The elevation in the boiling point of an aqueous urea solution is $0.104 \ K$. What is its $\Delta T_{f}$ (in $K$) value? (Given for water: $K_{b} = 0.52 \ K \ kg \ mol^{-1}$,$K_{f} = 1.86 \ K \ kg \ mol^{-1}$)

The specific heat of a certain substance is $0.86 \,J \,g^{-1} \,K^{-1}$. Assuming ideal solution behaviour,the energy required (in $J$) to heat $10 \,g$ of $1 \,molal$ of its aqueous solution from $300 \,K$ to $310 \,K$ is closest to $.... \,J$
[Given: Molar mass of the substance $= 58 \,g \,mol^{-1}$; specific heat of water $= 4.2 \,J \,g^{-1} \,K^{-1}$]

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 $K$)?

$A$ solution has a $1:4$ mole ratio of pentane to hexane. The vapour pressure of the pure hydrocarbons at $20 \ ^oC$ are $440 \ mm \ Hg$ for pentane and $120 \ mm \ Hg$ for hexane. The mole fraction of pentane in the vapour phase would be

At $35^{\circ} C$,the vapour pressure of $CS_{2}$ is $512 \; mm \; Hg$ and that of acetone is $344 \; mm \; Hg$. $A$ solution of $CS_{2}$ in acetone has a total vapour pressure of $600 \; mm \; Hg$. The false statement amongst the following is

$1.22 \, g$ of an organic acid is separately dissolved in $100 \, g$ of benzene $(K_{b}=2.6 \, K \, kg \, mol^{-1})$ and $100 \, g$ of acetone $(K_{b}=1.7 \, K \, kg \, mol^{-1})$. The acid is known to dimerize in benzene but remain as a monomer in acetone. The boiling point of the solution in acetone increases by $0.17^{\circ} C$.
The increase in boiling point of solution in benzene in $^{\circ} C$ is $x \times 10^{-2}$. The value of $x$ is ..... .(Nearest integer)
$[$ Atomic mass : $C=12.0, H=1.0, O=16.0]$