The ratio of vapour densities of two gases at the same temperature is $\frac{4}{25}$. What is the ratio of their $r.m.s.$ velocities?

If the $r.m.s.$ velocity of a gas at a given temperature (Kelvin scale) is $300 \ m/s$,what will be the $r.m.s.$ velocity of a gas having twice the molecular weight and half the temperature on the Kelvin scale?

The $r.m.s.$ speed of a certain gas is $v$ at $400\,K.$ The temperature at which the $r.m.s.$ speed becomes two times,will be ...... $K$.

Three vessels $A$,$B$,and $C$ contain gases at the same temperature. Vessel $A$ contains $O_2$ gas,vessel $B$ contains $N_2$ gas,and vessel $C$ contains a mixture of $O_2$ and $N_2$ gases. If the average velocity of $O_2$ in vessel $A$ is $V_1$ and the average velocity of $N_2$ in vessel $B$ is $V_2$,what is the average velocity of $O_2$ in vessel $C$?

The temperature of the hydrogen at which the average speed of its molecules is equal to that of oxygen molecules at a temperature of $31\,^oC$ is ........ $^oC$.

$N$ $(N < 100)$ molecules of a gas have velocities $1, 2, 3, ..., N \text{ km/s}$ respectively. Then: