In Ni(CO)4, Nickel is in 0 oxidation state with configuration [Ar]3d84s2. CO is a strong field ligand, causing pairing of 4s electrons into 3d orbitals, resulting in 3d10 configuration. It is sp3 hybridized and diamagnetic (zero unpaired electrons).
In [Ni(CN)4]2−, Nickel is in +2 oxidation state with configuration [Ar]3d8. CN− is a strong field ligand, causing pairing of the two unpaired electrons in 3d orbitals. It is dsp2 hybridized (square planar) and diamagnetic.
In [NiCl4]2−, Nickel is in +2 oxidation state with configuration [Ar]3d8. Cl− is a weak field ligand and cannot cause pairing of electrons. It has two unpaired electrons in 3d orbitals, making it sp3 hybridized (tetrahedral) and paramagnetic.
Therefore, Ni(CO)4 and [Ni(CN)4]2− are diamagnetic, while [NiCl4]2− is paramagnetic.