JEE Main 2023 · 8 Apr 2023 Shift 1

The engine of a train moving with speed 10 ms⁻¹ towards a platform sounds a whistle at frequency 400 Hz. The frequency heard by a passenger inside the train is: (neglect air speed. Speed of sound in air = 330 ms⁻¹)

1. A200 Hz
2. B388 Hz
3. C412 Hz
4. D400 Hz

An air bubble of volume 1 cm³ rises from the bottom of a lake 40 m deep to the surface at a temperature of 12°C. The atmospheric pressure is 1×10⁵ Pa, the density of water is 1000 kg/m³ and g = 10 m/s². There is no difference of the temperature of water at the depth of 40 m and on the surface. The volume of air bubble when it reaches the surface will be:

1. A2 cm³
2. B3 cm³
3. C4 cm³
4. D5 cm³

Given below are two statements: Statement I: If heat is added to a system, its temperature must increase. Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase. In the light of the above statements, choose the correct answer from the options given below

1. ABoth Statement I and Statement II are true
2. BBoth Statement I and Statement II are false
3. CStatement I is true but Statement II is false
4. DStatement I is false but Statement II is true

An aluminium rod with Young’s modulus Y = 7.0×10¹⁰ N/m² undergoes elastic strain of 0.04%. The energy per unit volume stored in the rod in SI unit is:

1. A2800
2. B5600
3. C8400
4. D11200

Given below are two statements: Statement I: If E be the total energy of a satellite moving around the earth, then its potential energy will be E/2. Statement II: The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy E. In the light of the above statements, choose the most appropriate answer from the options given below

1. ABoth Statement I and Statement II are correct
2. BBoth Statement I and Statement II are incorrect
3. CStatement I is correct but Statement II is incorrect
4. DStatement I is incorrect but Statement II is correct

At any instant, the velocity of a particle of mass 500 g is (2t î + 3t² ĵ) ms⁻¹. If the force acting on the particle at t = 1s is (î + xĵ)N. Then the value of x will be:

1. A6
2. B4
3. C3
4. D2

Two forces having magnitude A and A/2 are perpendicular to each other. The magnitude of their resultant is:

1. A5A/2
2. B√5A/2
3. C√5A/4
4. D√5A²/2

The weight of a body on the earth is 400 N. Then weight of the body when taken to a depth half of the radius of the earth will be:

1. AZero
2. B100 N
3. C200 N
4. D300 N