The following solutions were prepared by dissolving 10 g of glucose (C₆H₁₂O₆) in 250 ml of water (P₁), 10 g of urea (CH₄N₂O) in 250 ml of water (P₂) and 10 g of sucrose (C₁₂H₂₂O₁₁) in 250 ml of water (P₃). The right option for the decreasing order of osmotic pressure of these solutions is :

The correct option is P₂ > P₁ > P₃.

To find the decreasing order of osmotic pressure for the given solutions, we can use the formula for osmotic pressure (represented by the symbol $\pi$):
$\pi =i·C·R·T$
where:
- $i$ is the van 't Hoff factor,
- $C$ is the molar concentration (molarity) of the solute,
- $R$ is the universal gas constant, and
- $T$ is the absolute temperature.

Since glucose, urea, and sucrose are all non-electrolytes, they do not dissociate or associate in water. Therefore, their van 't Hoff factor is the same:
$i=1$
Additionally, the mass of each solute dissolved is the same (10 g), the volume of water is the same (250 ml), and the temperature $T$ is constant. Thus, the osmotic pressure $\pi$ is directly proportional to the molar concentration $C$, which is determined by the number of moles of each solute:
$C=\frac{n}{V}=\frac{\text{mass}/\text{Molar Mass}}{V}$
Since the mass and volume $V$ are constant across all three solutions, the osmotic pressure is inversely proportional to the molar mass of the solute:
$\pi \propto \frac{1}{\text{Molar Mass}}$

Let's calculate the molar masses of the three solutes:
1. Urea (CH₄N₂O) in solution P₂:
Molar mass = 12 (C) + 4×1 (H) + 2×14 (N) + 16 (O) = 12 + 4 + 28 + 16 = 60 g/mol.
2. Glucose (C₆H₁₂O₆) in solution P₁:
Molar mass = 6×12 (C) + 12×1 (H) + 6×16 (O) = 72 + 12 + 96 = 180 g/mol.
3. Sucrose (C₁₂H₂₂O₁₁) in solution P₃:
Molar mass = 12×12 (C) + 22×1 (H) + 11×16 (O) = 144 + 22 + 176 = 342 g/mol.

Comparing the molar masses:
Molar Mass (Urea) < Molar Mass (Glucose) < Molar Mass (Sucrose)
60 g/mol < 180 g/mol < 342 g/mol

Since osmotic pressure is inversely proportional to the molar mass of the solute for equal masses dissolved in equal volumes:
${\pi }_{\text{urea}}>{\pi }_{\text{glucose}}>{\pi }_{\text{sucrose}}$
which corresponds to:
P₂ > P₁ > P₃