$1 \, \text{mole}$ of each of $A$ and $B$ form an ideal solution of vapour pressure $100 \, \text{mm Hg}$. Addition of $2 \, \text{moles}$ of $B$ to it decreases the vapour pressure by $20 \, \text{mm Hg}$. The vapour pressure of $A$ and $B$ in pure state are,respectively:

For a solution formed by mixing liquids $L$ and $M$,the vapour pressure of $L$ plotted against the mole fraction of $M$ in solution is shown in the following figure. Here $x_L$ and $x_M$ represent mole fractions of $L$ and $M$,respectively,in the solution. The correct statement$(s)$ applicable to this system is(are)
$A$. Attractive intermolecular interactions between $L-L$ in pure liquid $L$ and $M-M$ in pure liquid $M$ are stronger than those between $L-M$ when mixed in solution
$B$. The point $Z$ represents vapour pressure of pure liquid $M$ and Raoult's law is obeyed when $x_L \rightarrow 0$
$C$. The point $Z$ represents vapour pressure of pure liquid $L$ and Raoult's law is obeyed when $x_L \rightarrow 1$
$D$. The point $Z$ represents vapour pressure of pure liquid $M$ and Raoult's law is obeyed from $x_L=0$ to $x_L=1$

In the depression of freezing point experiment:
$A.$ Vapour pressure of the solution is less than that of pure solvent
$B.$ Vapour pressure of the solution is more than that of pure solvent
$C.$ Only solute molecules solidify at the freezing point
$D.$ Only solvent molecules solidify at the freezing point

Evaluate the following statements for their correctness.
$(A)$ The elevation in boiling point temperature of water will be same for $0.1 \ M \ NaCl$ and $0.1 \ M$ urea.
$(B)$ Azeotropic mixtures boil without change in their composition.
$(C)$ Osmosis always takes place from hypertonic to hypotonic solution.
$(D)$ The density of $32 \% \ H_2SO_4$ solution having molarity $4.09 \ M$ is approximately $1.26 \ g \ mL^{-1}$.
$(E)$ $A$ negatively charged sol is obtained when $KI$ solution is added to silver nitrate solution.
Choose the correct answer from the options given below:

$A$ saturated solution of $Ag_2SO_4$ shows a $0.003 \ K$ rise in boiling point. Calculate the $K_{sp}$ of $Ag_2SO_4$. Given: $K_b = 5 \ K \ kg \ mol^{-1}$ and $1 \ m = 1 \ M$.

Which one of the following statements is $FALSE$?