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 $K_b = 0.5 \ K \ kg \ mol^{-1}$)

If a $1 \ m$ solution of benzoic acid in benzene has a freezing point depression of $2.56 \ ^{\circ}C$ $(K_f = 5.12 \ ^{\circ}C \ kg \ mol^{-1})$ and a boiling point elevation of $2.53 \ ^{\circ}C$ $(K_b = 2.53 \ ^{\circ}C \ kg \ mol^{-1})$,select the correct statement$(s)$:
Statement $I$: There is dimer formation when undergoing freezing.
Statement $II$: There is no change when undergoing boiling.
Statement $III$: Reverse of $I$ and $II$.
Statement $IV$: Dimer formation in freezing and boiling state.

Distilled water boils at $373.15 \ K$ and freezes at $273.15 \ K$. $A$ solution of glucose in distilled water boils at $373.202 \ K$. What is the freezing point (in $K$) of the same solution? (For water, $K_{b}=0.52 \ K \ kg \ mol^{-1}, \ K_{f}=1.86 \ K \ kg \ mol^{-1}$)

Identify the correct statement from the following properties.

After adding a solute,the freezing point of the solution decreases to $-0.186 \ ^{\circ}C$. Calculate $\Delta T_b$ if $K_f = 1.86 \ K \ kg \ mol^{-1}$ and $K_b = 0.521 \ K \ kg \ mol^{-1}$. (Assume the freezing point of pure solvent is $0 \ ^{\circ}C$)

An aqueous solution freezes at $-0.186\,^\circ C$ ($K_f = 1.86\, K\, kg\, mol^{-1}$; $K_b = 0.512\, K\, kg\, mol^{-1}$). What is the elevation in boiling point?