Daily MCQ Paper — 23 March 2026

Daily MCQ Paper — 23 March 2026

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

1. Q1. Time of flight for a projectile fired at angle θ with speed u (from ground level) is?
   1. 2u sinθ / g
   2. u sinθ / g
   3. u² sinθ / g
   4. 2u / g
2. Q2. A projectile is launched at angle θ with speed u. Maximum range occurs when θ equals?
   1. 45°
   2. 30°
   3. 60°
   4. 90°
3. Q3. Trajectory equation of projectile motion is?
   1. y = x tanθ − gx²/(2u²cos²θ)
   2. y = x tanθ + gx²/2
   3. y = u tanθ x
   4. y = (g/2)t² only
4. Q4. Two vectors A and B at angle θ have resultant magnitude R given by?
   1. √(A² + B² + 2AB cosθ)
   2. √(A² + B²)
   3. A + B always
   4. |A − B|
5. Q5. Component of vector A along x-axis (with A making angle θ with x-axis) is?
   1. A cosθ
   2. A sinθ
   3. A tanθ
   4. A/cosθ
6. Q6. Centripetal acceleration in uniform circular motion of radius r and speed v equals?
   1. v²/r
   2. v/r
   3. v²r
   4. vr²
7. Q7. Maximum height of a projectile launched at angle θ with speed u is?
   1. u² sin²θ / (2g)
   2. u² sin 2θ / g
   3. u sinθ / g
   4. u² / (2g)
8. Q8. Centripetal force needed for a body of mass m moving with speed v on a circle of radius r is?
   1. mv²/r
   2. mv/r
   3. mvr
   4. mr²/v
9. Q9. Tangential acceleration in UNIFORM circular motion is?
   1. Zero
   2. v/r
   3. v²/r
   4. g
10. Q10. A boat moves at 5 m/s in still water; river flows at 3 m/s perpendicular. Resultant ground speed?
    1. √34 m/s
    2. 8 m/s
    3. 2 m/s
    4. 5 m/s
11. Q11. For a projectile, horizontal range = maximum height when tanθ equals?
    1. 4
    2. 1
    3. 2
    4. ½
12. Q12. The magnetic field at the centre of a circular loop of radius a carrying current I is?
    1. μ0 I / (2 a)
    2. μ0 I a / 2
    3. μ0 I / (4π a)
    4. μ0 I / a²
13. Q13. Capacitors in parallel store same?
    1. Voltage
    2. Charge
    3. Energy
    4. Current
14. Q14. Dipole moment of a system of two charges +q and -q separated by distance 2a is
    1. qa
    2. 2qa
    3. q/2a
    4. q/a
15. Q15. The Poisson ratio σ = (lateral strain)/(longitudinal strain) for an isotropic material lies in the theoretical range
    1. -1 to 0.5
    2. 0 to 1
    3. -1 to 1
    4. -0.5 to 0.5
16. Q16. Coefficient of static friction (mu_s) and kinetic friction (mu_k) for the same surfaces typically obey
    1. mu_s = mu_k
    2. mu_s > mu_k
    3. mu_s < mu_k
    4. mu_s = 0
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. Hofmann bromamide reaction converts RCONH₂ to which product (with one less carbon)?
    1. RNH₂ (primary amine)
    2. RCN
    3. RCH₂NH₂
    4. RCOOH
19. Q19. Bromination of aniline with excess Br₂/water gives?
    1. 2,4,6-tribromoaniline
    2. Bromobenzene
    3. o-bromoaniline only
    4. m-bromoaniline
20. Q20. Bechamp reduction of nitrobenzene uses?
    1. Sn + HCl
    2. LiAlH₄
    3. NaBH₄
    4. Pd/C only
21. Q21. Gabriel phthalimide synthesis specifically yields which class of amine?
    1. Primary aliphatic amines (pure)
    2. Aromatic amines
    3. Tertiary amines
    4. Quaternary salts
22. Q22. Aniline's basicity compared to ammonia is?
    1. Less basic than NH₃
    2. More basic than NH₃
    3. Equal to NH₃
    4. Non-basic
23. Q23. Order of basicity in aqueous solution among methylamines is?
    1. (CH₃)₂NH > CH₃NH₂ > (CH₃)₃N > NH₃
    2. (CH₃)₃N > (CH₃)₂NH > CH₃NH₂
    3. NH₃ > all
    4. All equal
24. Q24. Acetylation of aniline gives?
    1. Acetanilide
    2. Aniline hydrochloride
    3. Phenol
    4. Benzoic acid
25. Q25. Hinsberg's reagent (PhSO₂Cl) is used to?
    1. Distinguish 1°, 2°, 3° amines
    2. Reduce nitro to amine
    3. Couple diazonium
    4. Acetylate ROH
26. Q26. Carbylamine reaction is a test for which amine class?
    1. Primary amines
    2. Secondary amines
    3. Tertiary amines
    4. Quaternary salts
27. Q27. Diazotisation of aniline requires?
    1. NaNO₂ + dilute HCl, 0-5°C
    2. Hot HNO₃
    3. Cold KMnO₄
    4. Br₂/CCl₄
28. Q28. Direct nitration of aniline mostly gives meta product because?
    1. Aniline gets protonated to anilinium ion which is meta-directing
    2. -NH₂ is meta-directing
    3. Aniline doesn't react
    4. HNO₃ destroys ring
29. Q29. Hardy-Schulze rule states coagulation power is governed by?
    1. Valency of ion of charge opposite to colloid
    2. Same charge ion
    3. Mass of ion
    4. Concentration only
30. Q30. In [Co(NH3)6]Cl3, the coordination number of Co is
    1. 3
    2. 4
    3. 6
    4. 9
31. Q31. Fructose is a?
    1. Ketohexose
    2. Aldohexose
    3. Aldopentose
    4. Ketopentose
32. Q32. Glucose is a?
    1. Aldohexose
    2. Ketohexose
    3. Aldopentose
    4. Ketopentose
33. Q33. 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)
34. Q34. According to Crystal Field Theory, in an octahedral complex the d-orbitals split into
    1. Two t2g + three eg
    2. Three t2g + two eg
    3. Five degenerate orbitals
    4. Three eg + two t2g
35. Q35. If two rows of a determinant are identical, its value is?
    1. Zero
    2. Doubled
    3. Infinite
    4. Negative
36. Q36. Multiplying any row of a determinant by scalar k multiplies the determinant by?
    1. k
    2. k²
    3. k³
    4. 1
37. Q37. If two rows of a determinant are interchanged, its value?
    1. Changes sign
    2. Becomes zero
    3. Doubles
    4. Unchanged
38. Q38. Area of triangle with vertices (x₁,y₁), (x₂,y₂), (x₃,y₃) is?
    1. ½|x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|
    2. x₁ + x₂ + x₃
    3. ½ × base × height (only)
    4. x₁y₁ + x₂y₂
39. Q39. Three points are collinear if the area-determinant equals?
    1. 0
    2. 1
    3. ½
    4. Infinity
40. Q40. adj(A) for 2×2 matrix [[a,b],[c,d]] equals?
    1. [[d,−b],[−c,a]]
    2. [[a,c],[b,d]]
    3. [[d,b],[c,a]]
    4. [[a,−b],[−c,d]]
41. Q41. Cramer's rule gives unique solution to AX=B iff?
    1. |A| ≠ 0
    2. |A| = 0
    3. A is symmetric
    4. B = 0
42. Q42. For homogeneous system AX = 0 to have non-trivial solution?
    1. |A| = 0
    2. |A| ≠ 0
    3. A is identity
    4. A = 0
43. Q43. Inverse of square matrix A exists iff?
    1. |A| ≠ 0 (non-singular)
    2. A is symmetric
    3. A is upper triangular
    4. |A| = 0
44. Q44. If A is 3×3 and |A| = 5, then |adj A| equals?
    1. 25
    2. 5
    3. 125
    4. 1
45. Q45. Equation of line through (x₁,y₁) and (x₂,y₂) using determinants is?
    1. |x y 1; x₁ y₁ 1; x₂ y₂ 1| = 0
    2. x + y = 1
    3. xy = constant
    4. x − y = 0
46. Q46. Rolles theorem requires the function to be
    1. Continuous on [a,b], differentiable on (a,b) and f(a) = f(b)
    2. Only continuous on [a,b]
    3. Only differentiable on (a,b)
    4. Monotonic on [a,b]
47. Q47. Power set of a set with n elements has cardinality
    1. n
    2. 2^n
    3. n^2
    4. n!
48. Q48. Solution of differential equation dy/dx + y = 0 is
    1. y = C e^x
    2. y = C e^(-x)
    3. y = Cx
    4. y = C/x
49. Q49. The principal argument of z = -1 + i is
    1. π/4
    2. 3π/4
    3. -π/4
    4. -3π/4
50. Q50. Volume of a tetrahedron with three coterminous edges a, b, c is?
    1. (1/6) |[a b c]|
    2. ½ |[a b c]|
    3. |[a b c]|
    4. (1/3) |a × b|