To determine the order of increasing C-O bond lengths for CO, $$CO_3^{2-}$$ and CO₂, it's essential to understand the types of bonding in these molecules and ions.

1. Carbon Monoxide (CO):

Carbon monoxide has a triple bond between carbon and oxygen. Triple bonds are stronger and shorter compared to single and double bonds. Thus, CO has a very short bond length.

2. Carbon Dioxide (CO₂):

In CO₂, carbon is double-bonded to each oxygen atom. Double bonds are longer than triple bonds but shorter than single bonds. Therefore, the C-O bond length in CO₂ is longer than in CO but shorter than in a molecule with single bonds.

3. Carbonate Ion ($$CO_3^{2-}$$):

In the carbonate ion, the bond order for each C-O bond is 1.33. This is because the carbonate ion has a resonance structure where one carbon-oxygen bond is a double bond and the others are single bonds. Due to the resonance, the effective bond order between carbon and oxygen is between a single and a double bond, making its bond length longer than that in CO₂ and shorter than a pure single bond.

Therefore, the increasing order of C-O bond length is:

CO < CO₂ < $$CO_3^{2-}$$

The correct option is:

Option D

CO < CO₂ < $$CO_3^{2-}$$