Identify the compound $A$ in the following reaction: $A + CH_3MgBr$ $\xrightarrow{\text{dry ether}} \text{intermediate}$ $\xrightarrow{H_3O^+} CH_3CH_2OH + Mg(Br)(OH)$

The addition reaction of $HCN$ to carbonyl compounds is an example of which of the following?

Predict the products of the following reactions:
$(i)$ Cyclopentanone + $NH_2OH \xrightarrow{H^+} ?$
(ii) Cyclohexanone + $2,4-DNP \xrightarrow{H^+} ?$
(iii) $R-CH=CH-CHO + NH_2CONHNH_2 \xrightarrow{H^+} ?$
(iv) Acetophenone + $CH_3CH_2NH_2 \xrightarrow{H^+} ?$

The major product of the following reaction is:

Clemmensen reduction of a ketone is carried out in the presence of

Compound $(A)$ with molecular formula $C_6H_{12}O_3$ gives a positive iodoform test and a negative Tollens' test. Upon hydrolysis with a drop of $H_2SO_4$,it gives a product that shows a positive Tollens' test. Compound $(A)$ is: