In a mixture of camphor in nitrogen gas,the physical states of the solute and the solvent are,respectively:

After adding a non-volatile solute, the freezing point of water decreases to $-0.186^{\circ} C$. Calculate $\Delta T_b$ if $K_f = 1.86 \text{ K kg mol}^{-1}$ and $K_b = 0.521 \text{ K kg mol}^{-1}$. (in $\text{ K}$)

$20\%$ of acetic acid is dissociated when its $5\ g$ is added to $500\ mL$ of water. The depression in freezing point of such water is $..... \times 10^{-3} \ { }^{\circ}C$. Atomic mass of $C$,$H$,and $O$ are $12$,$1$,and $16 \ \text{a.m.u.}$ respectively.
[Given: Molal depression constant and density of water are $1.86 \ K \ kg \ mol^{-1}$ and $1 \ g \ cm^{-3}$ respectively.]

Which of the following pairs of solutions is isotonic?
$A$. $18 \ g/L$ of glucose solution and $6 \ g/L$ of urea solution
$B$. $10 \ g/L$ of glucose solution and $10 \ g/L$ of urea solution
$C$. $0.01 \ M \ NaOH$ solution and $0.02 \ M$ glucose solution
$D$. $0.01 \ M \ NaCl$ solution and $0.01 \ M$ glucose solution
(Assume that $NaCl$ undergoes complete dissociation)

$A$ solution is formed by the combination of two liquids such as dichloromethane and chloroform. The partial pressures of dichloromethane and chloroform in the solution are $285.5 \ mm \ Hg$ and $62.4 \ mm \ Hg$ respectively. What is the total pressure of the solution (in $mm \ Hg$)?

Properties such as boiling point,freezing point,and vapour pressure of a pure solvent change when solute molecules are added to get a homogeneous solution. These are called colligative properties. Applications of colligative properties are very useful in day-to-day life. One of its examples is the use of an ethylene glycol and water mixture as an anti-freezing liquid in the radiator of automobiles.
$A$ solution $M$ is prepared by mixing ethanol and water. The mole fraction of ethanol in the mixture is $0.9$.
Given: Freezing point depression constant of water $(K_{f}^{\text{water}}) = 1.86 \ K \ kg \ mol^{-1}$
Freezing point depression constant of ethanol $(K_{f}^{\text{ethanol}}) = 2.0 \ K \ kg \ mol^{-1}$
Boiling point elevation constant of water $(K_{b}^{\text{water}}) = 0.52 \ K \ kg \ mol^{-1}$
Boiling point elevation constant of ethanol $(K_{b}^{\text{ethanol}}) = 1.2 \ K \ kg \ mol^{-1}$
Standard freezing point of water $= 273 \ K$
Standard freezing point of ethanol $= 155.7 \ K$
Standard boiling point of water $= 373 \ K$
Standard boiling point of ethanol $= 351.5 \ K$
Vapour pressure of pure water $= 32.8 \ mm \ Hg$
Vapour pressure of pure ethanol $= 40 \ mm \ Hg$
Molecular weight of water $= 18 \ g \ mol^{-1}$
Molecular weight of ethanol $= 46 \ g \ mol^{-1}$
In answering the following questions,consider the solutions to be ideal dilute solutions and solutes to be non-volatile and non-dissociative.
$1.$ The freezing point of the solution $M$ is
$(A) \ 268.7 \ K \ (B) \ 268.5 \ K$
$(C) \ 234.2 \ K \ (D) \ 150.9 \ K$
$2.$ The vapour pressure of the solution $M$ is
$(A) \ 39.3 \ mm \ Hg \ (B) \ 36.0 \ mm \ Hg$
$(C) \ 29.5 \ mm \ Hg \ (D) \ 28.8 \ mm \ Hg$
$3.$ Water is added to the solution $M$ such that the mole fraction of water in the solution becomes $0.9$. The boiling point of this solution is
$(A) \ 380.4 \ K \ (B) \ 376.2 \ K$
$(C) \ 375.5 \ K \ (D) \ 354.7 \ K$
Give the answer for questions $1, 2$ and $3.$