NTA JEE Main 24th June 2022 Shift 1

Identify the pair of physical quantities which have different dimensions:

A projectile is projected with velocity of $$25$$ m s$$^{-1}$$ at an angle $$\theta$$ with the horizontal. After $$t$$ seconds its inclination with horizontal becomes zero. If $$R$$ represents horizontal range of the projectile, the value of $$\theta$$ will be : [use $$g = 10$$ m s$$^{-2}$$]

A boy ties a stone of mass $$100$$ g to the end of a $$2$$ m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of $$80$$ N. If the maximum speed with which the stone can revolve is $$\frac{K}{\pi}$$ rev min$$^{-1}$$. The value of $$K$$ is : (Assume the string is massless and un-stretchable)

A block of mass $$10$$ kg starts sliding on a surface with an initial velocity of $$9.8$$ ms$$^{-1}$$. The coefficient of friction between the surface and block is $$0.5$$. The distance covered by the block before coming to rest is : [use $$g = 9.8$$ ms$$^{-2}$$]

A particle experiences a variable force $$\vec{F} = \left(4x\hat{i} + 3y^2\hat{j}\right)$$ in a horizontal $$x - y$$ plane. Assume distance in meters and force in Newton. If the particle moves from point $$(1, 2)$$ to point $$(2, 3)$$ in the $$x - y$$ plane, then Kinetic Energy changes by :

The approximate height from the surface of earth at which the weight of the body becomes $$\frac{1}{3}$$ of its weight on the surface of earth is :
[Radius of earth $$R = 6400$$ km and $$\sqrt{3} = 1.732$$]

The bulk modulus of a liquid is $$3 \times 10^{10}$$ Nm$$^{-2}$$. The pressure required to reduce the volume of liquid by $$2\%$$ is :

Two metallic blocks $$M_1$$ and $$M_2$$ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of $$M_2$$ is $$K$$ then the thermal conductivity of $$M_1$$ will be : [Assume steady state heat conduction]

A Carnot engine whose heat sinks at $$27°$$C, has an efficiency of $$25\%$$. By how many degrees should the temperature of the source be changed to increase the efficiency by $$100\%$$ of the original efficiency?

The equations of two waves are given by :
$$y_1 = 5 \sin 2\pi(x - vt)$$ cm
$$y_2 = 3 \sin 2\pi(x - vt + 1.5)$$ cm
These waves are simultaneously passing through a string. The amplitude of the resulting wave is :