Step 1: Concept
Hinsberg's reagent (benzenesulfonyl chloride) reacts differently with $1^{\circ}$, $2^{\circ}$, and $3^{\circ}$ amines.
Step 2: Meaning
Secondary ($2^{\circ}$) amines react to form a sulfonamide that lacks an acidic hydrogen, making it insoluble in alkali (NaOH).
Step 3: Analysis
N-methylethanamine is a secondary amine. Primary amines (like ethanamine) form products soluble in NaOH, while tertiary amines do not react.
Step 4: Conclusion
Hence, the correct answer is N-methylethanamine.
Final Answer: (B)