Step 1: Factors affecting Basicity
In aqueous solution, the basicity of methyl-substituted amines is governed by three factors: Inductive effect ($+I$), Solvation effect (Hydrogen bonding), and Steric hindrance.
Step 2: Trends
- $+I$ effect: $3^\circ>2^\circ>1^\circ$
- Solvation/Steric: $1^\circ>2^\circ>3^\circ$
Step 3: Combined Effect for Methyl Amines
The experimental order for methyl-substituted amines in water is: Secondary ($2^\circ$)>Primary ($1^\circ$)>Tertiary ($3^\circ$).
Step 4: Conclusion
The order is $(CH_3)_2NH>CH_3NH_2>(CH_3)_3N$.
Final Answer:(B)