$(a)\;7:32\qquad(b)\;1:4\qquad(c)\;1:8\qquad(d)\;2:5$

Let weight of $O_2 = W_1$

Weight of $N_2 = W_2$

$\large\frac{W_1}{W_2} = \large\frac{1}{4}$

Also mole of $O_2 = \large\frac{W_1}{32}$

Mole of $N_2 = \large\frac{W_2}{28}$

$\large\frac{Mole\; of\; O_2}{Mole \;of \;N_2} = \large\frac{28}{32}\times\large\frac{1}{4}$

$\;\;\;\;\;\;\;\;\;\;\;\;= \large\frac{7}{32}$

Hence the ratio is 7:32

Thus answer is (a)

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