Daily MCQ Paper — 10 April 2026

Daily MCQ Paper — 10 April 2026

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

1. Q1. The magnetic moment of a bar magnet of pole strength m and length 2l is
   1. m/2l
   2. 2ml
   3. m*l
   4. m/l
2. Q2. A source moves towards a stationary observer with velocity vs. The apparent frequency f equals (v = sound speed, f0 = source frequency)
   1. f0 (v + vs)/v
   2. f0 v/(v – vs)
   3. f0 (v – vs)/v
   4. f0 v/(v + vs)
3. Q3. The horizontal component of Earths magnetic field at the equator is
   1. Maximum
   2. Zero
   3. Equal to vertical component
   4. Negative
4. Q4. In a stationary wave on a string fixed at both ends, the fundamental mode has
   1. One node and one antinode
   2. Two nodes and one antinode
   3. Two antinodes and one node
   4. Three nodes
5. Q5. The number of beats per second when two tuning forks of frequencies 256 Hz and 260 Hz are sounded together is
   1. 2
   2. 4
   3. 8
   4. 256
6. Q6. Curies law states that magnetic susceptibility of a paramagnetic material is
   1. Directly proportional to absolute temperature
   2. Inversely proportional to absolute temperature
   3. Independent of temperature
   4. Proportional to T squared
7. Q7. 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
8. Q8. The fundamental frequency of an organ pipe closed at one end of length L and sound speed v is
   1. v/(2L)
   2. v/(4L)
   3. v/L
   4. 2v/L
9. Q9. An open organ pipe and a closed organ pipe of the same length will have fundamental frequencies in ratio
   1. 1:1
   2. 2:1
   3. 1:2
   4. 4:1
10. Q10. Curie temperature of iron, above which it loses ferromagnetism, is approximately
    1. 770 K
    2. 1043 K
    3. 1300 K
    4. 1700 K
11. Q11. 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)
12. Q12. In a balanced Wheatstone bridge (P,Q,R,S), the condition is
    1. P/Q = R/S
    2. P/R = Q/S
    3. P·Q = R·S
    4. PQRS = 1
13. Q13. In an adiabatic process for an ideal gas
    1. PV = constant
    2. PV^γ = constant
    3. TV = constant
    4. P/T = constant
14. Q14. A body is projected with velocity 20 m/s at 60° to horizontal. Time of flight (g=10):
    1. 2 s
    2. 3.46 s
    3. 4 s
    4. 1.73 s
15. Q15. Young's modulus has dimensions of
    1. Force
    2. Pressure
    3. Energy
    4. Power
16. Q16. 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
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. The Kolbe-Schmitt reaction converts sodium phenoxide and CO2 (under pressure) to
    1. Salicylaldehyde
    2. Salicylic acid
    3. Picric acid
    4. Phthalic acid
19. Q19. Lucas reagent (anhydrous ZnCl2 + concentrated HCl) distinguishes alcohols. Tertiary alcohols give turbidity
    1. Immediately
    2. In about 5 minutes
    3. Only on warming
    4. Never
20. Q20. Which test gives a silver mirror with aldehydes but not ketones
    1. Fehlings test
    2. Tollens test
    3. Lucas test
    4. Iodoform test
21. Q21. The Reimer-Tiemann reaction converts phenol to
    1. Salicylaldehyde
    2. Benzaldehyde
    3. Salicylic acid
    4. Picric acid
22. Q22. The Etard reaction converts toluene to benzaldehyde using
    1. PCC
    2. CrO2Cl2 in CS2
    3. KMnO4
    4. SeO2
23. Q23. Fehlings solution gives a brick-red precipitate of which compound when treated with an aldehyde
    1. Cu
    2. Cu2O
    3. CuO
    4. Cu(OH)2
24. Q24. The Rosenmund reduction converts an acyl chloride to an aldehyde using
    1. LiAlH4
    2. NaBH4
    3. H2 / Pd-BaSO4 (poisoned)
    4. Zn-Hg/HCl
25. Q25. Hinsberg reagent (benzenesulphonyl chloride) is used to distinguish
    1. Alkyl halides
    2. 1°, 2°, 3° amines
    3. Alcohols
    4. Aldehydes from ketones
26. Q26. The Sandmeyer reaction converts an aryldiazonium salt (ArN2+Cl-) to ArCl using
    1. CuCl/HCl
    2. Cu/HCl
    3. HCl alone
    4. SnCl2/HCl
27. Q27. The Gattermann reaction differs from Sandmeyer in using
    1. CuCN
    2. Cu/HCl in place of CuCl/HCl
    3. HBF4
    4. HNO2
28. Q28. 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
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. 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
31. Q31. 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
32. Q32. The magnitude of crystal field splitting in tetrahedral vs octahedral (with same metal/ligand) is
    1. Equal
    2. Δt = (4/9)Δo
    3. Δt = (9/4)Δo
    4. Δt = 2Δo
33. Q33. Zeolites belong to the class of
    1. Borosilicates
    2. Aluminosilicates
    3. Carbonates
    4. Phosphates
34. Q34. The diagonal relationship in periodic table is between
    1. Li-Be
    2. Li-Mg
    3. Be-B
    4. Na-Mg
35. Q35. The general solution of cos x = cos alpha is
    1. x = n*pi + alpha
    2. x = 2n*pi +/- alpha
    3. x = n*pi +/- alpha
    4. x = (2n+1)*pi/2 + alpha
36. Q36. In any triangle ABC, by the sine rule a/sin A equals
    1. R
    2. 2R
    3. 3R
    4. R/2
37. Q37. The general solution of sin x = sin alpha is
    1. x = n*pi + alpha
    2. x = n*pi + (-1)^n * alpha
    3. x = 2n*pi + alpha
    4. x = n*pi – alpha
38. Q38. The area of triangle ABC in terms of two sides and included angle is
    1. (1/2) a b sin C
    2. (1/2) a b cos C
    3. a b sin C
    4. (1/2) a b tan C
39. Q39. The inradius r of a triangle is given by (s = semi-perimeter, Delta = area)
    1. Delta * s
    2. Delta / s
    3. s / Delta
    4. s * Delta
40. Q40. 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
41. Q41. The circumradius R of triangle is
    1. a*b*c/(4*Delta)
    2. Delta/(a*b*c)
    3. 4*Delta/(a*b*c)
    4. a*b*c/Delta
42. Q42. The exradius r1 opposite vertex A equals
    1. Delta/(s-a)
    2. Delta/s
    3. Delta/(s+a)
    4. (s-a)/Delta
43. Q43. A man at the foot of a tower observes the angle of elevation of its top as 60°. After walking 100 m back the angle becomes 30°. Height of tower (m)
    1. 50
    2. 50*sqrt 3
    3. 100*sqrt 3
    4. 100/sqrt 3
44. Q44. If A + B + C = pi (in a triangle), then tan A + tan B + tan C equals
    1. tan A tan B tan C
    2. sin A sin B sin C
    3. 1
    4. 0
45. Q45. In the expansion of (1+x)¹¹, the two middle terms are
    1. T6 and T7
    2. T5 and T6
    3. T6 and T8
    4. T11 and T12
46. Q46. 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
47. Q47. The shortest distance between two skew lines r = a₁+λb₁ and r = a₂+μb₂ is
    1. |(a₂-a₁)·(b₁×b₂)| / |b₁×b₂|
    2. |a₂-a₁|
    3. |b₁×b₂|
    4. |(a₂-a₁)×(b₁×b₂)|
48. Q48. 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)
49. Q49. 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
50. Q50. The differential equation modelling Newton's law of cooling is
    1. dT/dt = −k(T − Ts)
    2. dT/dt = k·T
    3. dT/dt = −kT^2
    4. dT/dt = k(T + Ts)