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Compare the two methods shown for the preparation of carboxylic acids.
Method $1$: $RBr$ $\xrightarrow[diethyl \ ether]{Mg} RMgBr$ $\xrightarrow[2. \ H_3O^{+}]{1. \ CO_2} RCO_2H$
Method $2$: $RBr$ $\xrightarrow{NaCN} RCN$ $\xrightarrow[heat]{H_2O, HCl} RCO_2H$
Which one of the following statements correctly describes this conversion for the given substrate ($1$-bromoadamantane)?

In this reaction,product $X$ is
$CH_3-CH_2-Br$ $\xrightarrow{alc. KCN} CH_3CH_2CN$ $\xrightarrow{HOH} X$

Considering the above chemical reaction,identify the product $X$.

What is $A$ in the following reaction?
$Cyclopropyl bromide \xrightarrow[(ii) CO_2, (iii) H_3O^+]{(i) Mg, Et_2O} A$

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Identify the product obtained when isopropyl magnesium chloride in dry ether reacts with dry ice $(CO_2)$ forming a complex, which is further hydrolysed.

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