Which of the following options are correct for the reaction?
$$2Au(CN)_2 ^-(aq) + Zn(s) \rightarrow 2Au(s) + Zn(CN)_4 ^{2-}(aq)$$
A. Redox reaction
B. Displacement reaction
C. Decomposition reaction
D. Combination reaction

We have the reaction:

$$2Au(CN)_2^-(aq) + Zn(s) \rightarrow 2Au(s) + Zn(CN)_4^{2-}(aq)$$

In $$Au(CN)_2^-$$, Au is in the +1 oxidation state, while in the product Au(s), Au is in the 0 oxidation state — so Au is reduced. Meanwhile, Zn goes from 0 (in Zn) to +2 (in $$Zn(CN)_4^{2-}$$), so Zn is oxidized. Since both oxidation and reduction occur, this is a redox reaction.

Now, Zn (a more reactive metal) displaces Au (a less reactive metal) from its complex ion, so this is also a displacement reaction.

This is not a decomposition reaction because no compound is breaking down into simpler substances on its own. It is also not a combination reaction because no two substances are combining to form a single product.

Hence, the correct answer is Option A and B only.