The complex cation which has two isomers is:

We need to identify which complex cation has two isomers.

Option (1): $$[Co(H_2O)_6]^{3+}$$

This complex has six identical monodentate ligands (water). In an octahedral complex with all identical ligands, there is no possibility of geometrical (cis-trans) isomerism or any other structural isomerism. No isomers.

Option (2): $$[Co(NH_3)_5Cl]^{2+}$$

This octahedral complex has five $$NH_3$$ and one $$Cl^-$$. With only one different ligand, there is only one possible arrangement (the $$Cl$$ can be at any vertex, and all positions are equivalent in an octahedral geometry). No isomers.

Option (3): $$[Co(NH_3)_5NO_2]^{2+}$$

This complex contains the ambidentate ligand $$NO_2^-$$. An ambidentate ligand can bind to the metal through different donor atoms. The nitrite ion ($$NO_2^-$$) can coordinate through:

- The nitrogen atom: giving the nitro isomer $$[Co(NH_3)_5(NO_2)]^{2+}$$ (N-bonded)

- The oxygen atom: giving the nitrito isomer $$[Co(NH_3)_5(ONO)]^{2+}$$ (O-bonded)

This is called linkage isomerism. So this complex has two isomers.

Option (4): $$[Co(NH_3)_5Cl]^{+}$$

Same situation as Option (2) - $$Cl^-$$ is not ambidentate and there is only one possible arrangement. No isomers.

The correct answer is Option (3): $$[Co(NH_3)_5NO_2]^{2+}$$.