NTA JEE Main 27th July 2022 Shift 2

An expression of energy density is given by $$u = \alpha \beta \sin\left(\frac{\alpha x}{kt}\right)$$, where $$\alpha, \beta$$ are constants, $$x$$ is displacement, $$k$$ is Boltzmann constant and $$t$$ is the temperature. The dimensions of $$\beta$$ will be

The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at $$(4 + x)$$ cm inside the block. The value of $$x$$ is

A body of mass 10 kg is projected at an angle of $$45^\circ$$ with the horizontal. The trajectory of the body is observed to pass through a point (20, 10). If $$T$$ is the time of flight, then its momentum vector, at time $$t = \frac{T}{\sqrt{2}}$$, is _____ . [Take $$g = 10 \ m s^{-2}$$]

A block of mass $$M$$ slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is $$\theta$$. The magnitude of the contact force will be :

A block $$A$$ takes 2 s to slide down a frictionless incline of $$30^\circ$$ and length $$l$$, kept inside a lift going up with uniform velocity $$v$$. If the incline is changed to $$45^\circ$$, the time taken by the block, to slide down the incline, will be approximately:

A body of mass $$m$$ is projected with velocity $$\lambda v_e$$ in vertically upward direction from the surface of the earth into space. It is given that $$v_e$$ is escape velocity and $$\lambda < 1$$. If air resistance is considered to be negligible, then the maximum height from the centre of earth, to which the body can go, will be ($$R$$ : radius of earth)

A steel wire of length 3.2 m $$(Y_S = 2.0 \times 10^{11} \ N m^{-2})$$ and a copper wire of length 4.4 m $$(Y_C = 1.1 \times 10^{11} \ N m^{-2})$$, both of radius 1.4 mm are connected end to end. When stretched by a load, the net elongation is found to be 1.4 mm. The load applied, in Newton, will be: (Given $$\pi = \frac{22}{7}$$)

In 1st case, Carnot engine operates between temperatures 300 K and 100 K. In 2nd case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in 2nd case) will be :

Which statements are correct about degrees of freedom?
A. A molecule with $$n$$ degrees of freedom has $${n^{2}}$$ different ways of storing energy.
B. Each degree of freedom is associated with $$\frac{1}{2}RT$$ average energy per mole.
C. A monoatomic gas molecule has 1 rotational degree of freedom whereas diatomic molecule has 2 rotational degrees of freedom.
D. $$CH_4$$ has a total of 6 degrees of freedom.
Choose the correct answer from the options given below:

A charge of $$4\mu C$$ is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be: