If the mole fraction of the solvent in a solution decreases,then:

$100 \ g$ each of two solutions,one containing $20 \%$ by mass of $NaOH$ and the other $40 \%$ by mass of $NaOH$,are mixed. The density of the resulting solution is $1.25 \ g/mL$. Find the new $\% \ w/v$ of $NaOH$ in the final solution.

$A$ solution of urea (molar mass $60 \, g \, mol^{-1}$) boils at $100.18 \, ^oC$ at atmospheric pressure. If $K_f$ and $K_b$ for water are $1.86$ and $0.512 \, K \, kg \, mol^{-1}$ respectively,the above solution will freeze at ........... $^oC$.

An aqueous solution of urea (molar mass $60 \ g \ mol^{-1}$) boils at $100.18 \ ^\circ C$ at $1 \ atm$ pressure. If $K_f$ and $K_b$ for water are $1.86$ and $0.512 \ K \ kg \ mol^{-1}$ respectively,at what temperature will this solution freeze (in $K$)?

$1$ molal $K_{4}[Fe(CN)_{6}]$ solution has a degree of dissociation of $0.4$. Its boiling point is equal to that of another solution which contains $18.1$ weight percent of a non-electrolytic solute $A$. The molar mass of $A$ is $.......\, u$. (Round off to the Nearest Integer). [Density of water $= 1.0\, g\, cm^{-3}$]

On dissolving $0.5 \ g$ of a non-volatile non-ionic solute to $39 \ g$ of benzene,its vapor pressure decreases from $650 \ mm \ Hg$ to $640 \ mm \ Hg$. The depression of freezing point of benzene (in $K$) upon addition of the solute is. . . . .
(Given data : Molar mass and the molal freezing point depression constant of benzene are $78 \ g \ mol^{-1}$ and $5.12 \ K \ kg \ mol^{-1}$,respectively)