$1-Methylcyclohexene$ $\xrightarrow[\text{cold}]{alkaline\,KMnO_4} A$ $\xrightarrow[CH_3COOH]{CrO_3} B$
$A$ and $B$ are

An oxygen-containing organic compound upon oxidation forms a carboxylic acid as the only organic product with its molecular mass higher by $14$ units. The organic compound is

Given below are two statements :
Statement $I$ :
In Lucas test,primary,secondary and tertiary alcohols are distinguished on the basis of their reactivity with conc. $HCl + ZnCl_{2}$,known as Lucas Reagent.
Statement $II$ :
Primary alcohols are most reactive and immediately produce turbidity at room temperature on reaction with Lucas Reagent.
In the light of the above statements,choose the most appropriate answer from the options given below :

Product $(B)$ of the above reaction is

The product formed when glycerol reacts with $PCl_5$ is -

An organic compound $X$ is oxidised by using acidified $K_{2}Cr_{2}O_{7}$. The product obtained reacts with phenyl hydrazine but does not answer the silver mirror test. The possible structure of $X$ is