What is the number of unpaired electron(s) in the highest occupied molecular orbital of the following…

The orbital in which last electron is present is called the highest occupied molecular orbital(HOMO).

${\mathrm{N}}_2$ : $\mathrm{\sigma }1{\mathrm{s}}^2{\mathrm{\sigma }}^{*}1{\mathrm{s}}^2\mathrm{\sigma }2{\mathrm{s}}^2{\mathrm{\sigma }}^{*}2{\mathrm{s}}^2\mathrm{\pi }2{\mathrm{p}}_{\mathrm{x}}^2=\mathrm{\pi }2{\mathrm{p}}_{\mathrm{y}}^2\frac{\mathrm{\sigma }2{\mathrm{p}}_{\mathrm{z}}^2}{\mathrm{HOMO}}$

${\mathrm{N}}_2^{+}: \mathrm{\sigma }1{\mathrm{s}}^2{\mathrm{\sigma }}^{*}1{\mathrm{s}}^2{\mathrm{\sigma }}^{*}2{\mathrm{s}}^2{\mathrm{\sigma }}^{*}2{\mathrm{s}}^2\mathrm{\pi }2{\mathrm{p}}_{\mathrm{x}}^2=\mathrm{\pi }2{\mathrm{p}}_{\mathrm{y}}^2\frac{\mathrm{\sigma }2{\mathrm{p}}_{\mathrm{z}}^1}{\mathrm{HOMO}}$

${\mathrm{O}}_2: \mathrm{\sigma }1{\mathrm{s}}^2{\mathrm{\sigma }}^{*}1{\mathrm{s}}^2{\mathrm{\sigma }}^{*}2{\mathrm{s}}^2\mathrm{\sigma }2{\mathrm{p}}_{\mathrm{z}}^2\mathrm{\pi }2{\mathrm{p}}_{\mathrm{x}}^1={\mathrm{\pi }}^{*}2{\mathrm{p}}_{\mathrm{y}}^1\left(\mathrm{HOMO}\right)$

${\mathrm{O}}_2^{+}: \mathrm{\sigma }1{\mathrm{s}}^2{\mathrm{\sigma }}^{*}1{\mathrm{s}}^2\mathrm{\sigma }2{\mathrm{s}}^2{\mathrm{\sigma }}^{*}2{\mathrm{s}}^2\mathrm{\sigma }2{\mathrm{p}}_{\mathrm{z}}^2\mathrm{\pi }2{\mathrm{p}}_{\mathrm{x}}^2=\mathrm{\pi }2{\mathrm{p}}_{\mathrm{y}}^2 {\mathrm{\pi }}^{*}2{\mathrm{p}}_{\mathrm{x}}^1={\mathrm{\pi }}^{*}2{\mathrm{p}}_{\mathrm{y}}^0\left(\mathrm{HOMO}\right)$

${\mathrm{N}}_2\Rightarrow 0$ unpaired ${\mathrm{e}}^{–}$ in $\mathrm{HOMO}$

${\mathrm{N}}_2^{+}\Rightarrow 1$ unpaired ${\mathrm{e}}^{-}$ in $\mathrm{HOMO}$

${\mathrm{O}}_2\Rightarrow 2$ unpaired ${\mathrm{e}}^{-}$ in $\mathrm{HOMO}$

${\mathrm{O}}_2^{+}\Rightarrow 1$ unpaired ${\mathrm{e}}^{-}$ in $\mathrm{HOMO}$