NTA JEE Main 28th July 2022 Shift 2

Consider the efficiency of Carnot's engine is given by $$\eta = \frac{\alpha\beta}{\sin\theta} \log_e\frac{\beta x}{kT}$$, where $$\alpha$$ and $$\beta$$ are constants. If $$T$$ is temperature, $$k$$ is Boltzmann constant, $$\theta$$ is angular displacement and $$x$$ has the dimensions of length. Then, choose the incorrect option.

At time $$t = 0$$ a particle starts travelling from a height $$7\hat{z}$$ cm in a plane keeping z coordinate constant. At any instant of time, it's position along the x and y directions are defined as $$3t$$ and $$5t^3$$ respectively. At $$t = 1$$ s acceleration of the particle will be

A uniform metal chain of mass $$m$$ and length $$L$$ passes over a massless and frictionless pulley. It is released from rest with a part of its length $$l$$ is hanging on one side and rest of its length $$(L-l)$$ is hanging on the other side of the pulley. At a certain point of time, when $$l = \frac{L}{x}$$, the acceleration of the chain is $$\frac{g}{2}$$. The value of $$x$$ is

A bullet of mass 200 g having initial kinetic energy 90 J is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to 40 J within 1 s, the minimum length of the pool, the bullet has to travel so that it completely comes to rest is

Assume there are two identical simple pendulum Clocks-1 is placed on the earth and Clock-2 is placed on a space station located at a height h above the earth surface. Clock-1 and Clock-2 operate at time periods 4 s and 6 s respectively. Then the value of h is (consider radius of earth $$R_E = 6400$$ km and $$g$$ on earth $$10 \ m s^{-2}$$)

A pressure-pump has a horizontal tube of cross-sectional area 10 cm$$^2$$ for the outflow of water at a speed of 20 m s$$^{-1}$$. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is: [given: density of water $$= 1000$$ kg m$$^{-3}$$]

Consider a cylindrical tank of radius 1 m is filled with water. The top surface of water is at 15 m from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of 5 m from the bottom. A force of $$5 \times 10^5$$ N is applied on the top surface of water using a piston. The speed of efflux from the hole will be: (given atmospheric pressure $$P_A = 1.01 \times 10^5$$ Pa, density of water $$\rho_w = 1000$$ kg m$$^{-3}$$ and gravitational acceleration $$g = 10 \ m s^{-2}$$)

A vessel contains 14 g of nitrogen gas at a temperature of $$27^\circ C$$. The amount of heat to be transferred to the gas to double the r.m.s. speed of its molecules will be: (Take $$R = 8.32$$ J mol$$^{-1}$$ K$$^{-1}$$)

A uniform electric field $$E = \frac{8m}{e}$$ V m$$^{-1}$$ is created between two parallel plates of length 1 m as shown in figure, (where $$m$$ = mass of electron and $$e$$ = charge of electron). An electron enters the field symmetrically between the plates with a speed of 2 m s$$^{-1}$$. The angle of the deviation $$\theta$$ of the path of the electron as it comes out of the field will be

A slab of dielectric constant K has the same cross-sectional area as the plates of a parallel plate capacitor and thickness $$\frac{3}{4}d$$, where $$d$$ is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be: (Given $$C_0$$ = capacitance of capacitor with air as medium between plates.)