At what temperature does the $r.m.s.$ speed of air molecules become double that at $N.T.P.$?

At what temperature $T$ (in $K$) will the $rms$ speed of $H_2$ be equal to the $rms$ speed of $O_2$ at $47^{\circ}C$?

$A$ vessel is partitioned into two equal halves by a fixed diathermic separator. Two different ideal gases are filled in the left $(L)$ and right $(R)$ halves. The $rms$ speed of the molecules in the $L$ part is equal to the mean speed of the molecules in the $R$ part. Then the ratio of the mass of a molecule in the $L$ part to that of a molecule in the $R$ part is

Select the incorrect statement about Maxwell's speed distribution.

The gas having an average speed four times that of $SO_2$ (molecular mass $64$) is

Column-$I$ represents the formula for ${v_{rms}}$ and Column-$II$ represents the corresponding condition (phenomena). Match them correctly:

Column-$I$	Column-$II$
$(a)$ ${v_{rms}} = \sqrt {\frac{3P}{\rho}}$	$(i)$ For $1 \text{ mole ideal gas}$
$(b)$ ${v_{rms}} = \sqrt {\frac{3RT}{M_0}}$	$(ii)$ For one molecule of gas
$(c)$ ${v_{rms}} = \sqrt {\frac{3{k_B}T}{m}}$	$(iii)$ On the basis of kinetic theory