Which is the major product of the following reaction?

The products obtained in the given reactions are shown below. The number of possible products for $x$ and $y$ are:

Which of the following reactions produce carboxylic acids?
$(a)$ $MnO_2$ with $CH_3COCH_3$
$(b)$ $Ph-CCl_3 \xrightarrow[(ii) H_2O/H^+]{(i) aq. NaOH} PhCOOH$
$(c)$ $C_2H_5Br \xrightarrow[(iii) H_2O/H^+]{(i) Mg, (ii) CO_2} C_2H_5COOH$
$(d)$ $CH_3CH=CHCH_3 \xrightarrow[\Delta]{K_2Cr_2O_7/H_2SO_4} 2CH_3COOH$

Acid hydrolysis of $X$ yields two different organic compounds. Which one of the following is $X$?

Ethanoic acid $+$ $3$-methylbutan-$1$-ol $\underset{\text{traces } H_2SO_4}{\longleftrightarrow} (A)$; Compound $(A)$ is

When compound $X$ is oxidised by acidified potassium dichromate,compound $Y$ is formed. Compound $Y$ on reduction with $LiAlH_4$ gives $X$. $X$ and $Y$ respectively are: