At $T(K)$, $2$ moles of liquid $A$ and $3$ moles of liquid $B$ are mixed. The vapour pressure of the ideal solution formed is $320 \ mm \ Hg$. At this stage, one mole of $A$ and one mole of $B$ are added to the solution. The vapour pressure is now measured as $328.6 \ mm \ Hg$. The vapour pressures of pure $A$ and pure $B$ (in $mm \ Hg$) 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 $x_L=1$

Select the correct statement.

$A$ liquid freezes at $7^{\circ} C$ and boils at $77^{\circ} C$. If $K_{f}$ and $K_{b}$ values for the liquid are $5.6$ and $2.5 \ ^{\circ} C \ kg \ mol^{-1}$ respectively,then the ratio of latent heat of vaporisation of the liquid to the latent heat of fusion is $:-$

Which of the following pairs of solutions is isotonic?
$A$. $18 \ g/L$ of glucose solution and $6 \ g/L$ of urea solution
$B$. $10 \ g/L$ of glucose solution and $10 \ g/L$ of urea solution
$C$. $0.01 \ M \ NaOH$ solution and $0.02 \ M$ glucose solution
$D$. $0.01 \ M \ NaCl$ solution and $0.01 \ M$ glucose solution
(Assume that $NaCl$ undergoes complete dissociation)

When a solute is added to a solvent,the freezing point of the solution decreases to $1.86 \ K$. What is the value of $\Delta T_b$? $[K_f = 1.86, K_b = 0.512]$