Decreasing order towards S _ N 1 reaction for the following...

The relative reactivity of alkyl halides in the S_N1 reaction depends on the stability of carbocation. Electron-withdrawing groups decrease the stability and electron-releasing groups increase the stability of carbocations. $- {NO}_{2}$ group is an electron-withdrawing group by $- M$ effect. $- OMe$ is electron-releasing groups by $+ M$ effect. Hence, the overall order is

$∴$ Reactivity order (b) > (d) > (c) > (a)