$KI$ in acetone undergoes $S_N2$ reaction with each $P, Q, R$ and $S$. The rates of the reaction vary as:
$P: CH_3-Cl$
$Q: (CH_3)_2CH-Cl$
$R: CH_2=CH-CH_2-Cl$
$S: C_6H_5-CO-CH_2-Cl$

Observe the following reactions:
$1$. $C_6H_5-CH=CH_2 + HBr \rightarrow X$
$2$. $C_6H_5-C(CH_3)=CH_2 + HBr \rightarrow Y$
$3$. $C_6H_5-CH=CH_2 + HBr \xrightarrow{(C_6H_5COO)_2} Z$
The correct order of reactivity of $X, Y, Z$ towards $S_N1$ reaction is:

Identify $A$ and $B$ in the following reaction:
$C_2H_5Cl \xrightarrow{A} C_2H_5OH \xleftarrow{B} C_2H_5Cl$

$A$ mixture of $1-$chloropropane and $2-$chloropropane when treated with alcoholic $KOH$ gives:

Given below are two statements: one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$ :
Assertion $(A)$ : $S_N2$ reaction of $C_6H_5CH_2Br$ occurs more readily than the $S_N2$ reaction of $CH_3CH_2Br$.
Reason $(R)$ : The partially bonded unhybridized $p$-orbital that develops in the trigonal bipyramidal transition state is stabilized by conjugation with the phenyl ring.
In the light of the above statements,choose the most appropriate answer from the options given below:

Give the chemical reactions for the following conversions:
$(1)$ Tertiary butyl alcohol from $1-$bromo$-2-$methylpropane
$(2)$ Ethanol from $1,2-$dibromoethane