To determine the increasing order of basic strength for the given compounds, we need to analyze the effect of substituents on the basicity of the amino group $(NH_2). \newline$The compounds are:$\newline$(I) Aniline $(C_6H_5NH_2) \newline$(II) p-Nitroaniline $(C_6H_4(NO_2)NH_2) \newline$(III) p-Toluidine $(C_6H_4(CH_3)NH_2) \newline$Basicity is influenced by the electron-donating or electron-withdrawing nature of substituents:$\newline$• Electron-donating groups increase basicity by increasing electron density on the nitrogen atom.$\newline$• Electron-withdrawing groups decrease basicity by decreasing electron density on the nitrogen atom.$\newline$Analysis of substituents:$\newline$1. In compound (I), there are no additional substituents, so it serves as a reference.$\newline$2. In compound (II), the nitro group $(NO_2)$ is a strong electron-withdrawing group, reducing the basicity of the amino group.$\newline$3. In compound (III), the methyl group $(CH_3)$ is an electron-donating group, increasing the basicity of the amino group.$\newline$Order of basic strength:$\newline$• Compound (II) has the lowest basicity due to the electron-withdrawing nitro group.$\newline$• Compound (I) has moderate basicity as there are no additional substituents.$\newline$• Compound (III) has the highest basicity due to the electron-donating methyl group.$\newline$Therefore, the correct increasing order of basic strength is:$\newline$Option 3: $II < I < III$