JEE Main 2024 · 31 Jan 2024 Shift 2

Consider two physical quantities A and B related to each other as E = (B − x²)/At where E, x and t have dimensions of energy, length and time respectively. The dimension of AB is

1. AL⁰M⁻¹T¹
2. BL²M⁻¹T¹
3. CL⁻²M¹T⁰
4. DL⁻²M⁻¹T¹

If two vectors A⃗ and B⃗ having equal magnitude R are inclined at an angle θ, then

1. A|A⃗ + B⃗| = 2R sin(θ/2)
2. B|A⃗ − B⃗| = 2R cos(θ/2)
3. C|A⃗ + B⃗| = 2R cos(θ/2)
4. D|A⃗ − B⃗| = √2R sin(θ/2)

A body of mass 2 kg begins to move under the action of a time dependent force given by F⃗ = (6t î + 6t² ĵ) N. The power developed by the force at the time t is given by:

1. A(6t⁴ + 9t⁵) W
2. B(9t⁵ + 6t³) W
3. C(3t³ + 6t⁵) W
4. D(9t³ + 6t⁵) W

The mass of the moon is 1/144 times the mass of a planet and its diameter is 1/16 times the diameter of a planet. If the escape velocity on the planet is v, the escape velocity on the moon will be:

1. Av/12
2. Bv/4
3. Cv/6
4. Dv/3

A small spherical ball of radius r, falling through a viscous medium of negligible density has terminal velocity ‘v’. Another ball of the same mass but of radius 2r, falling through the same viscous medium will have terminal velocity:

1. Av/2
2. Bv/4
3. C2v
4. D4v

The speed of sound in oxygen at S.T.P. will be approximately: (given, R = 8.3 JK⁻¹, γ = 1.4)

1. A341 m/s
2. B333 m/s
3. C325 m/s
4. D310 m/s

A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:

1. A21 RT
2. B27 RT
3. C29 RT
4. D20 RT

Force between two point charges q₁ and q₂ placed in vacuum at 'r' cm apart is F. Force between them when placed in a medium having dielectric constant K=5 at 'r/5' cm apart will be:

1. AF/5
2. B5F
3. CF/25
4. D25F