Memory based questions of JEE Main 21 January Shift 1.
Physics, Chemistry and Mathematics questions compiled for serious aspirants.
Physics Questions
Q1.
Two rods of equal length 60 cm are joined end to end. Coefficients of linear expansion are
24×10⁻⁶ °C⁻¹ and 1.2×10⁻⁵ °C⁻¹. Temperature rises from 30°C to 100°C. Find final length.
(A) 120.1321
(B) 120.1123
(C) 120.1512
(D) 120.1084
Q2.
An α-particle of kinetic energy 7.7 MeV approaches a gold nucleus (Z = 79). Find distance of closest approach.
(A) 1.72 nm
(B) 6.2 nm
(C) 16.8 nm
(D) 0.2 nm
Q3.
An ideal solenoid is kept vertical. A charge is thrown downward inside it. Current I₀ flows in solenoid.
Acceleration of charged particle is:
(A) g downward
(B) g upward
(C) Zero
(D) Depends on I₀
Q4.
Electric field of EM wave is E⃗ = 69 sin(ωt − kx) ĵ. Direction of magnetic field is:
(A) k̂
(B) −k̂
(C) (î + ĵ)/√2
(D) (î − ĵ)/√2
Q5.
Two waves travel on strings of equal length and tension. μ₁/μ₂ = 1/2.
Ratio of time taken by wave pulse is:
(A) 1/2
(B) 1/√2
(C) √2
(D) 2
Chemistry Questions
Q6.
MnO₄²⁻ in acidic medium undergoes disproportionation to form:
(A) MnO₂, MnO₄⁻
(B) MnO, MnO₂
(C) MnO₂, MnO
(D) MnO₄⁻, MnO
Q7.
80 mL organic compound burns with 264 mL O₂. After KOH, 64 mL gas remains.
Compound is:
(A) C₂H₄
(B) C₂H₂
(C) C₄H₁₀
(D) C₃H₆
Q8.
14 g Ca reacts with excess HCl. Choose incorrect option.
(A) CaCl₂ mass = 38.85 g
(B) Moles of H₂ = 0.35
(C) Volume of H₂ = 7.84 L
(D) CaCl₂ mass = 3.885 g
Q9.
How many compounds have tetrahedral geometry?
NH₄⁺, XeF₄, [NiCl₄]²⁻, [PtCl₄]²⁻, [Cu(NH₃)₄]²⁺, BF₃, Ni(CO)₄
Q10.
Correct statements are:
(A) Propanal & propanone functional isomers
(B) Ethoxyethane & methoxypropane metamers
(C) But-2-ene optical isomerism
(D) But-1-ene & But-2-ene functional isomers
(E) Pentane & neopentane chain isomers
Mathematics Questions
Q11.
Ellipse x²/36 + y²/16 = 1. Confocal hyperbola has eccentricity 5.
Length of latus rectum is:
(A) 96/√5
(B) 24√5
(C) 18√5
(D) 12√5
Q12.
If a₁ = 1 and
aₙ₊₁ = ½aₙ + (n² − 2n − 1)/(n²(n+1)²),
find Σ(aₙ − 2/n²).
Q13.
Evaluate ∫[π/6 to π] (π + 4x¹¹)/(1 − sin(|x| + π/6)) dx.
Q14.
If f(3)=18, f′(3)=0, f″(3)=4 then
lim x→1 ln[(f(x+2)/f(3))^(18/(x−1)²)].
Q15.
Area enclosed by x²+4y² ≤ 4, y ≤ |x|−1, y ≥ 1−|x|.