Product $B$ may be :

When $2-$Methylbut$-2-$ene is treated with hydrogen chloride,the major product formed is

The reaction of $4$-methyloct$-1-$ene $(P, 2.52 \ g)$ with $HBr$ in the presence of $(C_6H_5CO_2)_2O_2$ gives two isomeric bromides in a $9:1$ ratio,with a combined yield of $50 \%$. Of these,the entire amount of the primary alkyl bromide was reacted with an appropriate amount of diethylamine followed by treatment with aqueous $K_2CO_3$ to give a non-ionic product $S$ in $100 \% $ yield. The mass (in $mg$) of $S$ obtained is. . . . . . . [Use molar mass (in $g \ mol^{-1}$) : $H=1, C=12, N=14, Br=80$]

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

The product $(B)$ is

$A$ reagent used to test for unsaturation of alkene is