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A compound A of boron reacts with $NMe{}_{3}$ to give an adduct B, which on hydrolysis gives a compound C and a gas D. Compound C is an acid.
Compound A is:
A.Diborane
B.Boric acid
C.Borate salt
D.None of these

Answer
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Hint: Hydrolysis is the process in which the breakdown of polymers into monomers by using water molecules and an enzymatic catalyst. Hydrolysis reactions break bonds and release energy. For example: salt (Dissolving a salt of a weak acid or base is a good example of hydrolysis reaction).

Complete step by step answer:
First we will discuss about the chemical compounds which is given in the question,
Diborane is the chemical compound consisting of boron and hydrogen with formula $B{}_{2}H{}_{6}$. It is made by the action of acid on some borides. It is a good example of electron deficient bonding.
Boric acid is the chemical compound with formula $H{}_{3}BO{}_{3}$ and is the weakly acidic hydrate of boric oxide. It is also called hydrogen borate.
Borate salt includes sodium metaborate $NaBO{}_{2}$ and an alkaline mineral salt with the power dry white appearance.
Now we will discuss about the chemical reaction that given in the question,
$CompoundA+NMe{}_{3}\to compoundB\to CompoundC+GasD$
Compound (a) Diborane $\left( B{}_{2}H{}_{6} \right)+2NMe{}_{3}\to 2BH{}_{3}.NMe{}_{3}$(compound (B))
The compound B on hydrolysis gives boric acid, $H{}_{3}BO{}_{3}$
$BH{}_{3}.NMe{}_{3}+3H{}_{2}O\to H{}_{3}BO{}_{3}+NMe{}_{3}+3H{}_{2}$
 Compound B → Compound C + Gas D
When the compound A (Diborane) reacts with the $NMe{}_{3}$ as a result compound B is formed and when the compound B under hydrolysis gives boric acid (compound C) and hydrogen gas (compound D) liberated.
So according to this chemical reaction, the correct option is Diborane (A).

Note:
Boric acid is used as the preservative, buffer, anti fungal and antiseptics and is used as manufactured fireproof textile and wood. Diborane is a poisonous and reactive gas. Boric acid is used as a treatment of yeast infection and cold sores.