Explanation

(c)
$NO^{-}(16).$ According to MOT.
$\sigma 1s^{2},\ _{\sigma}^{*}1s^{2}\ ,\sigma 2s^{2},\ _{\sigma}^{*}2s^{2},\sigma 2p_{x}^{2},\ _{\left\{ \ _{\ _{\pi}^{*}2p_{z}^{1},}^{\ _{\pi}^{*}2p_{y}^{1}} \right.\ }^{\left\{ \ _{\pi 2p_{z}^{2},}^{\pi p_{y}^{2}} \right.\ }$
Bond order = $\frac{bonding\ electrons - antibonding\ electrons}{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{10 - 6}{2} = 2$
$NO^{+}(14).$
$\sigma 1s^{2},\ _{\sigma}^{*}1s^{2}\ ,\sigma 2s^{2},\ _{\sigma}^{*}2s^{2},\sigma 2p_{x}^{2},\left\{ \ _{\pi 2p_{z}^{2},}^{\pi 2p_{y}^{2}} \right.\ \ _{\ }^{\ }$
Bond order = $\ = \frac{10 - 4}{2} = 3$
$NO^{\ }(15)$
$\sigma 1s^{2},\ _{\sigma}^{*}1s^{2}\ ,\sigma 2s^{2},\ _{\sigma}^{*}2s^{2},\sigma 2p_{x}^{2},\ _{\left\{ \ _{\ _{\pi}^{*}2p_{z}^{0}}^{\ _{\pi}^{*}2p_{y}^{1}} \right.\ }^{\left\{ \ _{\pi 2p_{z}^{2},}^{\pi 2p_{y}^{2}} \right.\ }$
Bond order = $\ = \frac{10 - 5}{2} = 2.5$
(iv)$NO^{2 +}(13).$
$\sigma 1s^{2},\ _{\sigma}^{*}1s^{2}\ ,\sigma 2s^{2},\ _{\sigma}^{*}2s^{2},\sigma 2p_{x}^{2},\left\{ \ _{\pi 2p_{z}^{2},}^{\pi 2p_{y}^{2}} \right.\ \ _{\ }^{\ }$
Bond order = $\ = \frac{9 - 4}{2} = 2.5$
$NO^{2 -}(17)$
$\sigma 1s^{2},\ _{\sigma}^{*}1s^{2}\ ,\sigma 2s^{2},\ _{\sigma}^{*}2s^{2},\sigma 2p_{x}^{2},\ _{\left\{ \ _{\ _{\pi}^{*}2p_{z}^{1}}^{\ _{\pi}^{*}2p_{y}^{2}} \right.\ }^{\left\{ \ _{\pi 2p_{z}^{2},}^{\pi{2p}_{y}^{2}} \right.\ }$
Bond order = $\ = \frac{10 - 7}{2} = 1.5$
The order of bond order is
$NO^{2 -} < NO^{-} < NO^{2 +} \approx NO <$ $NO^{+}$