NTA JEE Mains 9th April 2024 Shift 2

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

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

A $$1 \text{ kg}$$ mass is suspended from the ceiling by a rope of length $$4 \text{ m}$$. A horizontal force '$$F$$' is applied at the mid point of the rope so that the rope makes an angle of $$45°$$ with respect to the vertical axis as shown in figure.

The magnitude of $$F$$ is : (Assume that the system is in equilibrium and $$g = 10 \text{ m/s}^2$$)

A satellite of $$10^3 \text{ kg}$$ mass is revolving in circular orbit of radius $$2R$$. If $$\frac{10^4 R}{6} \text{ J}$$ energy is supplied to the satellite, it would revolve in a new circular orbit of radius (use $$g = 10 \text{ m/s}^2$$, $$R$$ = radius of earth)

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:

A spherical ball of radius $$1 \times 10^{-4} \text{ m}$$ and density $$10^5 \text{ kg/m}^3$$ 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 $$9.8 \times 10^{-6} \text{ N s/m}^2$$)

A real gas within a closed chamber at $$27°C$$ undergoes the cyclic process as shown in figure. The gas obeys $$PV^3 = RT$$ equation for the path $$A$$ to $$B$$. The net work done in the complete cycle is (assuming $$R = 8 \text{ J/molK}$$):

The temperature of a gas is $$-78°C$$ and the average translational kinetic energy of its molecules is $$K$$. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes $$2K$$ is :

Five charges $$+q, +5q, -2q, +3q$$ and $$-4q$$ are situated as shown in the figure.

The electric flux due to this configuration through the surface $$S$$ is :

The effective resistance between $$A$$ and $$B$$, if resistance of each resistor is $$R$$, will be