NTA JEE Main 30th January 2023 Shift 2

Match List I with List II

A vehicle travels $$4$$ km with speed of $$3$$ km h$$^{-1}$$ and another $$4$$ km with speed of $$5$$ km h$$^{-1}$$, then its average speed is:

An object is allowed to fall from a height $$R$$ above the earth, where $$R$$ is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be:

A block of $$\sqrt{3}$$ kg is attached to a string whose other end is attached to the wall. An unknown force $$F$$ is applied so that the string makes an angle of $$30°$$ with the wall. The tension $$T$$ is: (Given $$g = 10$$ m s$$^{-2}$$)

A machine gun of mass $$10$$ kg fires $$20$$ g bullets at the rate of $$180$$ bullets per minute with a speed of $$100$$ m s$$^{-1}$$ each. The recoil velocity of the gun is:

A force is applied to a steel wire $$A$$, rigidly clamped at one end. As a result elongation in the wire is $$0.2$$ mm. If same force is applied to another steel wire $$B$$ of double the length and a diameter $$2.4$$ times that of the wire $$A$$, the elongation in the wire $$B$$ will be (wires having uniform circular cross sections)

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Efficiency of a reversible heat engine will be highest at $$-273°$$C temperature of cold reservoir.
Reason R: The efficiency of Carnot's engine depends not only on temperature of cold reservoir but it depends on the temperature of hot reservoir too and is given as $$\eta = \left(1 - \frac{T_2}{T_1}\right)$$
In the light of the above statements, choose the correct answer from the options given below:

A flask contains hydrogen and oxygen in the ratio of $$2 : 1$$ by mass at temperature $$27°$$C. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is:

For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is $$1$$ kg, the angular frequency is $$\omega_1$$. When the mass block is $$2$$ kg the angular frequency is $$\omega_2$$. The ratio $$\frac{\omega_2}{\omega_1}$$ is:

As shown in the figure, a point charge $$Q$$ is placed at the centre of conducting spherical shell of inner radius $$a$$ and outer radius $$b$$. The electric field due to charge $$Q$$ in three different regions I, II and III is given by:
(I: $$r < a$$, II: $$a < r < b$$, III: $$r > b$$)