Step 1: Understanding the Question:
We need to identify which amine among the choices undergoes a reaction with chloroform and ethanolic KOH to yield a product with a characteristic foul smell.
Step 2: Detailed Explanation:
The reaction described is the famous Carbylamine reaction (or isocyanide test).
This test is exclusively given by primary ($1^\circ$) aliphatic and aromatic amines.
When a primary amine is heated with chloroform ($CHCl_3$) and an alcoholic solution of potassium hydroxide ($KOH$), it forms an alkyl isocyanide (carbylamine), which possesses an incredibly unpleasant, foul odor.
The general chemical equation is:
$R-NH_2 + CHCl_3 + 3KOH \xrightarrow{\Delta} R-N \equiv C + 3KCl + 3H_2O$
Analyzing the options:
(a) $(CH_3)_3N$ is a tertiary ($3^\circ$) amine.
(b) $(CH_3)_2NH$ is a secondary ($2^\circ$) amine.
(c) $(CH_3CH_2)_2NH$ is a secondary ($2^\circ$) amine.
(d) $CH_3CH_2NH_2$ is a primary ($1^\circ$) amine (ethylamine).
Step 3: Final Answer:
Only the primary amine, $CH_3CH_2NH_2$, will undergo the reaction and produce the foul smell. This makes option (d) correct.