$\mathrm{N}$ 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:
A$6$
B$3$
C$4$
D$2$
JEE MAIN 2024, Diffcult
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C$4$
c $\mathrm{f}_{\mathrm{eq}}=\frac{\mathrm{n}_1 \mathrm{f}_1+\mathrm{n}_2 \mathrm{f}_2}{\mathrm{n}_1+\mathrm{n}_2}$
For diatomic gas $\mathrm{f}_{\mathrm{eq}}=5$
$ 5=\frac{(N)(6)+(2)(3)}{N+2} $
$ 5 N+10=6 N+6 $
$ N=4$
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