${\text{Glycerol}}$ $\xrightarrow{KHSO_4} (A)$ $\xrightarrow{LiAlH_4} (B)$; $(A)$ and $(B)$ are respectively:

In the given reaction,$X$ will be:
Cyclohexene $\xrightarrow{NBS}$ $\xrightarrow[ether]{Mg}$ $\xrightarrow[2.H^{+}]{1.CO_2} X$

Which of the following compounds forms $1-$bromo$-1-$methylcyclohexane when treated with $HBr$?

Which of the following is obtained on oxidation of $prop-1-ene$ with acidic $KMnO_4$?

The reaction of $1,3$-butadiene with $1$ equivalent of $HBr$ at different temperatures yields products $A$ and $B$. Identify the relationship between $A$ and $B$. The reaction scheme is as follows:
$CH_2=CH-CH=CH_2 + HBr (1 \text{ eq}) \xrightarrow{25^{\circ}C} A$
$CH_2=CH-CH=CH_2 + HBr (1 \text{ eq}) \xrightarrow{-80^{\circ}C} B$

$(R)-3-$bromocyclopentene (shown below) reacts with $Br_2/CCl_4$ to form two products,$Y$ and $Z$. $Y$ is not optically active (does not rotate plane-polarized light). What is the structure of $Y$?