Arrange the following compounds in increasing order of `S_(N^(1))` reactivity.
(a). (I). `ClCH_(2)CH=CHCH_(2)CH_(3)`, (II). `CH_(3)C(Cl)=CHCH_(2)CH_(3)`, (III). `CH_(3)CH=CHCH_(2)CH_(2)Cl`
(b). (I). `CH_(3)CH_(2)Br`, (II). `CH_(2)=CHCH(Br)CH_(3)`, (III). `CH_(2)=CHBr,`
(IV). `CH_(3)CH(Br)CH_(3)`
(c). (I). `(CH_(3))_(3)CBr`, (II). `(CH_(3))_(2)CHBr`, (III). `CH_(3)CH_(2)CH_(2)Br`,

Explanation

The order of reactivyt of alkyl halies towards `S_(N^(1))` reactions is:
Allylic gt Tertiary gt Secondary gt primary gt Vinylic
Based on this, the increasing order of reactivity in different alkyl halides listed above is:
(a) (II) `lt(III)lt(I)`
(b). `(III)lt(I)lt(IV)lt(II)`
(c). `(III) lt (II) lt (I)`.