The correct order of $\text{C-O}$ bond length among $\text{CO}$, ${\text{CO}}_3^{2-}$, ${\text{CO}}_2$ is:

Bond length is inversely proportional to bond order.$\text{CO}$: Triple bond, Bond Order $=3$.${\text{CO}}_2$: Double bond, Bond Order $=2$.${\text{CO}}_3^{2-}$: Resonance hybrid, Bond Order $=\frac{\text{Total bonds}}{\text{Resonating structures}}=\frac{4}{3}=1.33$.Increasing order of Bond Order: ${\text{CO}}_3^{2-}(1.33)<{\text{CO}}_2(2)<\text{CO}(3)$.Decreasing order of Bond Length: ${\text{CO}}_3^{2-}>{\text{CO}}_2>\text{CO}$.Order: $\text{CO}<{\text{CO}}_2<{\text{CO}}_3^{2-}$.