For a gas at a particular temperature on an average,the quantity which remains same for all molecules is

According to the kinetic theory of gases,the average kinetic energy of $1$ gram-mole of a gas is given by which of the following expressions?

Two gases $A$ and $B$ are contained in the same vessel which is at temperature $T$. The number of molecules of gas $A$ is $N$ and the mass of each molecule is $m$. The number of molecules of gas $B$ is $2N$ and the mass of each molecule is $2m$. If the mean square velocity of the $x$-component of velocity of gas $B$ is $v^2$ and the mean square velocity of the $x$-component of velocity of molecules of gas $A$ is $u_x^2$,then $\frac{u_x^2}{v^2}$ is:

In a vessel,an ideal gas is at a pressure $P$. If the mass of all the molecules is halved and their speed is doubled,then the resultant pressure of the gas will be

The average translational kinetic energy of the oxygen molecules at a temperature of $127^{\circ} C$ is (Boltzmann constant $= 1.38 \times 10^{-23} \,J \,K^{-1}$)

The pressure exerted by a gas is $P_0$. If the mass of the molecules is halved and their velocity is doubled,the pressure will become .......