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Q. $\left(\text{CH}\right)_{3} \text{COOH} \overset{\left(\text{Br}\right)_{2} / \text{P}}{ \rightarrow } (Y) \rightarrow _{\left(\text{(ii) H}\right)_{3} \left(\text{O}\right)^{+}}^{\text{(i) KCN}} \text{(X)}$
Here (X) is:

NTA AbhyasNTA Abhyas 2020

Solution:

Acetic acid in the presence of bromine and red phosphorus undergo Hell-Volhard-zelinsky reaction. It is an alpha substituting of halogen reaction. The halo product undergo substitution reaction with KCN which undergo hydrolysis gives malonic acid.
$\overset{\text{α}}{\left(\text{CH}\right)_{3}}\text{COOH} & \rightarrow _{\left(\text{Br}\right)_{2} / \text{P}}^{\text{H.V.Z}} & \left(\text{BrCH}\right)_{2}\text{COOH} & \rightarrow _{\left(\text{H}\right)_{3} \left(\text{O}\right)^{\oplus}}^{\text{KCN}} & \text{HOOC}-\left(\text{CH}\right)_{2}-\text{COOH} \\ & & \left(\text{Y}\right) & & \left(\text{X}\right)Malonic acid$