Daily MCQ Paper — 22 March 2026

Daily MCQ Paper — 22 March 2026

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

1. Q1. A projectile is launched at angle θ with speed u. Maximum range occurs when θ equals?
   1. 45°
   2. 30°
   3. 60°
   4. 90°
2. Q2. 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)
3. Q3. Centripetal acceleration in uniform circular motion of radius r and speed v equals?
   1. v²/r
   2. v/r
   3. v²r
   4. vr²
4. Q4. 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
5. Q5. 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
6. Q6. 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
7. Q7. 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|
8. Q8. 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
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. In an ideal step-down transformer, if N_p > N_s, then
    1. V_s < V_p, I_s > I_p
    2. V_s > V_p, I_s < I_p
    3. V_s = V_p
    4. Both V and I decrease
13. Q13. For an adiabatic process of an ideal gas, the relation between pressure and volume is
    1. PV=const
    2. PV^γ=const where γ=Cp/Cv
    3. TV=const
    4. PT=const
14. Q14. Force per unit area between plates of a parallel plate capacitor is?
    1. σ²/(2ε₀)
    2. σ²/ε₀
    3. σ/ε₀
    4. σ²ε₀
15. Q15. For a prism in minimum deviation position (δm), the refractive index is
    1. μ = sin((A+δm)/2) / sin(A/2)
    2. μ = sin A / sin δm
    3. μ = δm / A
    4. μ = (A-δm)/A
16. Q16. Stable nuclei in the binding-energy-per-nucleon curve peak around mass number
    1. A = 8
    2. A = 28
    3. A = 56
    4. A = 200
17. Q17. Eddy currents are utilised in
    1. Electric brakes and induction furnaces
    2. Galvanometer suspension wires
    3. Capacitors
    4. Diodes
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. Gabriel phthalimide synthesis specifically yields which class of amine?
    1. Primary aliphatic amines (pure)
    2. Aromatic amines
    3. Tertiary amines
    4. Quaternary salts
20. Q20. Aniline's basicity compared to ammonia is?
    1. Less basic than NH₃
    2. More basic than NH₃
    3. Equal to NH₃
    4. Non-basic
21. Q21. 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
22. Q22. 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
23. Q23. Acetylation of aniline gives?
    1. Acetanilide
    2. Aniline hydrochloride
    3. Phenol
    4. Benzoic acid
24. Q24. Bromination of aniline with excess Br₂/water gives?
    1. 2,4,6-tribromoaniline
    2. Bromobenzene
    3. o-bromoaniline only
    4. m-bromoaniline
25. Q25. Bechamp reduction of nitrobenzene uses?
    1. Sn + HCl
    2. LiAlH₄
    3. NaBH₄
    4. Pd/C only
26. Q26. Hinsberg's reagent (PhSO₂Cl) is used to?
    1. Distinguish 1°, 2°, 3° amines
    2. Reduce nitro to amine
    3. Couple diazonium
    4. Acetylate ROH
27. Q27. Diazotisation of aniline requires?
    1. NaNO₂ + dilute HCl, 0-5°C
    2. Hot HNO₃
    3. Cold KMnO₄
    4. Br₂/CCl₄
28. Q28. Carbylamine reaction is a test for which amine class?
    1. Primary amines
    2. Secondary amines
    3. Tertiary amines
    4. Quaternary salts
29. Q29. Strongest oxoacid of chlorine is
    1. HOCl
    2. HClO2
    3. HClO3
    4. HClO4
30. Q30. When alkali metals are dissolved in liquid ammonia, a deep blue colour is produced due to
    1. Free ammonium
    2. Ammoniated electrons (solvated free electrons) absorbing in the visible region
    3. Sodium amide
    4. Hydrogen evolution
31. Q31. Kohlrausch’s law of independent migration of ions states that
    1. Conductivity is independent of concentration
    2. Limiting molar conductivity is the sum of independent contributions of cation and anion
    3. Conductivity is zero at infinite dilution
    4. None
32. Q32. 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
33. Q33. In a body-centred cubic (BCC) unit cell, the number of atoms is
    1. 1
    2. 2
    3. 4
    4. 8
34. Q34. Tyndall effect arises due to?
    1. Scattering of light by colloidal particles
    2. Refraction
    3. Diffraction
    4. Reflection
35. Q35. If two rows of a determinant are identical, its value is?
    1. Zero
    2. Doubled
    3. Infinite
    4. Negative
36. Q36. If two rows of a determinant are interchanged, its value?
    1. Changes sign
    2. Becomes zero
    3. Doubles
    4. Unchanged
37. Q37. 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
38. Q38. Multiplying any row of a determinant by scalar k multiplies the determinant by?
    1. k
    2. k²
    3. k³
    4. 1
39. Q39. Cramer's rule gives unique solution to AX=B iff?
    1. |A| ≠ 0
    2. |A| = 0
    3. A is symmetric
    4. B = 0
40. Q40. Three points are collinear if the area-determinant equals?
    1. 0
    2. 1
    3. ½
    4. Infinity
41. Q41. 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]]
42. Q42. Inverse of square matrix A exists iff?
    1. |A| ≠ 0 (non-singular)
    2. A is symmetric
    3. A is upper triangular
    4. |A| = 0
43. Q43. For homogeneous system AX = 0 to have non-trivial solution?
    1. |A| = 0
    2. |A| ≠ 0
    3. A is identity
    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. Solution of dy/dx = -y/x is
    1. y = Cx
    2. xy = C
    3. y = C/x
    4. y – x = C
47. Q47. The dot product a·b equals?
    1. |a||b| cos θ
    2. |a||b| sin θ
    3. |a×b|
    4. a + b
48. Q48. Tangent to y=x² at (1,1) has slope?
    1. 2
    2. 1
    3. ½
    4. 3
49. Q49. The general solution of dy/dx = y is
    1. y = Cx
    2. y = Ce^x
    3. y = ln x + C
    4. y = x + C
50. Q50. The cross product a × b is?
    1. |a||b| sin θ n̂
    2. |a||b| cos θ
    3. a · b
    4. a + b