$(A)$ $B_2: \sigma 1 s^2 \sigma 1 s^2 \sigma 2 s^2 \sigma 2 s^2\left|\begin{array}{l}\pi 2 p_y^1 \\ \pi 2 p_z^1\end{array}\right|$ paramagnetic. Bond order
$=\frac{6-4}{2}=1$
Bond is formed by mixing of $s$ and p orbitals. $B_2$ undergoes both oxidation \& reduction as
$B_2+O_2 \xrightarrow{\text { Heat }} B_2 O_3 \text { (Oxidation) } B_2+H_2 \rightarrow B_2 H_6 \text { (Reduction) }$
$(B)$ $N_2: \sigma 1 s^2 \sigma 1 s^2 \sigma 2 s^2 \sigma 2 s^2 \sigma 2 p_x^2\left|\begin{array}{c}\pi 2 p_y^2 \\ \pi 2 p_z^2\end{array}\right|$ diamagnetic. Bond order
$=\frac{10-4}{2}=3 > 2$
$N_2$ undergoes both oxidation and reduction as
$N _2+ O _2 \xrightarrow{\Delta} NO , N _2+3 H _2 \xrightarrow{\text { Catalyst }} NH _3$
In $N_2$, bonds are formed by mixing of s and p orbitals.
$(C)$ $O_2: \sigma 1 s^2{ }_\sigma^{\star} 1 s^2 \sigma 2 s^2 \sigma 2 s^2 \sigma 2 p_x^2\left|\begin{array}{l}\pi 2 p_y^2 \\ \pi 2 p_z^2\end{array}\right|\left|\begin{array}{l}\stackrel{\star}{\pi} 2 p_y^2 \\ \stackrel{\star}{\pi} 2 p_z^1\end{array}\right| \stackrel{\star}{\sigma} 2 p_x^0$
Paramagnetic with bond order $=1.5 . O_2^{-}$undergoes both oxidation and reduction
$(D)$ $O_2: \sigma 1 s^2{ }_\sigma^{\star} 1 s^2 \sigma 2 s^2 \sigma 2 s^2 \sigma 2 p_x^2\left|\begin{array}{l}\pi 2 p_y^2 \\ \pi 2 p_z^2\end{array}\right|\left|\begin{array}{l}\stackrel{\star}{\pi} 2 p_y^1 \\ \stackrel{\star}{\pi} 2 p_z^1\end{array}\right| \stackrel{\star}{\sigma} 2 p_x^0$
Paramagnetic with bond order $=2 . O _2$ undergoes reduction and oxidation