Distilled water boils at $373.15 \ K$ and freezes at $273.15 \ K$. $A$ solution of glucose in distilled water boils at $373.202 \ K$. What is the freezing point (in $K$) of the same solution? (For water, $K_{b}=0.52 \ K \ kg \ mol^{-1}, \ K_{f}=1.86 \ K \ kg \ mol^{-1}$)

Given: Molar mass of $C$, $H$, $O$, $Cl$ are $12$, $1$, $16$ and $35.5 \text{ g mol}^{-1}$, respectively. Statement $I$: In $30\%$ (w/w) solution of methanol in $CCl_4$ (at $T \text{ K}$), the mole fraction of $CCl_4$ is equal to $0.33$. Statement $II$: Mixture of methanol and $CCl_4$ shows positive deviation from Raoult's law.

Solid Lead nitrate is dissolved in $1 \, L$ of water. The solution was found to boil at $100.15^{\circ}C$. When $0.2 \, mol$ of $NaCl$ is added to the resulting solution,it was observed that the solution froze at $-0.8^{\circ}C$. The solubility product of $PbCl_2$ formed is $........... \times 10^{-6}$ at $298 \, K$. (Nearest integer) Given: $K_b = 0.5 \, K \, kg \, mol^{-1}$ and $K_f = 1.8 \, K \, kg \, mol^{-1}$. Assume molality to be equal to molarity in all cases.

Which of the following mixtures represents Proof Spirit (by volume)?

Assertion : If one component of a solution obeys Raoult's law over a certain range of composition,the other component will not obey Henry's law in that range.
Reason : Raoult's law is a special case of Henry's law.

$A$ concentrated solution of copper sulphate,which is dark blue in colour,is mixed at room temperature with a dilute solution of copper sulphate,which is light blue. For this process: