$${\rm I}$$ 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 : $${\rm I}V > {\rm I} > {\rm I}{\rm I}{\rm I}$$

$$O$$ 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

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

$$4$$-chlorotoluene

$$4$$-methylchlorobenzene

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

tert-butanol and 2-methylpropan-2-ol

tert-butanol and 1, 1-dimethylethan-1-ol

n-butanol and butan-1-ol

iso-butyl alcohol and 2-methylpropan-1-ol