Daily MCQ Paper — 11 April 2026

Daily MCQ Paper — 11 April 2026

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

1. Q1. 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)
2. Q2. 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
3. Q3. 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
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. 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
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. 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
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 Davisson-Germer experiment confirmed
    1. Particle nature of light
    2. Wave nature of electrons
    3. Quantization of charge
    4. Existence of neutron
12. Q12. 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
13. Q13. Power delivered by a constant force F on a body moving with velocity v is
    1. F·v
    2. F²/v
    3. F·v²
    4. ½Fv
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. Fourier law of heat conduction is dQ/dt =
    1. -kA dT/dx
    2. kA dT
    3. kA T^4
    4. -k dT/dx
16. Q16. Two identical capacitors, charged to potentials V1 and V2, are connected in parallel. Common potential is
    1. (V1+V2)/2
    2. V1V2/(V1+V2)
    3. (V1V2)/2
    4. (V1-V2)/2
17. Q17. The energy of the n-th hydrogen orbit is given by
    1. -13.6/n² eV
    2. -13.6n² eV
    3. 13.6/n eV
    4. -3.4n eV
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 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
21. Q21. 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
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. 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
25. Q25. 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
26. Q26. The most stable conformation of n-butane is
    1. Gauche
    2. Eclipsed
    3. Anti (180°)
    4. Skew
27. Q27. 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
28. Q28. 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
29. Q29. According to Le Chatelier's principle, increasing pressure on N2+3H2⇌2NH3 will
    1. Shift equilibrium left
    2. Shift equilibrium right (towards NH3)
    3. Have no effect
    4. Decompose NH3
30. Q30. Bakelite is a polymer of
    1. Phenol + formaldehyde
    2. Urea + formaldehyde
    3. Vinyl chloride
    4. Styrene + butadiene
31. Q31. 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)
32. Q32. Diborane (B₂H₆) has bonding involving
    1. Only 2c-2e bonds
    2. Two 3c-2e (banana) bonds + four 2c-2e bonds
    3. Only 3c-2e bonds
    4. Hydrogen bonds only
33. Q33. Nylon 6,6 is a
    1. Addition polymer
    2. Condensation polymer of hexamethylenediamine and adipic acid
    3. Natural polymer
    4. Vulcanised rubber
34. Q34. Van der Waals equation corrects ideal gas law for
    1. Inter-molecular attraction and finite size
    2. Mass and energy
    3. Vibration and rotation
    4. Quantum effects
35. Q35. The eccentricity of the ellipse x²/25 + y²/9 = 1 is
    1. 3/5
    2. 4/5
    3. 5/3
    4. 5/4
36. Q36. The length of the latus rectum of the parabola y² = 16x is
    1. 4
    2. 8
    3. 16
    4. 32
37. Q37. 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
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 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
43. Q43. 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)
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. ∫ x·e^x dx (by parts) =
    1. xe^x + e^x + C
    2. xe^x − e^x + C
    3. x^2·e^x/2 + C
    4. e^x/x + C
46. Q46. The number of 5-digit numbers with all distinct digits using {0..9} is
    1. 9 × 9P4
    2. 10P5
    3. 9 × 10P4
    4. 9P5
47. Q47. lim_{x->0} (1-cos x)/x^2 equals
    1. 0
    2. 1/2
    3. 1
    4. infinity
48. Q48. 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
49. Q49. The dot product a·b of two vectors a and b is
    1. |a||b|sinθ
    2. |a||b|cosθ
    3. |a×b|
    4. |a|+|b|
50. Q50. tan^-1 x + tan^-1 y = tan^-1((x + y)/(1 – xy)) holds when
    1. xy < 1
    2. xy > 1
    3. xy = 1
    4. x + y = 0