Step 1: Classification of Amines
- Primary ($1^\circ$): $-NH_2$
- Secondary ($2^\circ$): $-NH-$
- Tertiary ($3^\circ$): $-N<$
Step 2: Structure Analysis
- (A) Phenylmethanamine: $C_6H_5CH_2NH_2$ ($1^\circ$)
- (B) N-Methylethanamine: $CH_3-NH-C_2H_5$ ($2^\circ$)
- (C) N,N-Dimethylethanamine: $(CH_3)_2N-C_2H_5$ ($3^\circ$)
- (D) Prop-2-en-1-amine: $CH_2=CHCH_2NH_2$ ($1^\circ$)
Step 3: Conclusion
N-Methylethanamine is a secondary amine.
Final Answer:(B)