To determine the correct order of basic strength of methyl-substituted amines in aqueous solution, we need to consider several factors:$\newline$1. The basicity of amines is influenced by the availability of the lone pair of electrons on the nitrogen atom.$\newline$2. Alkyl groups, such as methyl groups, are electron-releasing and increase the electron density on nitrogen, enhancing basicity.$\newline$3. In aqueous solution, solvation effects also play a significant role. Solvation stabilizes the conjugate acid formed by protonation of the amine.$\newline$Let's analyze the given amines:$\newline$• $CH_3NH_2$ (methylamine): A primary amine with one methyl group.$\newline$• $(CH_3)_2NH$ (dimethylamine): A secondary amine with two methyl groups.$\newline$• $(CH_3)_3N$ (trimethylamine): A tertiary amine with three methyl groups.$\newline$In aqueous solution:$\newline$• Dimethylamine $((CH_3)_2NH)$ is the most basic due to optimal electron donation and solvation.$\newline$• Methylamine $(CH_3NH_2)$ is less basic than dimethylamine but more basic than trimethylamine.$\newline$• Trimethylamine $((CH_3)_3N)$ is the least basic because the bulky methyl groups hinder solvation of the protonated form.$\newline$Thus, the correct order of basic strength in aqueous solution is:$\newline (CH_3)_2NH > CH_3NH_2 > (CH_3)_3N \newline$This corresponds to Option 1.