If a set $A$ has $n$ elements,then the total number of subsets of $A$ is:

$A$ monoatomic ideal gas initially at temperature $T_1$ is enclosed in a cylinder fitted with a massless,frictionless piston. By releasing the piston suddenly,the gas is allowed to expand adiabatically to a temperature $T_2$. If $L_1$ and $L_2$ are the lengths of the gas columns before and after expansion respectively,then $\frac{T_2}{T_1}$ is

The mechanism of the reaction $2NO_2 + F_2 \to 2NO_2F$ is given by:
$(i)$ $NO_2 \xrightarrow{slow} NO_2^*$
$(ii)$ $NO_2^* + F_2 \xrightarrow{fast} NO_2F + F$
$(iii)$ $F + NO_2 \xrightarrow{fast} NO_2F$
Select the correct statement regarding this reaction.

In a rectangle $ABCD$ where $BC = 2AB$,the moment of inertia will be minimum along which of the following axes?

An aircraft executes a horizontal loop with a speed of $150 \, m/s$ with its wings banked at an angle of $12^\circ$. The radius of the loop is .......... $km$. $(g = 10 \, m/s^2)$

The period of a simple pendulum, whose bob is a hollow metallic sphere, is $T$. The period is $T_1$ when the bob is filled with sand, $T_2$ when it is filled with mercury, and $T_3$ when it is half-filled with mercury. Which of the following is true?