JEE Main 2024 · 9 Apr 2024 Shift 2

The de-Broglie wavelength associated with a particle of mass m and energy E is h/√2mE. The dimensional formula for Planck's constant is :

1. A[M²L²T⁻²]
2. B[ML²T⁻¹]
3. C[ML⁻¹T⁻²]
4. D[MLT⁻²]

Two cars are travelling towards each other at speed of 20 m s⁻¹ each. When the cars are 300 m apart, both the drivers apply brakes and the cars retard at the rate of 2 m s⁻². The distance between them when they come to rest is :

1. A50 m
2. B100 m
3. C200 m
4. D25 m

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of 2:1. After disintegration they will move :

1. Ain the same direction with same speed.
2. Bin opposite directions with speed in the ratio of 1:2 respectively.
3. Cin opposite directions with speed in the ratio of 2:1 respectively.
4. Din opposite directions with the same speed.

A hydrogen atom in ground state is given an energy of 10.2 eV. How many spectral lines will be emitted due to transition of electrons ?

1. A1
2. B3
3. C6
4. D10

The energy released in the fusion of 2 kg of hydrogen deep in the sun is E_H and the energy released in the fission of 2 kg of ²³⁵U is E_U. The ratio E_H/E_U is approximately: (Consider the fusion reaction as ⁴₁H + 2e⁻ → ⁴₂He + 2ν + 6γ + 26.7 MeV, energy released in the fission reaction of ²³⁵U is 200 MeV per fission nucleus and N_A = 6.023 × 10²³)

1. A7.62
2. B9.13
3. C25.6
4. D15.04

A satellite of 10³ kg mass is revolving in circular orbit of radius 2R. If 10⁴R/6 J energy is supplied to the satellite, it would revolve in a new circular orbit of radius : (use g = 10 m/s², R = radius of earth)

1. A2.5 R
2. B3 R
3. C4 R
4. D6 R

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

1. A1 : 3
2. B1 : 9
3. C1 : 27
4. D1 : 81

A spherical ball of radius 1 × 10⁻⁴ m and density 10⁵ kg/m³ falls freely under gravity through a distance h before entering a tank of water. If after entering in water the velocity of the ball does not change, then the value of h is approximately: (The coefficient of viscosity of water is 9.8 × 10⁻⁶ N s/m²)

1. A2296 m
2. B2249 m
3. C2396 m
4. D2518 m