Explanation

(b) Let one mole of each gas has same volumes as V. when they are mixed, then density of mixture is
$\rho_{mixture} = \frac{mass\ of\ O_{2} + mass\ of\ H_{2}}{volume\ of\ O_{2} + volume\ of\ H_{2}}$
$= \frac{32 + 2}{V + V}$
$= \frac{34}{2V} = \frac{17}{V}$
Also, $\rho_{H_{2}} = \frac{2}{V}$
Now, velocity $v = \left( \frac{\gamma p}{\rho} \right)^{1/2}$
Or
$v \propto \frac{1}{\sqrt{\rho}}$
$\therefore\ \ \frac{v_{mixture}}{V_{H_{2}}} = \ \sqrt{\left( \frac{\rho_{H_{2}}}{\rho_{mixture}} \right)}$
$= \sqrt{\left( \frac{2/v}{17/v} \right)} = \sqrt{\left( \frac{2}{17} \right)}$