Oxidation number is the charge left on the central atom when all the bonding pairs of electrons are removed, with the charge devolved to the most electronegative atom
For $Ni(CO)_4$ , we break the $Ni−CO$ bond and we get $Ni^0 +4\times ^-C ≡ O^+$
And thus nickel has a formal oxidation state of ZERO .
A complex in which central atom carries zero oxidation state is $Ni(CO)_4$
Hence (c) is the correct answer.