(a)
Given electronic configuration of anion X is
$\sigma 1s^{2},\ _{\sigma}^{*}1s^{2}\ ,\sigma 2s^{2},\ _{\sigma}^{*}2s^{2}\ ,\ \pi 2p_{x}^{2} = \pi 2p_{y\ }^{2},\sigma 2p_{z\ }^{2},\ _{\pi}^{*}2p_{x}^{1}$
$\therefore$ Total number of electrons of anion X = 15
Hence, the anion X is $N_{2}^{-}.$