$x \ g$ of a solute is dissolved in $y \ g$ of two different liquids $A$ and $B$. The relative lowering of vapor pressure of the solution in $A$ is twice that of the solution in $B$. If the moles of solute are negligible compared to the moles of solvent,which of the following statements regarding the molar masses $M_A$ and $M_B$ of the solvents is correct?

Vapour pressure of a pure solvent at $90\,^{\circ}C$ is $1020\, torr$. $A$ solution of $0.1\, m$ concentration has a vapour pressure of $1000\, torr$. What is the molecular weight of the solvent?

What is the vapour pressure of a solution containing $1 \ mol$ of a non-volatile solute in $36 \ g$ of water $\left(P_1^0 = 32 \ mm \ Hg\right) (in $mm \ Hg$)?$

What is the vapor pressure of a solution containing a solid solute and a liquid solvent?

Two liquids $A$ and $B$ form an ideal solution. At $320 \ K$,the vapour pressure of the solution,containing $3 \ mol$ of $A$ and $1 \ mol$ of $B$ is $500 \ mm \ Hg$. At the same temperature,if $1 \ mol$ of $A$ is further added to this solution,the vapour pressure of the solution increases by $20 \ mm \ Hg$. The vapour pressure (in $mm \ Hg$) of $B$ in the pure state is . . . . . . (Nearest integer).

Select the correct option using $T$ (True) or $F$ (False) for the following statements: $(1)$ The decrease in vapour pressure is equal to the mole fraction of the solute. $(2)$ The relative lowering of vapour pressure is directly proportional to the amount of solute. $(3)$ The relative lowering of vapour pressure is equal to the mole fraction of the solute. $(4)$ The vapour pressure of the solution is equal to the mole fraction of the solvent.