Vapour pressure of solvent is $17.5 \ mm \ Hg$ while that of dilute solution is $17.45 \ mm \ Hg$; the mole fraction of solvent is

Vapour pressure of water at $293 \, K$ is $17.535 \, mm \, Hg$. Calculate the vapour pressure of water at $293 \, K$ when $25 \, g$ of glucose is dissolved in $450 \, g$ of water.

When a non-volatile solute is added to the solvent,the vapour pressure of the solvent decreases by $10 \ mm \ Hg$. The mole fraction of the solute in the solution is $0.2$. What would be the mole fraction of the solvent if the decrease in vapour pressure is $20 \ mm \ Hg$?

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.

Assertion $(A)$: The vapour pressure of $0.1 \ M$ sugar solution is less than that of $0.1 \ M$ $KCl$ solution.
Reason $(R)$: Lowering of vapour pressure is directly proportional to the number of particles of non-volatile solute present in the solution.
The correct answer is

The vapor pressure of water at a certain temperature is $3000 \ N \ m^{-2}$. When a non-electrolyte solute is added,it decreases by $300 \ N \ m^{-2}$. The molality of the solution is ............. $m$.