Daily MCQ Paper — 3 April 2026

Daily MCQ Paper — 3 April 2026

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

1. Q1. The efficiency of a Carnot engine operating between source 400 K and sink 300 K is
   1. 100%
   2. 25%
   3. 75%
   4. 33.3%
2. Q2. 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
3. Q3. In an isothermal process for an ideal gas, the work done by the gas in expansion from V1 to V2 is
   1. PΔV
   2. nRT ln(V2/V1)
   3. nCvΔT
   4. Zero
4. Q4. The Coefficient of Performance (COP) of a refrigerator working between T1 (hot) and T2 (cold) is
   1. T1/T2
   2. T2/(T1-T2)
   3. T1-T2
   4. (T1-T2)/T1
5. Q5. Curie's law for paramagnetic susceptibility states that χ varies with temperature T as
   1. χ ∝ T
   2. χ = C/T (inversely proportional to absolute temperature)
   3. χ ∝ T^2
   4. χ independent of T
6. Q6. On the magnetic axial line of a short bar magnet of moment m at distance r, the magnetic field is
   1. μ0m/(4πr3)
   2. 2μ0m/(4πr3)
   3. μ0m/(4πr2)
   4. Zero
7. Q7. In a pure inductor connected to AC source, the current
   1. Leads voltage by 90°
   2. Lags voltage by 90°
   3. Is in phase with voltage
   4. Lags by 45°
8. Q8. The capacitive reactance XC of a capacitor C in an AC circuit at angular frequency ω is
   1. ωC
   2. 1/(ωC)
   3. ω/C
   4. ω^2C
9. Q9. At resonance in a series LCR circuit, the current is
   1. Zero
   2. Maximum, with impedance Z=R and circuit purely resistive
   3. Half of source current
   4. Imaginary
10. Q10. The quality factor Q of a series LCR resonant circuit is
    1. R/L
    2. (1/R)√(L/C) = ωrL/R
    3. RC
    4. LC
11. Q11. 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
12. Q12. 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
13. Q13. For a thin lens, the lens maker formula in air is
    1. 1/f = (n-1)(1/R1 – 1/R2)
    2. 1/f = n(1/R1 + 1/R2)
    3. f = (R1 + R2)/2
    4. f = R/2
14. Q14. Wien's displacement law states that lambda_max * T equals approximately
    1. 2.9 x 10^-3 m K
    2. 5.67 x 10^-8 W/m^2K^4
    3. 6.63 x 10^-34 J s
    4. 9.0 x 10^9 Nm^2/C^2
15. Q15. 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
16. Q16. The rms speed of gas molecules of molar mass M at temperature T is
    1. sqrt(RT/M)
    2. sqrt(2RT/M)
    3. sqrt(3RT/M)
    4. sqrt(8RT/πM)
17. Q17. de Broglie wavelength of an electron with KE 100 eV is approximately
    1. 0.123 nm
    2. 1.23 nm
    3. 12.3 nm
    4. 0.0123 nm
18. Q18. Markovnikov's rule for HX addition to an unsymmetrical alkene states that the H atom attaches to
    1. The carbon with fewer H atoms
    2. The carbon with more H atoms (giving the more stable carbocation intermediate)
    3. The terminal carbon always
    4. The carbon with double bond
19. Q19. SN2 reaction is favoured by
    1. Tertiary alkyl halide
    2. Primary alkyl halide with strong nucleophile in polar aprotic solvent (DMSO, DMF, acetone)
    3. Bulky substrates
    4. Weak nucleophile
20. Q20. Anti-Markovnikov addition of HBr to an alkene occurs in the presence of
    1. Pure HBr in dark
    2. Peroxides (Kharasch effect) — proceeds via free radical mechanism
    3. Sunlight only
    4. Acid catalyst
21. Q21. The Wurtz reaction couples two alkyl halides using
    1. HCl
    2. Sodium metal in dry ether: 2 RX + 2 Na → R-R + 2 NaX
    3. Magnesium
    4. Zinc
22. Q22. Glucose, a monosaccharide aldohexose, exists primarily in solution as
    1. Open chain only
    2. Cyclic hemiacetal forms (α and β anomers in equilibrium with open chain — mutarotation)
    3. Cyclic acetal
    4. Dimer
23. Q23. Vitamin C (ascorbic acid) deficiency causes
    1. Beriberi
    2. Scurvy — bleeding gums, poor wound healing, weakness
    3. Pellagra
    4. Rickets
24. Q24. Sucrose is a non-reducing sugar because
    1. It has no anomeric carbon
    2. Both anomeric carbons of glucose and fructose are involved in the glycosidic α,β-1,2 linkage
    3. It is a polysaccharide
    4. It cannot dissolve
25. Q25. The secondary structure of proteins is stabilised primarily by
    1. Disulfide bonds
    2. Hydrogen bonds between C=O and N-H of peptide backbone giving α-helix and β-pleated sheet
    3. Hydrophobic forces
    4. Ionic bonds
26. Q26. DNA has a double-helical structure proposed by Watson and Crick in 1953 with strands held by
    1. Covalent bonds
    2. Hydrogen bonds: A-T (2 H-bonds) and G-C (3 H-bonds) base pairing, antiparallel orientation
    3. Ionic bonds
    4. π-π stacking only
27. Q27. Iodoform CHI3 is prepared by treating ethanol with
    1. HCl + ZnCl2
    2. I2 + NaOH (haloform reaction) producing yellow crystals — used as antiseptic
    3. HNO3
    4. HBr
28. Q28. Which test gives a silver mirror with aldehydes but not ketones
    1. Fehlings test
    2. Tollens test
    3. Lucas test
    4. Iodoform test
29. Q29. Number of moles in 22 g of CO₂ (M=44)
    1. 0.5
    2. 1
    3. 2
    4. 0.25
30. Q30. Hybridisation of carbon in methane is
    1. sp
    2. sp2
    3. sp3
    4. sp3d
31. Q31. 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
32. Q32. In a tetrahedral crystal field, the d-orbitals split into
    1. e (lower) and t2 (higher)
    2. t2 (lower) and e (higher)
    3. t2g and eg
    4. No splitting
33. Q33. For a spontaneous process at constant T and P
    1. ΔG > 0
    2. ΔG = 0
    3. ΔG < 0
    4. ΔS = 0
34. Q34. Decarboxylation of sodium salts of carboxylic acids with sodalime gives
    1. Higher hydrocarbons
    2. Hydrocarbons with one less carbon
    3. Aldehydes
    4. Alcohols
35. Q35. Rolle's theorem requires f to be
    1. Continuous on (a,b) only
    2. Continuous on [a,b], differentiable on (a,b), and f(a)=f(b) — guarantees ∃c∈(a,b) with f'(c)=0
    3. Differentiable everywhere
    4. Linear
36. Q36. Lagrange Mean Value Theorem states that for f continuous on [a,b] and differentiable on (a,b), there exists c in (a,b) such that
    1. f'(c)=0
    2. f(b)-f(a)=f'(c)(b-a)
    3. f(b)+f(a)=2f'(c)
    4. f(c)=0
37. Q37. If f'(x0)=0 and f''(x0)<0, then x0 is a
    1. Point of inflection
    2. Local maximum
    3. Local minimum
    4. Saddle point
38. Q38. Four points P1, P2, P3, P4 in 3D are coplanar iff
    1. They lie on x-axis
    2. Scalar triple product [P2-P1, P3-P1, P4-P1]=0
    3. They are equidistant
    4. They form a parallelogram
39. Q39. The Fundamental Theorem of Calculus relates differentiation and integration as
    1. Independent operations
    2. d/dx[∫_a^x f(t)dt]=f(x) and ∫_a^b f(x)dx=F(b)-F(a) where F'=f
    3. Always equal
    4. Reciprocal
40. Q40. The integral ∫_-a^a f(x) dx for an odd function equals
    1. 2∫_0^a f(x)dx
    2. 0
    3. ∞
    4. f(a)
41. Q41. The "king property" of definite integrals states ∫_a^b f(x)dx equals
    1. ∫_a^b f(a+b-x) dx
    2. ∫_a^b f(b-x) dx
    3. ∫_a^b f(x+a) dx
    4. -∫_a^b f(x) dx
42. Q42. The scalar triple product [a b c]=a·(b×c) represents
    1. Length of a vector
    2. Volume of the parallelepiped formed by vectors a, b, c
    3. Dot product
    4. Cross product magnitude
43. Q43. The vector triple product a×(b×c) equals
    1. (a·c)b – (a·b)c
    2. (a·b)c – (a·c)b
    3. a·(b×c)
    4. b×(a×c)
44. Q44. The shortest distance between two skew lines r=a1+λb1 and r=a2+μb2 is
    1. |(a2-a1)·(b1×b2)|/|b1×b2|
    2. Always zero
    3. |a1-a2|
    4. |b1-b2|
45. Q45. 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
46. Q46. ∫ e^x dx =
    1. e^x + C
    2. e^x/x + C
    3. x·e^x + C
    4. e^(x+1)/(x+1) + C
47. Q47. The directrix of the parabola y² = 12x is
    1. x = -3
    2. x = 3
    3. y = -3
    4. y = 3
48. Q48. 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
49. Q49. 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
50. Q50. Karl Pearson correlation coefficient r lies in
    1. [0, 1]
    2. [-1, 1]
    3. [0, infinity)
    4. (-infinity, infinity)