What is the product of the following reaction?

Ester and acetamide are distinguished by

Match the compounds possessing carbonyl carbon in Column-$I$ with their formulas in Column-$II$ and examples in Column-$III$:

Column-$I$ (Name)	Column-$II$ (Formula)	Column-$III$ (Example)
$(A)$ Ketone	$(i)$ $R-CO-OH$	$(p)$ $CH_3CHO$
$(B)$ Carboxylic acid	$(ii)$ $R-CO-H$	$(q)$ $CH_3COOH$
$(C)$ Amide	$(iii)$ $R-CO-R'$	$(r)$ $CH_3CONH_2$
$(D)$ Aldehyde	$(iv)$ $R-CO-NH_2$	$(s)$ $CH_3COC_2H_5$

Product $(X)$ is

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 $NaHCO_3$

Which $\beta$-keto acid shown will not undergo decarboxylation?