(a)
$As - CH_{3}$ group has a strong $+ I$ effect and $–OCH_{3}$ group has a weak $–I$ but strong $+ R$ effect, hence they increase the electron density on oxygen atom and $O - H$ bond becomes stronger. On the other hand, $- NO_{2}$ group has a strong $–I$ and $–R$ effect. It withdraws electrons from benzene ring as well as oxygen atom of $–OH$ group and proton is easily removed. Order of esterification is $I > II > III > IV$