Consider the following reactions :

$$ \begin{aligned} & \mathrm{NaCl}+\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7+\mathrm{H}_2 \mathrm{SO}_4 \rightarrow \mathrm{~A}+\mathrm{KHSO}_4+\mathrm{NaHSO}_4+\mathrm{H}_2 \mathrm{O} \\ & \mathrm{~A}+\mathrm{NaOH} \rightarrow \mathrm{~B}+\mathrm{NaCl}+\mathrm{H}_2 \mathrm{O} \\ & \mathrm{~B}+\mathrm{H}_2 \mathrm{SO}_4+\mathrm{H}_2 \mathrm{O}_2 \rightarrow \mathrm{C}+\mathrm{Na}_2 \mathrm{SO}_4+\mathrm{H}_2 \mathrm{O} \end{aligned} $$

In the product ' $C^{\prime}$, ' $X$ ' is the number of $O_2^{2-}$ units, ' $Y$ ' is the total number oxygen atoms present and ' $Z$ ' is the oxidation state of $C r$. The value of $X+Y+Z$ is $\_\_\_\_$ .

The pH and conductance of a weak acid $(\mathrm{HX})$ was found to be 5 and $4 \times 10^{-5} \mathrm{~S}$, respectively. The conductance was measured under standard condition using a cell where the electrode plates having a surface area of $1 \mathrm{~cm}^2$ were at a distance of 15 cm apart. The value of the limiting molar conductivity is $\_\_\_\_$ $\mathrm{S} \mathrm{m}^2 \mathrm{~mol}^{-1}$. (nearest integer)

(Given : degree of dissociation of the weak acid $(\alpha) \ll 1$ )

Consider the following reaction sequence

The percentage of nitrogen in product ' T ' formed is $\_\_\_\_$ %. (Nearest integer)

(Given molar mass in $\mathrm{g} \mathrm{mol}^{-1} \mathrm{H}: 1, \mathrm{C}: 12, \mathrm{~N}: 14, \mathrm{O}: 16$ )

Let the mean and variance of 7 observations $2,4,10, x, 12,14, y, x>y$, be 8 and 16 respectively. Two numbers are chosen from $\{1,2,3, x-4, y, 5\}$ one after another without replacement, then the probability, that the smaller number among the two chosen numbers is less than 4 , is :