Select the correct statement.

An aqueous solution of a non-volatile solute boils at $100.15\,^{\circ}C$. If the solution is diluted with an equal volume of water,the freezing point of the resulting solution will be ...... $^{\circ}C$. (Given: $K_b = 0.512\,K\,kg\,mol^{-1}$ and $K_f = 1.86\,K\,kg\,mol^{-1}$ for water)

The number of pairs of solutions having the same value of osmotic pressure from the following is:
(Assume $100\%$ ionization)
$A.$ $0.500 \ M \ C_2H_5OH \ (aq)$ and $0.25 \ M \ KBr \ (aq)$
$B.$ $0.100 \ M \ K_4[Fe(CN)_6] \ (aq)$ and $0.100 \ M \ FeSO_4(NH_4)_2SO_4 \ (aq)$
$C.$ $0.05 \ M \ K_4[Fe(CN)_6] \ (aq)$ and $0.25 \ M \ NaCl \ (aq)$
$D.$ $0.15 \ M \ NaCl \ (aq)$ and $0.1 \ M \ BaCl_2 \ (aq)$
$E.$ $0.02 \ M \ KCl \cdot MgCl_2 \cdot 6H_2O \ (aq)$ and $0.05 \ M \ KCl \ (aq)$

After adding a non-volatile solute, the freezing point of water decreases to $-0.186^{\circ} C$. Calculate $\Delta T_b$ if $K_f = 1.86 \text{ K kg mol}^{-1}$ and $K_b = 0.521 \text{ K kg mol}^{-1}$. (in $\text{ K}$)

Select the correct statement for an ideal solution of a non-volatile solute in a liquid solvent.

$A$ solution at $20\,^oC$ is composed of $1.5\,mol$ of benzene and $3.5\,mol$ of toluene. If the vapour pressure of pure benzene and pure toluene at this temperature are $74.7\,torr$ and $22.3\,torr,$ respectively,then the total vapour pressure of the solution and the benzene mole fraction in equilibrium with it will be,respectively