1. Identify the process

   The reaction is: $Cu^{2+}(aq) + S^{2-}(aq) \rightleftharpoons CuS(s)$

   This is a precipitation reaction.

2. Analyze the Assertion (A)

   Assertion says that when $Cu^{2+}$ and $S^{2-}$ ions are mixed, they react extremely quickly to give a solid.

   • Ionic precipitation reactions in aqueous solution are generally very fast.
   • $CuS$ is a highly insoluble salt, so on mixing the ions, precipitate forms almost immediately.

   Therefore, Assertion (A) is true.

3. Analyze the Reason (R)

   Reason says that the equilibrium constant of $Cu^{2+}(aq) + S^{2-}(aq) \rightleftharpoons CuS(s)$ is high because the solubility product is low.

   For the dissolution equilibrium: $CuS(s) \rightleftharpoons Cu^{2+}(aq) + S^{2-}(aq)$ the equilibrium constant is the solubility product: $K_{sp} = [Cu^{2+}][S^{2-}]$

   For the precipitation reaction written in the question, $Cu^{2+}(aq) + S^{2-}(aq) \rightleftharpoons CuS(s)$ the equilibrium constant is: $K = \frac{1}{K_{sp}}$

   Since $CuS$ has a very low $K_{sp}$, its precipitation equilibrium constant $K$ is very high.

   Therefore, Reason (R) is true.

4. Check whether R explains A

   • A very low $K_{sp}$ means the product $CuS$ is highly insoluble.
   • Hence, as soon as $Cu^{2+}$ and $S^{2-}$ meet in solution, the equilibrium strongly favors formation of solid $CuS$.
   • This explains why solid forms essentially immediately on mixing.

   So, (R) is the correct explanation of (A).

5. Evaluate options

   • A: (A) false, (R) true → incorrect
   • B: both true but (R) not explanation → incorrect
   • C: both true and (R) is explanation → correct
   • D: both false → incorrect

Final Answer

$\boxed{C}$