$${\rm I}$$ and $${\rm I}$$$${\rm I}$$$${\rm I}$$ follow $${S_N}1$$ mechanism

$${\rm I}$$ and $${\rm II}$$ follow $${S_N}2$$ mechanism

Compound $${\rm IV}$$ undergoes inversion of configuration

The order of reactivity for $${\rm I},$$ $${\rm I}{\rm I}{\rm I}$$ and $${\rm IV}$$ is : $${\rm I}V > {\rm I} > {\rm I}{\rm I}{\rm I}$$

$$1$$-chloro-$$4$$-methylbenzene

$$4$$-chlorotoluene

$$4$$-methylchlorobenzene

$$1$$-methyl-$$4$$-chlorobenzene

$$O$$ and $$P$$ are identical molecules

($$M$$ and $$O$$) and ($$N$$ and $$P$$) are two pairs of diastereomers

($$M$$ and $$O$$) and ($$N$$ and $$P$$) are two pairs of enantiomers

Bromination proceeds through trans-addition in both the reactions

$$\sigma \to \pi$$ (empty) and $$\sigma \to \pi^*$$ electron delocalisations

$$\sigma \to \sigma^*$$ and $$\sigma \to \pi$$ electron delocalisations

$$\sigma \to p$$ (filled) and $$\sigma \to \pi$$ electron delocalisations

p (filled) $$\to \sigma^*$$ and $$\sigma \to \pi^*$$ electron delocalisations