The total number of carboxylic acid groups in the product $P$ is

What are $\underline{A}, \underline{B}, \underline{C}$ in the following reactions?
$(I)$ $(CH_3 CO_2)_2 Ca \stackrel{\Delta}{\longrightarrow} \underline{A}$
$(II)$ $CH_3 CO_2 H \underset{\text{Red P}}{\stackrel{HI}{\longrightarrow}} \underline{B}$
$(III)$ $2 CH_3 CO_2 H \stackrel{P_4 O_{10}}{\longrightarrow} \underline{C}$
$\underline{A} \quad \underline{B} \quad \underline{C}$

Product $(A)$ of the reaction is:

Give the expected product of the following reaction.

Choose the response that matches the correct functional group classification with the following group of structural formulas.

An organic compound $[A]$,molecular formula $C_{10}H_{20}O_2$,was hydrolyzed with dilute sulphuric acid to give a carboxylic acid $[B]$ and an alcohol $[C]$. Oxidation of $[C]$ with $CrO_3-H_2SO_4$ produced $[B]$. Which of the following structures are not possible for $[A]$?