NTA JEE Main 24th January 2023 Shift 2

If two vectors $$\vec{P} = \hat{i} + 2m\hat{j} + m\hat{k}$$ and $$\vec{Q} = 4\hat{i} - 2\hat{j} + m\hat{k}$$ are perpendicular to each other. Then, the value of $$m$$ will be

The frequency ($$\nu$$) of an oscillating liquid drop may depend upon radius ($$r$$) of the drop, density ($$\rho$$) of liquid and the surface tension ($$s$$) of the liquid as: $$\nu = r^a \rho^b s^c$$. The values of $$a$$, $$b$$ and $$c$$ respectively are

The velocity-time graph of a body moving in a straight line is shown in figure.

The ratio of displacement and distance travelled by the body in time 0 to 10 s is

A body of mass 200 g is tied to a spring of spring constant 12.5 N m$$^{-1}$$, while the other end of spring is fixed at point $$O$$. If the body moves about $$O$$ in a circular path on a smooth horizontal surface with constant angular speed 5 rad s$$^{-1}$$, then the ratio of extension in the spring to its natural length will be:

Given below are two statements:
Statement I: Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.
Statement II: Acceleration due to earth's gravity is same at a height 'h' and depth 'd' from earth's surface, if $$h = d$$.
In the light of above statements, choose the most appropriate answer form the options given below

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion $$A$$: A pendulum clock when taken to Mount Everest becomes fast.
Reason $$R$$: The value of g (acceleration due to gravity) is less at Mount Everest than its value on the surface of earth.
In the light of the above statements, choose the most appropriate answer from the options given below

If the distance of the earth from Sun is $$1.5 \times 10^6$$ km, then the distance of an imaginary planet from Sun, if its period of revolution is 2.83 years is:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion (A): Steel is used in the construction of buildings and bridges.
Reason (R): Steel is more elastic and its elastic limit is high.
In the light of above statements, choose the most appropriate answer from the options given below

In an Isothermal change, the change in pressure and volume of a gas can be represented for three different temperature; $$T_3 > T_2 > T_1$$ as:

Let $$\gamma_1$$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and $$\gamma_2$$ be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio $$\frac{\gamma_1}{\gamma_2}$$ is: