The respective speeds of five molecules are $2, 1.5, 1.6, 1.6$ and $1.2 \, km/s$. The most probable speed in $km/s$ is:

$Assertion :$ The root mean square and most probable speeds of the molecules in a gas are the same.
$Reason :$ The Maxwell distribution for the speed of molecules in a gas is symmetrical.

At $300\,K$,the rms speed of oxygen molecules is $\sqrt{\frac{\alpha+5}{\alpha}}$ times its average speed in the gas. Then,the value of $\alpha$ will be (use $\pi=\frac{22}{7}$):

The speeds of $5$ molecules of a gas (in arbitrary units) are as follows: $2, 3, 4, 5, 6$. The root mean square speed for these molecules is

For a given gas at $1\,atm$ pressure,the $rms$ speed of the molecules is $200\,m/s$ at $127\,^oC$. At $2\,atm$ pressure and at $227\,^oC$,the $rms$ speed of the molecules will be:

At what temperature will the molecules of nitrogen have the same $r.m.s.$ velocity as the molecules of oxygen at $127^{\circ}C$ (in $^{\circ}C$)?