At $\mathrm{T}(\mathrm{K}), 100 \mathrm{~g}$ of $98 \% \mathrm{H}_2 \mathrm{SO}_4(\mathrm{w} / \mathrm{w})$ aqueous solution is mixed with 100 g of $49 \% \mathrm{H}_2 \mathrm{SO}_4(\mathrm{w} / \mathrm{w})$ aqueous solution. What is the mole fraction of $\mathrm{H}_2 \mathrm{SO}_4$ in the resultant solution?

(Given : Atomic mass $\mathrm{H}=1 \mathrm{u} ; \mathrm{S}=32 \mathrm{u} ; \mathrm{O}=16 \mathrm{u}$ ).

(Assume that temperature after mixing remains constant)

Consider a solution of $\mathrm{CO}_2(\mathrm{~g})$ dissolved in water in a closed container.

Which one of the following plots correctly represents variation of log (partial pressure of $\mathrm{CO}_2$ in vapour phase above water) $[y$-axis $]$ with $\log$ (mole fraction of $\mathrm{CO}_2$ in water) $[x$-axis $]$ at $25^{\circ} \mathrm{C}$ ?

Given below are two statements :

Statement I : The Henry's law constant $\mathrm{K}_{\mathrm{H}}$ is constant with respect to variations in solution's concentration over the range for which the solution is ideally dilute.

Statement II : $\mathrm{K}_{\mathrm{H}}$ does not differ for the same solute in different solvents.

In the light of the above statements, choose the correct answer from the options given below

Elements P and Q form two types of non-volatile, non-ionizable compounds PQ and $\mathrm{PQ}_2$. When 1 g of $P Q$ is dissolved in 50 g of solvent ' $A^{\prime}, \Delta T_b$ was 1.176 K while when 1 g of $P Q_2$ is dissolved in 50 g of solvent ' $\mathrm{A}^{\prime}, \Delta \mathrm{T}_{\mathrm{b}}$ was 0.689 K . ( $\mathrm{K}_{\mathrm{b}}$ of ' $\mathrm{A}^{\prime}=5 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$ ). The molar masses of elements P and Q (in $\mathrm{g} \mathrm{mol}^{-1}$ ) respectively, are :