Explanation

(a)
Paramagnetic species has unpaired electron.
$B_{2} = 5 + 5 = 10\ \sigma 1s^{2},\ _{\sigma}^{*}1s^{2}\ ,\sigma 2s^{2},\ _{\sigma}^{*}2s^{2}\ ,\ \pi 2p_{x}^{1} = \pi 2p_{y}^{1}$
$C_{2} = 6 + 6 = 12 = \ \sigma 1s^{2},\ _{\sigma}^{*}1s^{2}\ ,\sigma 2s^{2},\ _{\sigma}^{*}2s^{2}\ ,\ \pi 2p_{x}^{2} = \pi 2p_{y}^{2}$
$N_{2} = 7 + 7 = 14 = \ \sigma 1s^{2},\ _{\sigma}^{*}1s^{2}\sigma 2s^{2},\ _{\sigma}^{*}2s^{2,}\ \pi 2p_{x}^{2} = \pi 2p_{y\ }^{2},\ \sigma 2p_{z\ }^{2}$
$F_{2} = 9 + 9 = 18 = \sigma 1s^{2,}\ _{\sigma}^{*}1s^{2}\ ,\sigma 2s^{2,}\ _{\sigma}^{*}2s^{2}\ ,\ \sigma 2p_{z\ }^{2},\pi 2p_{x}^{2} = \pi 2p_{y\ }^{2},\ _{\pi}^{*}2p_{x}^{2} = \ _{\pi}^{*}2p_{y}^{2}\$
$\therefore$ $B_{2}$ is paramagnetic because it has unpaired electron.