$A$ solution containing $1.8 \ g$ of a compound (empirical formula $CH_2O$) in $40 \ g$ of water is observed to freeze at $-0.465 \ ^oC$. The molecular formula of the compound is ($K_f$ of water $= 1.86 \ K \ kg \ mol^{-1}$)

$A$ non-volatile solute is dissolved in water. The $\Delta T_b$ of the resultant solution is $0.052 \ K$. What is the freezing point of the solution (in $K$)?
($K_b$ of water $= 0.52 \ K \ kg \ mol^{-1}$; $K_f$ of water $= 1.86 \ K \ kg \ mol^{-1}$,Freezing point of water $= 273 \ K$)

Identify the correct statements :
$(A)$ The molality of $2.5 \text{ g}$ of ethanoic acid (Molar mass : $60 \text{ g mol}^{-1}$) in $75 \text{ g}$ of benzene solution is $0.556 \text{ m}$.
$(B)$ The molarity of a solution containing $5 \text{ g}$ of NaOH (molar mass : $40 \text{ g mol}^{-1}$) in $450 \text{ mL}$ of solution is $0.278 \text{ M}$ at $298 \text{ K}$.
$(C)$ Aquatic species are more comfortable in cold water.
$(D)$ The solubility of gas increases with decrease in pressure.
$(E)$ For a binary mixture of $A$ and $B$, the number of moles of $A$ and $B$ are $n_{A}$ and $n_{B}$ respectively. The mole fraction of $B$ will be $x_{B} = n_{A} / (n_{A} + n_{B})$.
Choose the correct answer from the options given below :

$A$ solution at $20\,^oC$ is composed of $1.5\,mol$ of benzene and $3.5\,mol$ of toluene. If the vapour pressure of pure benzene and pure toluene at this temperature are $74.7\,torr$ and $22.3\,torr,$ respectively,then the total vapour pressure of the solution and the benzene mole fraction in equilibrium with it will be,respectively

The vapour pressure of a non-ideal two-component solution is given below. Identify the correct $B.P.-x$ curve for the same mixture.

The freezing point depression of $0.001 \ M$ of $A_x B_y[Fe(CN)_6]$ is $5.58 \times 10^{-3} \ K$. If the oxidation state of $Fe$ is $+2$ and $K_f = 1.86 \ K \ kg \ mol^{-1}$, then the total number of possibilities for different types of $A$ and $B$ cations are