Consider the following statement.
I. When ${\mathrm{O}}_2$ is converted into ${\mathrm{O}}_2^{2+}$ bond order decreases.
II. ${\mathrm{O}}_2$ molecule is paramagnetic because it contains two unpaired electrons in ${\mathrm{\pi }}^{*}2{\mathrm{p}}_{\mathrm{x}}$ and ${\mathrm{\pi }}^{*}2{\mathrm{p}}_{\mathrm{y}}$ molecular orbitals.
III. The bond length in NO is greater than ${\mathrm{NO}}^{+}$.
Choose the correct option.

Statement II and III are correct.

The molecular orbital configuration of ${\text{O}}_{\text{2}}$  molecule is as follows:
$\mathrm{ }\mathrm{\sigma }\mathrm{ 1}{\mathrm{s}}^{\mathrm{2}}\mathrm{,}{\mathrm{ }\mathrm{\sigma }\mathrm{ }}^{\mathrm{*}}\mathrm{1}{\mathrm{s}}^{\mathrm{2}}\mathrm{, }\mathrm{\sigma }\mathrm{ 2}{\mathrm{s}}^{\mathrm{2}}\mathrm{, }{\mathrm{ }\mathrm{\sigma }\mathrm{ }}^{\mathrm{*}}\mathrm{2}{\mathrm{s}}^{\mathrm{2}}\mathrm{, }\mathrm{\sigma }\mathrm{ 2}{{\mathrm{p}}^{\mathrm{2}}}_{\mathrm{z}},\mathrm{\pi }2{\mathrm{p}}_{\mathrm{x}}^{\mathrm{2}}\mathrm{ }=\mathrm{\pi }2{\mathrm{p}}_{\mathrm{y}}^{\mathrm{2}}\mathrm{ } ,{\mathrm{\pi }}^{*}2{\mathrm{p}}_{\mathrm{x}}^1={\mathrm{\pi }}^{*}2{\mathrm{p}}_{\mathrm{y}}^1$
There are 10 bonding and 6 nonbonding electrons in the orbitals according to the molecular orbital configuration.

Therefore,  $\text{Bond order =}{\displaystyle \frac{\text{1}}{\text{2}}}\left[\text{Bonding-antibonding}\right]$
= $\frac{1}{2}\left[10-6\right]={\displaystyle \frac{1}{2}}\left(4\right)=2$
Thus, the bond order ${\text{O}}_{\text{2}}$ is 2.

 The molecular orbital configuration of ${\mathrm{O}}_2^{+2}$ is 
$\mathrm{\sigma }1{\mathrm{s}}^2,{\mathrm{\sigma }}^{*}1{\mathrm{s}}^2,\mathrm{\sigma }2{\mathrm{s}}^2,{\mathrm{\sigma }}^{*}2{\mathrm{s}}^2,\mathrm{\sigma }2{\mathrm{p}}_{\mathrm{z}}^2,\mathrm{\pi }2{\mathrm{p}}_{\mathrm{x}}^2=\mathrm{\pi }2{\mathrm{p}}_{\mathrm{y}}^2$
There are 10 bonding  and 4 nonbonding electrons in the orbitals according to the molecular orbital configuration.
Therefore, $\text{Bond order =}{\displaystyle \frac{\text{1}}{\text{2}}}\left[\text{Bonding-antibonding}\right]$
$=\frac{1}{2}[10-4]=3$.

Hence statement I is incorrect.