Concept:
The reaction of an amine with chloroform ($CHCl_3$) and alcoholic KOH producing a foul-smelling isocyanide is called the Carbylamine reaction.
General reaction:
\[
RNH_2 + CHCl_3 + 3KOH \rightarrow RNC + 3KCl + 3H_2O
\]
This test is given only by:
\[
\text{Primary amines } (1^\circ)
\]
Secondary and tertiary amines do not give this reaction.
Step 1: Check Option A: Ethanamine
\[
CH_3CH_2NH_2
\]
Nitrogen is attached to one alkyl group and two hydrogens.
\[
\Rightarrow \text{Primary amine}
\]
Hence gives carbylamine test.
Step 2: Check Option B: Ethylmethylamine
\[
CH_3CH_2NHCH_3
\]
Nitrogen attached to two alkyl groups.
\[
\Rightarrow \text{Secondary amine}
\]
Does not give test.
Step 3: Check Option C: Ethyldimethylamine
\[
CH_3CH_2N(CH_3)_2
\]
Nitrogen attached to three alkyl groups.
\[
\Rightarrow \text{Tertiary amine}
\]
Does not give test.
Step 4: Check Option D: Diethylmethylamine
\[
(CH_3CH_2)_2NCH_3
\]
Nitrogen attached to three alkyl groups.
\[
\Rightarrow \text{Tertiary amine}
\]
Does not give test.
Step 5: Final Answer
The compound which gives foul smell with $CHCl_3$ and KOH is:
\[
\boxed{\text{Ethanamine } (CH_3CH_2NH_2)}
\]
Quick Tip:
Carbylamine test is used to identify only primary amines.