JEE Main 2024 previous year paper practice · PYQ-pattern set

JEE Main 2024 PYQ-pattern questions

Showing 10 of the 16 PYQ-pattern questions in this set — freshly worded in that year's pattern, not the original questions. Answers and solutions open under each question.

1. Q1 · Physics and Measurement

   A screw gauge has 60 divisions on its circular scale and the pitch is 0.6 mm. When the jaws are closed, the 8th division on the circular scale coincides with the reference line. When a wire is placed between the jaws, the main scale reading is 3 mm and the 35th division on the circular scale coincides with the reference line. What is the true diameter of the wire?

   • A. 3.27 mm
   • B. 3.35 mm
   • C. 3.19 mm
   • D. 3.43 mm
   Answer and solution

   Answer: A

   Least count = 0.6/60 = 0.01 mm. Measured reading = 3 + 35×0.01 = 3.35 mm. Zero error = +8×0.01 = +0.08 mm. True diameter = 3.35 - 0.08 = 3.27 mm.

2. Q2 · Gravitation

   The gravitational potential at a point at height h above the Earth's surface is (M is Earth's mass, R is Earth's radius):

   • A. -GM/(R+h)
   • B. -GMh/R²
   • C. GM/(R+h)
   • D. -GM/R
   Answer and solution

   Answer: A

   Gravitational potential V = -GM/r, where r is the distance from Earth's center. At height h above surface, r = R + h, so V = -GM/(R+h).

3. Q3 · Kinetic Theory of Gases

   An ideal gas is enclosed in a container of volume V at a pressure P and temperature 300 K. If the temperature is increased to 600 K keeping the volume constant, what will be the new pressure?

   • A. P/2
   • B. P
   • C. 2P
   • D. 4P
   Answer and solution

   Answer: C

   For an ideal gas at constant volume, pressure is directly proportional to temperature (Gay-Lussac's Law): P₁/T₁ = P₂/T₂. Therefore P₂ = P × (600/300) = 2P.

4. Q4 · Atoms and Nuclei

   A hydrogen atom absorbs a photon and its electron transitions from the ground state (n = 1) to the n = 3 state. The energy of the absorbed photon is closest to:

   • A. 10.2 eV
   • B. 12.1 eV
   • C. 13.6 eV
   • D. 1.5 eV
   Answer and solution

   Answer: B

   Energy absorbed = 13.6 eV × (1/1² - 1/3²) = 13.6 × (1 - 1/9) = 13.6 × 8/9 = 12.09 eV ≈ 12.1 eV.

5. Q5 · Atomic Structure

   For a hydrogen-like ion, the ratio of the radii of the third and first Bohr orbits is:

   • A. 3:1
   • B. 9:1
   • C. 27:1
   • D. 6:1
   Answer and solution

   Answer: B

   The radius of nth orbit in a hydrogen-like ion is proportional to n²/Z. For the same ion (constant Z), r₃/r₁ = 3²/1² = 9/1.

6. Q6 · Solutions

   A 0.15 M aqueous solution of KCl has a freezing point depression of 0.52 K. If Kf for water is 1.86 K kg mol⁻¹, what is the degree of dissociation of KCl in this solution?

   • A. 0.72
   • B. 0.86
   • C. 0.93
   • D. 0.65
   Answer and solution

   Answer: B

   For electrolyte dissociation: ΔTf = i × Kf × m. Here, 0.52 = i × 1.86 × 0.15, giving i = 1.86. For KCl dissociating into 2 ions: i = 1 + α, so α = 0.86.

7. Q7 · d- and f-Block Elements

   Among Ti²⁺, V²⁺, Cr²⁺, and Mn²⁺, which ion is the strongest reducing agent in aqueous solution? (Given their 3d electron configurations)

   • A. Ti²⁺
   • B. V²⁺
   • C. Cr²⁺
   • D. Mn²⁺
   Answer and solution

   Answer: C

   Cr²⁺ (3d⁴) is the strongest reducing agent among these because it readily loses an electron to form the stable Cr³⁺ (3d³, half-filled t2g configuration). The E° for Cr³⁺/Cr²⁺ is about -0.41 V, the most negative among these couples, making Cr²⁺ easily oxidized and thus the best reducing agent.

8. Q8 · Some Basic Principles of Organic Chemistry

   The correct order of stability of the following carbocations is: (I) (CH₃)₃C⁺ (II) (CH₃)₂CH⁺ (III) CH₃CH₂⁺ (IV) CH₃⁺

   • A. I > II > III > IV
   • B. IV > III > II > I
   • C. II > I > III > IV
   • D. I > III > II > IV
   Answer and solution

   Answer: A

   Carbocation stability increases with the number of electron-donating alkyl groups due to the +I inductive effect and hyperconjugation. Tertiary carbocations are most stable, followed by secondary, primary, and methyl.

9. Q9 · Biomolecules

   The number of chiral carbon atoms present in D-glucose is:

   • A. 3
   • B. 4
   • C. 5
   • D. 6
   Answer and solution

   Answer: B

   D-glucose has four chiral carbon atoms at positions C-2, C-3, C-4, and C-5 in its open-chain form. C-1 (aldehyde carbon) and C-6 (primary alcohol) are not chiral.

10. Q10 · Complex Numbers and Quadratic Equations

    If z is a complex number satisfying |z - 3 - 4i| = 5, then the maximum value of |z| is:

    • A. 5
    • B. 10
    • C. 15
    • D. 12
    Answer and solution

    Answer: B

    The locus of z is a circle centered at (3, 4) with radius 5. The maximum distance from the origin occurs at the farthest point on the circle: |z|_max = √(3² + 4²) + 5 = 5 + 5 = 10.