The freezing point of a solution containing $10 \ mL$ of non-volatile and non-electrolyte liquid $A$ in $500 \ g$ of water is $-0.413^{\circ} C$. If $K_f$ of water is $1.86 \ K \ kg \ mol^{-1}$ and the molecular weight of $A = 60 \ g \ mol^{-1}$,what is the density of the solution in $g \ mL^{-1}$? (Assume $\Delta_{\text{mix}} V = 0$)

Given below are two statements $:$
Statement $(I) :$ Molal depression constant $K_{f}$ is given by $\frac{M_1 R T_f^2}{1000 \Delta H_{\text {fus }}}$,where symbols have their usual meaning. (Note: The provided formula in the prompt was corrected to the standard thermodynamic expression $K_f = \frac{M_1 R T_f^2}{\Delta H_{\text {fus }}}$).
Statement $(II) :$ $K_{f}$ for benzene is less than the $K_{f}$ for water.
In the light of the above statements,choose the most appropriate answer from the options given below $:$

$0.05 \ mol$ of a non-volatile solute is dissolved in $500 \ g$ of water. What is the depression in freezing point of the resultant solution (in $K$)? $(K_f(H_2O) = 1.86 \ K \ kg \ mol^{-1})$

Which of the following aqueous solutions has the highest freezing point?

Identify $(i)$,$(ii)$ and $(iii)$ in the following diagram representing the depression in freezing point:

If the freezing point of a $5\% \ w/w$ aqueous solution of sucrose is $271 \ K$ and pure water has a freezing point of $273.15 \ K$,then calculate the freezing point of a $5\% \ w/w$ aqueous solution of glucose. (in $K$)