Which of the following compounds evolves $2 \ mole$ of $CO_2$ on gentle heating?

Arrange the following compounds in the increasing order of their $pK_a$ values:
$I.$ Phenol
$II.$ $p$-Nitrophenol
$III.$ Ethanol
$IV.$ $p$-Nitrobenzoic acid

With reference to the scheme given,which of the given statement$(s)$ about $T$,$U$,$V$ and $W$ is (are) correct?
$A$. $T$ is soluble in hot aqueous $NaOH$
$B$. $U$ is optically active
$C$. Molecular formula of $W$ is $C_{10}H_{18}O_4$
$D$. $V$ gives effervescence on treatment with aqueous $NaHCO_3$

The product $(C)$ of the given reaction sequence is:

$CH_3COOH \xrightarrow{LiAlH_4} A$
$A + CH_3COOH \xrightarrow{H_3O^+} B + H_2O$
In the above reactions,'$A$' and '$B$' respectively are:

Match Column-$I$ with Column-$II$ :
| Column-$I$ | Column-$II$ |
| :--- | :--- |
| $(A)$ Cyclopentanone + $2,4-$$DNP$ $\xrightarrow{\text{mild } H^+}$ Cyclopentanone$-2,4-$$DNP$ derivative | $(P)$ Electrophilic substitution |
| $(B)$ $4-$phenyl$-2-$methylbutan$-2-$ol $\xrightarrow{\text{Conc. } H_2SO_4}$ $1,1-$dimethyl$-1,2,3,4-$tetrahydronaphthalene | $(Q)$ Nucleophilic substitution |
| $(C)$ $4-$chlorocyclohexanethiol $\xrightarrow{\text{Base}}$ $7-$thiabicyclo[$2.2$.$1$]heptane | $(R)$ Nucleophilic addition |