1. Write the given reaction

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

We need to identify which type(s) of reaction it is.

2. Check whether it is a redox reaction

Let us determine oxidation states of the metals.

For gold in $[\mathrm{Au}(\mathrm{CN})_2]^-$

Each $\mathrm{CN}^-$ ligand has charge $-1$.

Let oxidation state of Au be $x$.

$x + 2(-1) = -1$ $x - 2 = -1$ $x = +1$

So, Au is in the $+1$ oxidation state initially.

In the product, gold is:

$\mathrm{Au}(s) = 0$

Thus, Au goes from $+1$ to $0$, so Au is reduced.

For zinc

Initially:

$\mathrm{Zn}(s) = 0$

In $[\mathrm{Zn}(\mathrm{CN})_4]^{2-}$, let oxidation state of Zn be $y$:

$y + 4(-1) = -2$ $y - 4 = -2$ $y = +2$

So, Zn goes from $0$ to $+2$, so Zn is oxidized.

Since oxidation and reduction both occur, this is a redox reaction.

So, A is correct.

3. Check whether it is a displacement reaction

Zinc displaces gold from its complex ion:

• Zn enters the complex form as $[\mathrm{Zn}(\mathrm{CN})_4]^{2-}$
• Au is released as elemental gold

This is essentially a displacement reaction, specifically a metal displacement based on relative reactivity.

So, B is correct.

4. Check whether it is a decomposition reaction

A decomposition reaction involves one compound breaking into simpler substances.

Here, two reactants are involved:

$[\mathrm{Au}(\mathrm{CN})_2]^- \text{ and } \mathrm{Zn}$

So this is not a decomposition reaction.

Thus, C is incorrect.

5. Check whether it is a combination reaction

A combination reaction involves two or more reactants combining to form a single product.

Here, products are:

$2\mathrm{Au}(s) \text{ and } [\mathrm{Zn}(\mathrm{CN})_4]^{2-}$

There is not a single combined product, so this is not a combination reaction.

Thus, D is incorrect.

6. Conclusion

Correct statements are:

• A. Redox reaction ✔️
• B. Displacement reaction ✔️
• C. Decomposition reaction ✖️
• D. Combination reaction ✖️

Hence, the correct option is:

$\boxed{\text{A: A and B only}}$