The correct statement about the synthesis of erythritol (C(CH_2OH)_4) used in the preparation of PETN is

A hydroxy compound $(\mathrm{X})$ with molar mass $122 \mathrm{~g} \mathrm{~mol}^{-1}$ is acetylated with acetic anhydride, using a large excess of the reagent ensuring complete acetylation of all hydroxyl groups. The product obtained has a molar mass of $290 \mathrm{~g} \mathrm{~mol}^{-1}$. The number of hydroxyl groups present in compound (X) is:

Given below are two statements: Statement I: Benzene is nitrated to give nitrobenzene, which on further treatment with $\mathrm{CH}_{3} \mathrm{COCl} / \mathrm{AlCl}_{3}$ will give  Statement II: $-\mathrm{NO}_{2}$ group is a $m$-directing, and deactivating group. In the light of the above statements, choose the most appropriate answer from the options given below

Given below are two statements: Statement I: $\left(\mathrm{CH}_{3}\right)_{3} \stackrel{\oplus}{\mathrm{C}}$ is more stable than $\stackrel{\oplus}{\mathrm{C}} \mathrm{H}_{3}$ as nine hyperconjugation interactions are possible in $\left(\mathrm{CH}_{3}\right)_{3} \stackrel{\oplus}{\mathrm{C}}$. Statement II: $\stackrel{\oplus}{\mathrm{C}} \mathrm{H}_{3}$ is less stable than $\left(\mathrm{CH}_{3}\right)_{3} \stackrel{\oplus}{\mathrm{C}}$ as only three hyperconjugation interactions are possible in $\stackrel{\oplus}{\mathrm{C}} \mathrm{H}_{3}$. In the light of the above statements, choose the correct answer from the options given below

Sucrose hydrolyses in acidic medium into glucose and fructose by first order rate law with $t_{1/2} = 3$ hour. The percentage of sucrose remaining after $6$ hours is _______. (Nearest integer) (Given: $\log 2 = 0.3010$ and $\log 3 = 0.4771$)

Consider the following reaction sequence  Compound $(\mathrm{y})$ develops characteristic colour with neutral $\mathrm{FeCl}_{3}$ solution. Identify the INCORRECT statement from the following for the above sequence.