The electron releasing groups attached to benzene increases the reactivity towards Friedel-Crafts alkylation whereas the electron withdrawing groups decreases the reactivity.
Among the given groups, −NO2 and COOCH3 are electron withdrawing group EWG, so they will decrease the reactivity where NO2 shows stronger −I effect than COOCH3. So, the reactivity of nitrobenzene towards Friedel-Craft alkylation will be least. OCH3 is an electron donating group, so it will increasing the reactivity.
Thus, the order of reactivity towards Friedel-Craft alkylation is
(iv) > (ii) > (iii) > (i)