When the temperature of a gas is increased from 30 ° C to 930 ° C , the root mean square speed of…

Root-mean-square is directly proportional to the square root of temperature.

${\mathrm{u}}_{\mathrm{rms}}=\sqrt{\frac{3\mathrm{RT}}{\mathrm{M}}}$

At the different temperature of same gas, the mass will be same.

Temperature ${\mathrm{T}}_1=30+273=303\mathrm{K}$

Temperature ${\mathrm{T}}_2=930+273=1203\mathrm{K}$

So,

$$\begin{gathered} \frac{{\mathrm{u}}_1}{{\mathrm{u}}_2}=\frac{\sqrt{{\mathrm{T}}_1}}{\sqrt{{\mathrm{T}}_2}}=\frac{\sqrt{303}}{\sqrt{1203}}=\frac{17.41}{3.68} \\ {\mathrm{u}}_2=2{\mathrm{u}}_1 \end{gathered}$$

Hence, the root mean square speed of the gas would get doubled.