Product $A$ is

In the given reaction,$[X]$ will be:

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.

Provide the chemical reactions for the following conversions:
$1$. $2$-bromopropane and $1$-bromopropane from propene.
$2$. $2$-bromopropane from $1$-bromopropane.

Ethylene dichloride and ethylidene chloride are isomeric compounds. The false statement about these isomers is that they

Consider the following statements:
$(1)$ Bridgehead halides are inert towards both $S_{N^1}$ and $S_{N^2}$ reactions (until one of the ring size is an eight-membered ring).
$(2)$ The first step in both $S_{N^1}$ and $E_1$ reactions is the same.
$(3)$ $S_{N^2}$ reactions proceed with total retention of configuration.
$(4)$ $E_2$ eliminations are favored by the use of a solvent of low polarity and a high concentration of a strong base.
Which of the above statements are correct?