NTA JEE Mains 1st Feb 2023 Shift 1

$$\left(P + \frac{a}{V^2}\right)(V - b) = RT$$ represents the equation of state of some gases. Where $$P$$ is the pressure, $$V$$ is the volume, $$T$$ is the temperature and $$a, b, R$$ are the constants. The physical quantity, which has dimensional formula as that of $$\frac{b^2}{a}$$, will be :

An object moves with speed $$v_1, v_2$$ and $$v_3$$ along a line segment $$AB, BC$$ and $$CD$$ respectively as shown in figure. Where $$AB = BC$$ and $$AD = 3AB$$, then average speed of the object will be 

A child stands on the edge of the cliff 10 m above the ground and throws a stone horizontally with an initial speed of $$5 \text{ m s}^{-1}$$. Neglecting the air resistance, the speed with which the stone hits the ground will be ______ $$\text{m s}^{-1}$$ (given, $$g = 10 \text{ m s}^{-2}$$).

A block of mass 5 kg is placed at rest on a table of rough surface. Now, if a force of 30 N is applied in the direction parallel to surface of the table, the block slides through a distance of 50 m in an interval of time 10 s. Coefficient of kinetic friction is (given, $$g = 10 \text{ m s}^{-2}$$):

If earth has a mass nine times and radius twice to the of a planet $$P$$. Then $$\frac{v_e}{3}\sqrt{x} \text{ ms}^{-1}$$ will be the minimum velocity required by a rocket to pull out of gravitational force of $$P$$, where $$v_e$$ is escape velocity on earth. The value of $$x$$ is

Given below are two statements :
Statement-I: Acceleration due to gravity is different at different places on the surface of earth.
Statement-II: Acceleration due to gravity increases as we go down below the earth's surface.
In the light of the above statements, choose the correct answer from the options given below

A mercury drop of radius $$10^{-3}$$ m is broken into 125 equal size droplets. Surface tension of mercury is $$0.45 \text{ N m}^{-1}$$. The gain in surface energy is:

A sample of gas at temperature $$T$$ is adiabatically expanded to double its volume. The work done by the gas in the process is given, (given $$\gamma = \frac{3}{2}$$) :

The average kinetic energy of a molecule of the gas is

A steel wire with mass per unit length $$7.0 \times 10^{-3} \text{ kg m}^{-1}$$ is under tension of 70 N. The speed of transverse waves in the wire will be: