Correct Answer - A
In `[Ni(H_(2)O)_(6)]^(2+)` central metal ion is `Ni^(2+)` has `[Ar]^(18)3d^(8)` configuration, It forms the octahedral complex with `sp^(3)d^(2)`- hybridisation thus having two unpaired electrons. As such, it is paramagnetic. In `[Fe(CN)_(6)]^(4-)` central metal ion `Fe^(2+)` has `[Ar]^(18)3d^(6)` configuration. `CN^(-)` is a strong ligand and pair up these six d-electrons in three d-orbitals . It forms the octahedral complex with `d^(2)sp^(3)`-hybridisation thus have no unpaired electron. As such it is not paramagneic.
For structure of `Ni(CO)_(4) and [Ni(CN)_(4)]^(2-)` , see hint to Q. 26 . They are both diamagnetic.