M.O. configuration of ${\mathrm{N}}_2$ is
${\mathrm{\sigma }1\mathrm{s}}^2{<{\mathrm{\sigma }}^{\mathrm{*}}1\mathrm{s}}^2<{\mathrm{\sigma }2\mathrm{s}}^2<{{\mathrm{\sigma }}^{\mathrm{*}}2\mathrm{s}}^2<{{\mathrm{\pi }}^2{\mathrm{p}}_{\mathrm{x}}}^2={\mathrm{\pi }2{\mathrm{p}}_{\mathrm{y}}}^2<{\mathrm{\sigma }2{\mathrm{p}}_{\mathrm{z}}}^2$
B.O. of ${\mathrm{N}}_2=\frac{10-4}{2}=3$
M.O. configuration of ${\mathrm{N}}_2^{+}$ is
${\mathrm{\sigma }1\mathrm{s}}^2<{{\mathrm{\sigma }}^{\mathrm{*}}1\mathrm{s}}^2<{\mathrm{\sigma }2\mathrm{s}}^2<{{\mathrm{\sigma }}^{\mathrm{*}}2\mathrm{s}}^2<{\mathrm{\pi }2{\mathrm{p}}_{\mathrm{x}}}^2={\mathrm{\pi }2{\mathrm{p}}_{\mathrm{y}}}^2<{\mathrm{\sigma }2{\mathrm{p}}_{\mathrm{z}}}^1$
B.O. of ${\mathrm{N}}_2^{+}=\frac{9-4}{2}=2.5$
M.O. of configuration of ${\mathrm{O}}_2$ is
${\mathrm{\sigma }1\mathrm{s}}^2<{{\mathrm{\sigma }}^{\mathrm{*}}1\mathrm{s}}^2<{\mathrm{\sigma }2\mathrm{s}}^2<{{\mathrm{\sigma }}^{\mathrm{*}}\mathrm{}2\mathrm{s}}^2<{\mathrm{\sigma }2{\mathrm{p}}_{\mathrm{z}}}^2<{\mathrm{\pi }2{\mathrm{p}}_{\mathrm{x}}}^2<{{\mathrm{\pi }2{\mathrm{p}}_{\mathrm{y}}}^{}}^2<{{\mathrm{\pi }}^{\mathrm{*}}2{\mathrm{p}}_{\mathrm{x}}}^1<{{\mathrm{\pi }}^{\mathrm{*}}2{\mathrm{p}}_{\mathrm{y}}}^1$
$\therefore$ B.O. of ${\mathrm{O}}_2=\frac{10–6}{2}=2$
As it is paramagnetic so option $\left(\mathrm{a}\right)$ is incorrect.
M.O. configuration of ${\mathrm{O}}_2^{+}$ is
${\mathrm{\sigma }1\mathrm{s}}^2<{{\mathrm{\sigma }}^{\mathrm{*}}1\mathrm{s}}^2<{\mathrm{\sigma }2\mathrm{s}}^2<{{\mathrm{\sigma }}^{\mathrm{*}}2\mathrm{s}}^2<{\mathrm{\sigma }2{\mathrm{p}}_{\mathrm{x}}}^2<{\mathrm{\pi }2{\mathrm{p}}_{\mathrm{y}}}^2\cong {\mathrm{\pi }2{\mathrm{p}}_{\mathrm{z}}}^2<{{\mathrm{\pi }}^{\mathrm{*}}2{\mathrm{p}}_{\mathrm{y}}}^1\cong {{\mathrm{\pi }}^{\mathrm{*}}2{\mathrm{p}}_{\mathrm{z}}}^0$
B.O. of ${\mathrm{O}}_2^{+}=\frac{10-5}{2}=2.5$
B.O. $\propto$ Bond energy $\propto \frac{1}{\mathrm{B}\mathrm{o}\mathrm{n}\mathrm{d }\mathrm{}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h}}$