NTA JEE Mains 27th Jan 2024 Shift 2

The equation of state of a real gas is given by $$\left(P + \frac{a}{V^2}\right)(V - b) = RT$$, where $$P$$, $$V$$ and $$T$$ are pressure, volume and temperature respectively and $$R$$ is the universal gas constant. The dimensions of $$\frac{a}{b^2}$$ is similar to that of :

A bullet is fired into a fixed target looses one third of its velocity after travelling 4 cm. It penetrates further $$D \times 10^{-3}$$ m before coming to rest. The value of $$D$$ is :

Given below are two statements :
Statement (I) : The limiting force of static friction depends on the area of contact and independent of materials.
Statement (II) : The limiting force of kinetic friction is independent of the area of contact and depends on materials.
In the light of the above statements, choose the most appropriate answer from the options given below :

A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle ($$\theta$$) of thread deflection in the extreme position will be :

A heavy iron bar of weight 12 kg is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle 60° with the horizontal, the normal force applied by the man on bar is :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun.
Reason (R) : The moon takes less time to move around the earth than the time taken by the earth to move around the sun.
In the light of the above statements, choose the most appropriate answer from the options given below :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The property of body, by virtue of which it tends to regain its original shape when the external force is removed, is Elasticity.
Reason (R) : The restoring force depends upon the bonded inter atomic and inter molecular force of solid.
In the light of the above statements, choose the correct answer from the options given below :

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of $$\frac{C_p}{C_v}$$ for the gas is :

The total kinetic energy of 1 mole of oxygen at 27°C is :
[Use universal gas constant (R) = 8.31 J mol$$^{-1}$$ K$$^{-1}$$]

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Work done by electric field on moving a positive charge on an equipotential surface is always zero.
Reason (R) : Electric lines of forces are always perpendicular to equipotential surfaces.
In the light of the above statements, choose the most appropriate answer from the options given below :