Increasing order of carbon-oxygen bond length In

$\mathrm{CO},{ \mathrm{CO}}_2$ and ${\mathrm{CO}}_3^{2-}$ is

As we know that the bond order is inversely proportional to the bond length. The bond order of CO is maximum. Hence it will has the lowest bond order.

$\begin{array}{l}\text{ B.O. }\propto \frac{1}{\text{ B.L. }};\end{array}$

The bond order is found as,

$\begin{array}{l}\mathrm{CO}3.0\end{array}$

$\begin{array}{l}{\mathbf{CO}}_{\mathbf{2}}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{2.0}\\ \end{array}$

${\mathbf{CO}}_{\mathbf{3}}^{\mathbf{2}\mathbf{-}}\frac{\mathbf{4}}{\mathbf{3}}$

The correct increasing order of carbon-oxygen bond length is, $\mathrm{CO}<{\mathrm{CO}}_2<{\mathrm{CO}}_3^{2-}$.