$100 \ g$ 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.

$PbCl_2$ is dissolved in water to make its saturated solution. What will be the freezing point of this solution?
Given: $K_f (H_2O) = 2 \ K \ kg \ mol^{-1}$,$K_{sp} (PbCl_2) = 4 \times 10^{-6}$
(Assume molarity to be equal to molality) $..... ^oC$

If the freezing point of an aqueous solution of salt $MX_4$ $(\alpha = 90\%)$ is $-3\ ^oC$,then its boiling point will be ........ $^oC$. (Assume it is $100\%$ ionized at the boiling temperature and $k_f = 1.86\ K\ kg\ mol^{-1}$,$k_b = 0.52\ K\ kg\ mol^{-1}$)

An aqueous solution contains $6\%$ and $4\%$ by weight of a weak acid $(HA)$ and urea respectively. If the depression in freezing point is $\frac{13.6}{3} \, ^{\circ}C$,calculate the $K_a$ of $HA$. [Given: $K_f = 1.8 \, K \, kg/mol$,Molecular weight of $HA = 60$,$d_{solution} = 1 \, g/mL$]

When $1 \ g$ each of compounds $AB$ and $AB_2$ are dissolved in $15 \ g$ of water separately,they increase the boiling point of water by $2.7 \ K$ and $1.5 \ K$ respectively. The atomic mass of $A$ (in $amu$) is $........ \times 10^{-1}$ (Nearest integer). (Given: Molal boiling point elevation constant $K_b = 0.5 \ K \ kg \ mol^{-1}$)

An aqueous solution of a solute $AB$ has a $b.p.$ of $101.08^\circ C$ ($AB$ is $100\%$ ionized at the boiling point of the solution) and freezes at $-1.80^\circ C$. Given $K_b / K_f = 0.3$,the solute $AB$: