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$\mathrm{N}$ moles of a polyatomic gas $(f=6)$ must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of $\mathrm{N}$ is:
The relation between root mean square speed $\left( v _{ rms }\right)$ and most probable speed $\left( v _{ p }\right)$ for the molar mass $M$ of oxygen gas molecule at the temperature of $300\, K$ will be