If the $K_f$ value of $H_2O$ is $1.86 \ K \ kg \ mol^{-1}$,the value of $\Delta T_f$ for a $0.1 \ m$ solution of a non-volatile solute is:

$A$ camphor sample melts at $176^{\circ} C$. $K_f$ for camphor is $40 \ K \ kg \ mol^{-1}$. $A$ solution of $0.02 \ g$ of a hydrocarbon in $0.8 \ g$ of camphor melts at $156.77^{\circ} C$. The hydrocarbon is made up of $92.3 \%$ of carbon. What is the molecular formula of the hydrocarbon?

The normal freezing point $(f.p.)$ of nitrobenzene is $278.82 \ K$. If a non-volatile solute is dissolved in it and a solution of $0.25 \ molality$ is prepared,the observed freezing point of the solution is $276.82 \ K$. Evaluate the cryoscopic constant $(K_f)$ of nitrobenzene in $K \ kg \ mol^{-1}$.

The solution containing $6 \ g$ urea (molar mass $60$) per $dm^3$ of water and another solution containing $9 \ g$ of solute $A$ per $dm^3$ water freeze at the same temperature. What is the molar mass of $A$?

Two solutions $A$ and $B$ are prepared by dissolving $1 \ g$ of non-volatile solutes $X$ and $Y$ respectively in $1 \ kg$ of water. The ratio of depression in freezing points for $A$ and $B$ is found to be $1: 4$. The ratio of molar masses of $X$ and $Y$ is.

Which of the following will show maximum depression in freezing point when the concentration is $0.1 \ M$?