The temperature at which oxygen molecules have the same root mean square speed as helium atoms have at $300 \ K$ is (Atomic masses: $He = 4 \ u$,$O = 16 \ u$) (in $K$)

By how many folds will the temperature of a gas increase when the root mean square velocity of the gas molecules in a container of fixed volume is increased from $5 \times 10^4 \ cm/s$ to $10 \times 10^4 \ cm/s$?

The ratio of most probable velocity to that of average velocity is

What is the $rms$ velocity of $O_2$ at $STP$ (in $cm/s$)?

In which of the following pairs do the gaseous species diffuse with the same rate of diffusion under similar conditions of temperature and pressure?

At $256 \ K$,the $rms$ speed of $SO_2$ gas molecules is $3.16 \times 10^2 \ ms^{-1}$. What is the most probable velocity (in $ms^{-1}$) of the same gas at the same temperature?