this reaction will peoceed through SN1 path

first step is protonation(H⁺ from HBr) & formation of O⁺H2 , this group is highly strong leaving group ...

now , carbocation formation takes place & reactivity is governed on the basis of carbocation stablity ...

most stable III , due to presence ofO-CH3 group , this will disperse +ve charge on carbon ...

then I , coz here no electron withdrawing groups ...

then IV , highly unstable due to EW effect of Br ..

then II , highly unstable coz EW (inductive as well as resonance) effect of NO2

option A) is correct

option-A is correct...

bcoz -NO2 group increases the acidity of p-nitrobenzylalcohol more than of p-bromobenzylalcohol by -Br group while -OCH3 group decreases the acidity of p-methoxybenzylalcohol than that of benzylalcohol...

decreasing order of acidity is.......-NO2>-Br>-H>-OCH3

therefore,  decreasing order of reactivity is......-OCH3>-H>-Br>-NO2

So, option A is correct....

approve if u like....