What are $X$ and $Y$ respectively in the following reaction sequence?
$C_3H_6$ $\xrightarrow[\text{(C}_6\text{H}_5\text{CO)}_2\text{O}_2]{\text{HBr}} X$ $\xrightarrow{\text{Na/ dry ether}} Y$

Which of the following is $NOT$ obtained when a mixture of chloroethane and $1-$chloropropane is treated with sodium metal in dry ether?

The given product cannot be obtained in the above reaction. Identify the correct product obtained.

Match the reactants in Column-$I$ with their products in Column-$II$.

Column-$I$ (Reactants)	Column-$II$ (Products)
$A$. $H_2C=CH_2 + Br_2 \xrightarrow{CCl_4}$	$i$. $CH_3CH_2CH_2Br$
$B$. $CH_3CH=CH_2 + HI \rightarrow$	$ii$. $BrCH_2-CH_2Br$
$C$. $C_6H_5N_2^+X^- + KI \rightarrow$	$iii$. $CH_3CHICH_3$
$D$. $CH_3CH=CH_2 + HBr \xrightarrow{peroxide}$	$iv$. $C_6H_5I$

$(Z)-2$-Butene reacts with $Br_2/H_2O$. The resulting bromohydrin when treated with methoxide in methanol undergoes an intramolecular $S_N2$ reaction. Taking into consideration the stereochemical consequences of the reaction mechanism involved, choose the final product$(s)$ of these transformations.

Given below are two statements:
Statement $I$: $C-Cl$ bond is stronger in $CH_2=CH-Cl$ than $CH_3-CH_2-Cl$.
Statement $II$: The given optically active molecule on hydrolysis gives a solution that can rotate the plane polarized light.
In the light of the above statements, choose the correct answer from the options given below.