The ratio of average velocity to most probable velocity is

Among the following,identify the gas which has the greatest average speed of its molecules?

The ratio among most probable velocity,mean velocity and root mean square velocity is given by

The $RMS$ velocity $(u_{rms})$ of one mole of an ideal gas was measured at different temperatures and the following graph is obtained. What is the slope $(m)$ of the straight line?
($x$-axis $= T$ $(K)$; $y$-axis $= (u_{rms})^2$; $M =$ molar mass; $R =$ gas constant)

If the $RMS$ speed of nitrogen at a certain temperature is $3000 \ ms^{-1}$,the approximate kinetic energy of one mole of nitrogen at that temperature in $kJ$ is (assume nitrogen as ideal gas)

If the value of $u_{rms}$ at $27\,^{\circ}C$ is $30\sqrt{R}$,what is the molar mass of the gas in kilograms?