Step 1: Understanding the Concept:
In the carbylamine reaction, a primary amine heated with chloroform and ethanolic KOH forms an isocyanide (carbylamine), which has a very foul smell.
Step 2: Key Formula or Approach:
\[ \text{R-NH}_2 + \text{CHCl}_3 + 3\text{KOH} \to \text{R-NC} + 3\text{KCl} + 3\text{H}_2\text{O} \]
Only compounds with a free \(-\text{NH}_2\) group take part.
Step 3: Detailed Explanation:
Benzenamine (aniline) is a primary aromatic amine, so it gives phenyl isocyanide.
Propan-2-amine is a primary aliphatic amine, so it gives isopropyl isocyanide.
Phenylmethanamine (benzylamine) is a primary amine, so it gives benzyl isocyanide.
N,N-Dimethylaniline is a tertiary amine with no N-H hydrogen. It cannot form an isocyanide, so there is no foul smell.
Final Answer:
N,N-Dimethylaniline does not give the test, option (B).
\[ \boxed{\text{N,N-Dimethylaniline (B)}} \]