These reactions are purely S_N2 reactions as in reaction (i) and (ii) there is no rearrangement takes place (rearrangement occurs in S_N1 mechanism). Simple substitution of nucleophile takes place.

The order of reactivity is dependent on the stability of the intermediate carbocation formed by cleavage of C—X bond. The 3° carbocation formed in III will be more stable than its 2° homologue (IV) which in turn will be more stable than arenium ion (I). Moreover, the aryl halide has a double bond character in the C—X bond which makes the cleavage more difficult. On other hand II will be more reactive than I due to presence of electron withdrawing —NO₂ group. C—X bond becomes weak and undergoes nucleophilic substitution reaction

So Correct order is I < II < IV < III.

S_N1 reactions involve the formation of carbocations, hence higher the stability of intermediate carbocation, more will be reactivity of the parent alkyl halide. The tertiary carbocation formed from (c) is stabilized by two phenyl groups and one methyl group, hence most stable.