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Arrange the following compounds in the decreasing order of their reactivity towards nucleophilic addition reactions:
$(I) \, HCHO \, (II) \, CH_3CHO \, (III) \, CH_3COCH_3$

$A$ and $B$ are isomers; Isomer $B$ is

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What will be the product $S$ in the following reaction?
$CH_3COOH$ $\xrightarrow{SOCl_2} P$ $\xrightarrow[Anhyd. AlCl_3]{Benzene} Q$ $\xrightarrow{HCN} R$ $\xrightarrow{HOH} S$

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$CH_3-C(O)-CH_2-CH_2-CH_2-CH_2-CHO \xrightarrow{HO^{-} / \Delta} (A) (73\%)$
Product $(A)$ is

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Identify $A$ in the following reaction:

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