NTA JEE Main 31st January 2023 Shift 1

If $$R$$, $$X_L$$ and $$X_C$$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:

The initial speed of a projectile fired from ground is $$u$$. At the highest point during its motion, the speed of projectile is $$\dfrac{\sqrt{3}}{2}u$$. The time of flight of the projectile is:

As shown in figure, a 70 kg garden roller is pushed with a force of $$\vec{F} = 200$$ N at an angle of 30° with horizontal. The normal reaction on the roller is (Given $$g = 10$$ m s$$^{-2}$$)

100 balls each of mass $$m$$ moving with speed $$v$$ simultaneously strike a wall normally and reflected back with same speed, in time $$t$$ s. The total force exerted by the balls on the wall is

At a certain depth $$d$$ below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height $$3R$$ above earth surface. Where $$R$$ is Radius of earth (Take $$R = 6400$$ km). The depth $$d$$ is equal to

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following {Assume negligible air friction}

If 1000 droplets of water of surface tension 0.07 N m$$^{-1}$$, having same radius 1 mm each, combine to form a single drop. In the process the released surface energy is- (Take $$\pi = \dfrac{22}{7}$$)

The pressure of a gas changes linearly with volume from $$A$$ to $$B$$ as shown in figure. If no heat is supplied to or extracted from the gas then change in the internal energy of the gas will be

The correct relation between $$\gamma = \dfrac{C_P}{C_V}$$ and temperature $$T$$ is:

The maximum potential energy of a block executing simple harmonic motion is 25 J. A is amplitude of oscillation. At $$\dfrac{A}{2}$$, the kinetic energy of the block is