The correct option is
C (ii)<(iii)<(i)The reaction is a nucleophilic substitution reaction. The reaction site i.e. CH2 is highly hindered thus will follow SN1 mechanism. In SN1 mechanism, the reaction involves the first slow step of carbocation formation followed by an attack of the incoming nucleophile (Br^-/Cl^-$).
1. R−OH+HX→R−+OH2+X−→R++H2O+X−: slow step
2. R++X−→R−X: fast
since slow step controls the reactivity, therefore stability and ease of formation of the carbocation will decide the reactivity of the molecule.
In case p−NO2 group it is strongly electron-withdrawing group by -Inductive and -Mesomeric effect and thus will destabilize the carbocation and will therefore not favour the reaction.
In case p−Cl group it is strongly electron-withdrawing group by -Inductive and also shows +Mesomeric effect due to the presence of its lone pair of electrons. As a result, the electron-withdrawing tendency is relatively lower than NO2 group by is still decreases the electron density in the ring. Thus will destabilize the carbocation and will therefore not favour the reaction.
In case of no such destabilizing factor C6H5CH2OH will undergo substitution with relative ease.
order of reactivity will be: p−(NO2)C6H4CH2OH<p−(Cl)C6H4CH2OH<C6H5CH2OH
Therefore the correct increasing order of reactivity of the given compounds with HBr/HCl is (ii)<(iii)<(i)