Step 1: Understanding the oxidation state of Ni.
In \( \text{Ni(CO)}_4 \), carbon monoxide (CO) acts as a neutral ligand, meaning it does not contribute any charge to the nickel ion. The oxidation state of nickel is zero because there are no other charges in the complex.
Step 2: Analysis of options.
(A) 0: Correct — In \( \text{Ni(CO)}_4 \), the oxidation state of Ni is zero because CO is a neutral ligand.
(B) 1: This is incorrect, as Ni in \( \text{Ni(CO)}_4 \) has no charge.
(C) 2: This is incorrect, as Ni does not have a +2 charge in this complex.
(D) 4: This is incorrect; Ni does not have a +4 charge in this complex.
Step 3: Conclusion.
The correct answer is (A) because the oxidation state of Ni in \( \text{Ni(CO)}_4 \) is zero.