Which of the following is the correct order of decarboxylation of $\beta$-keto carboxylate anion?

In the following reaction sequence,the major product $P$ is formed. Glycerol reacts completely with excess $P$ in the presence of an acid catalyst to form $Q$. Reaction of $Q$ with excess $NaOH$ followed by the treatment with $CaCl_2$ yields $Ca$-soap $R$,quantitatively. Starting with one mole of $Q$,the amount of $R$ produced in gram is. . . . [Given,atomic weight: $H=1, C=12, N=14, O=16, Na=23, Cl=35, Ca=40$ ]

In the following reaction,$X$ and $Y$ are respectively
$CH_3 COOH + NH_3$ $\longrightarrow X \stackrel{\Delta}{}$ ${\longrightarrow} Y + H_2 O$

Which of the following reactions produce carboxylic acids?
$(a)$ $MnO_2$ with $CH_3COCH_3$
$(b)$ $Ph-CCl_3 \xrightarrow[(ii) H_2O/H^+]{(i) aq. NaOH} PhCOOH$
$(c)$ $C_2H_5Br \xrightarrow[(iii) H_2O/H^+]{(i) Mg, (ii) CO_2} C_2H_5COOH$
$(d)$ $CH_3CH=CHCH_3 \xrightarrow[\Delta]{K_2Cr_2O_7/H_2SO_4} 2CH_3COOH$

The product $(P)$ of the given reaction is:

Which is the major product of the following reaction?