Daily MCQ Paper — 4 April 2026

Daily MCQ Paper — 4 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. 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
3. Q3. 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
4. Q4. 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
5. Q5. 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
6. Q6. 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
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. Brewsters law states that at the polarising angle iB
    1. tan iB = mu
    2. sin iB = mu
    3. cos iB = mu
    4. cot iB = mu
12. Q12. In Youngs double slit experiment with slit separation d and screen distance D, fringe width is
    1. lambda * D / d
    2. lambda * d / D
    3. D / (lambda * d)
    4. d / (lambda * D)
13. Q13. 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
14. Q14. The number of degrees of freedom of a diatomic molecule at room temperature is
    1. 3
    2. 5
    3. 6
    4. 7
15. Q15. 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)
16. Q16. Power delivered by a constant force F to a body moving with velocity v is
    1. Fv
    2. Fv²
    3. F·v (dot product)
    4. F/v
17. Q17. 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
18. Q18. 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
19. Q19. 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
20. Q20. 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
21. Q21. 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
22. Q22. 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
23. Q23. 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
24. Q24. 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
25. Q25. Vitamin C (ascorbic acid) deficiency causes
    1. Beriberi
    2. Scurvy — bleeding gums, poor wound healing, weakness
    3. Pellagra
    4. Rickets
26. Q26. 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
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. Bond order of O2 from MO theory is
    1. 1
    2. 1.5
    3. 2
    4. 3
29. Q29. The Arrhenius equation is
    1. k = A·e^(−Ea/RT)
    2. k = A·e^(Ea/RT)
    3. k = A/RT
    4. k = ln(A) − Ea/RT
30. Q30. The major contributor to acid rain is
    1. CO2
    2. SO2 and NOx
    3. CH4
    4. CFCs
31. Q31. The Nernst equation for cell EMF at 298 K (in volts) is
    1. E = E° – (0.0591/n) log Q
    2. E = E° + (0.0591/n) log Q
    3. E = E°
    4. E = (RT/F) ln Q
32. Q32. Adsorption of a gas on solid is generally
    1. Endothermic
    2. Exothermic
    3. Athermic
    4. Variable
33. Q33. EMF of a Daniell cell (Zn|Zn2+ || Cu2+|Cu) under standard conditions is approximately
    1. +0.34 V
    2. +0.76 V
    3. +1.10 V
    4. +1.50 V
34. Q34. Coupling of diazonium salt with phenol in mildly alkaline medium gives
    1. Methyl orange
    2. para-Hydroxyazobenzene
    3. Aniline yellow
    4. Indigo
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. 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
37. Q37. 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
38. Q38. 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
39. Q39. 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
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 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)
42. Q42. 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
43. Q43. 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|
44. Q44. 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
45. Q45. The locus of |z – 2| = |z + 2| in the complex plane is
    1. Circle
    2. Real axis
    3. Imaginary axis
    4. Parabola
46. Q46. If x = a cos t and y = a sin t, then dy/dx equals
    1. -cot t
    2. -tan t
    3. tan t
    4. cot t
47. Q47. Newtons law of cooling states that dT/dt is proportional to
    1. (T – T0)
    2. (T0 – T)
    3. -(T – T0)
    4. T^2
48. Q48. The directrix of the parabola y² = 12x is
    1. x = -3
    2. x = 3
    3. y = -3
    4. y = 3
49. Q49. The differential equation dy/dx = ky has solution
    1. y = kx + C
    2. y = Ce^(kx)
    3. y = C·sin(kx)
    4. y = k/x + C
50. Q50. 2 tan^-1 x equals (for |x| < 1)
    1. tan^-1 (2x / (1 – x^2))
    2. tan^-1 (2x / (1 + x^2))
    3. sin^-1 (1 – x^2)
    4. cos^-1 (2x)