The average force applied on the walls of a closed container depends on $T^{x}$ where $T$ is the temperature of an ideal gas. The value of '$x$' is

Two particles $A$ and $B$ initially at rest move towards each other under a mutual force of attraction. At the instant when the velocity of $A$ is $v$ and that of $B$ is $2v$,the velocity of the centre of mass of the system is

If $y=\tan ^{-1}\left(\frac{\sqrt{1+a^2 x^2}-1}{a x}\right)$,then $\left(1+a^2 x^2\right) y^{\prime \prime}+2 a^2 x y^{\prime}$ is equal to

The $pH$ of blood does not appreciably change by a small addition of an acid or a base because blood

The magnetic susceptibility of the material of a rod is $499$. Permeability of vacuum is $4 \pi \times 10^{-7} \ H/m$. Absolute permeability of the material of the rod in $H/m$ is:

$A$ body executes simple harmonic motion under the action of a force $F_1$ with a time period $T_1 = \frac{4}{5} \ s$. If the force is changed to $F_2$,it executes $SHM$ with a time period $T_2 = \frac{3}{5} \ s$. If both the forces $F_1$ and $F_2$ act simultaneously in the same direction on the body,what is its new time period in seconds?