)
    2. tan⁻¹(5/5) = 45°
    3. tan⁻¹|(2-(-3))/(1+2(-3))| = tan⁻¹(1) = 45°
    4. tan⁻¹(7)
43. Q43. The perpendicular distance from the point (3, -2) to the line 4x – 3y + 5 = 0 is
    1. 23/5
    2. 19/5
    3. 17/5
    4. 11/5
44. Q44. 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
45. Q45. Shortest distance between two skew lines with vectors a₁, a₂ and directions b₁, b₂ is
    1. |(a₂-a₁)·(b₁×b₂)| / |b₁×b₂|
    2. |b₁·b₂|
    3. |a₂-a₁|
    4. 0
46. Q46. ∫ 1/x dx =
    1. x ln x + C
    2. ln|x| + C
    3. 1/x + C
    4. −1/x^2 + C
47. Q47. For a binomial distribution B(n,p), mean and variance are
    1. np, np
    2. np, npq
    3. n²p, npq
    4. np, p²q
48. Q48. By the Newton-Leibniz theorem, d/dx ∫(a to x) f(t) dt =
    1. f(a)
    2. f(x)
    3. f(x) − f(a)
    4. F(x) − F(a)
49. Q49. lim_{x->0} (sin x)/x equals
    1. 0
    2. 1
    3. infinity
    4. undefined
50. Q50. For positive numbers AM-GM inequality states AM
    1. >= GM
    2. <= GM
    3. = GM always
    4. > GM strictly always