Which of the following is likely to undergo racemization during alkaline hydrolysis by $SN^1$ mechanism?

$MMPP \to$ Magnesium monoperoxyphthalate. Product $(X)$ is

The reaction of $4-$bromobenzyl chloride with sodium cyanide in ethanol leads to the formation of

For the following compounds,the correct statement$(s)$ with respect to nucleophilic substitution reactions is(are):
$I$: Benzyl bromide $(C_6H_5CH_2Br)$
$II$: Cyclohexylmethyl bromide $(C_6H_{11}CH_2Br)$
$III$: tert-Butyl bromide $((CH_3)_3CBr)$
$IV$: $1-$Phenylethyl bromide $(C_6H_5CH(CH_3)Br)$
$A$. $I$ and $III$ follow $S_{N}1$ mechanism
$B$. $I$ and $II$ follow $S_{N}2$ mechanism
$C$. Compound $IV$ undergoes inversion of configuration
$D$. The order of reactivity for $I$,$III$ and $IV$ is: $IV > I > III$

$A$ solution of $1$-chloro-$1$-phenylethane in toluene undergoes direct racemization in the presence of a small amount of $SbCl_5$ due to the formation of:

Among the given pairs,in which pair does the first compound react faster than the second compound in an $S_{N}1$ reaction?