At $0^{\circ} C$, a urea solution has an osmotic pressure of $400 \ mm$. On dilution by $x$ times, its osmotic pressure decreases to $100 \ mm$ at $20^{\circ} C$. The dilution factor $x$ is approximately

When $10 \ g$ of glucose (osmotic pressure $P_1$),$10 \ g$ of urea (osmotic pressure $P_2$),and $10 \ g$ of sucrose (osmotic pressure $P_3$) are dissolved in $250 \ mL$ of water,the correct relationship between the osmotic pressures of these solutions is:

Which of the following pairs of solutions is expected to be isotonic at the same temperature?

If $3 \ g$ of glucose (mol. wt. $180$) is dissolved in $60 \ g$ of water at $15 \ ^oC$. Then the osmotic pressure of this solution will be .......... $atm$.

$A$ $5.25\%$ solution of a substance is isotonic with a $1.5\%$ solution of urea (molar mass $= 60\ g\ mol^{-1}$) in the same solvent. If the densities of both the solutions are assumed to be equal to $1.0\ g\ cm^{-3},$ the molar mass of the substance will be .............. $g\ mol^{-1}$.

If $3 \ g$ of glucose (molar mass $= 180 \ g \ mol^{-1}$) is dissolved in $60 \ g$ of water at $15^{\circ} C$,the osmotic pressure of the solution will be (in $atm$)