Step 1: Understanding the Complex.
In the complex \( [Ni(CN)_4]^{2-} \), the oxidation state of Ni is +2. The electronic configuration of Ni is \( [Ar] 3d^8 4s^2 \), and for \( Ni^{2+} \), the configuration becomes \( [Ar] 3d^8 \).
Step 2: Determining the Hybridization.
The cyanide ions (CN\(^-\)) are strong field ligands, leading to low-spin configuration and \( d^{sp^2} \) hybridization.
Step 3: Conclusion.
The correct answer is (B) \( [Ni(CN)_4]^{2- \) has a \( d^{sp^2} \) configuration.}