To solve this problem, we need to analyze the reaction and the hydrolysis of the given compound to determine the number of moles of HF produced.
1. Analyzing the Reaction:
From the reaction between \( \text{Xe} \) and \( \text{O}_2\text{F}_2 \), a xenon compound \( P \) is formed. The xenon compound formed is likely to be xenon tetrafluoride (XeF₄), as this is a common product in such reactions involving xenon and oxygen difluoride. The reaction can be represented as follows:
\[ \text{Xe} + \text{O}_2\text{F}_2 \rightarrow \text{XeF}_4 + \text{O}_2 \]
2. Hydrolysis of Xenon Tetrafluoride (XeF₄):
When xenon tetrafluoride (\( \text{XeF}_4 \)) undergoes complete hydrolysis, it reacts with water to produce xenon dioxide (XeO₂) and hydrofluoric acid (HF). The reaction for the hydrolysis of 1 mole of xenon tetrafluoride is:
\[ \text{XeF}_4 + 4\text{H}_2\text{O} \rightarrow \text{XeO}_2 + 4\text{HF} \]
3. Conclusion:
For each mole of xenon tetrafluoride (\( \text{XeF}_4 \)) hydrolyzed, 4 moles of hydrofluoric acid (HF) are produced.
Final Answer:
The number of moles of HF produced by the complete hydrolysis of 1 mole of \( P \) (which is \( \text{XeF}_4 \)) is 4.
\(\text{Xe} + 2\text{O}_2 + \text{F}_2 \rightarrow \text{XeF}_4 + 2\text{O}_2\)
\(3\text{XeF}_4 + 6\text{H}_2\text{O} \rightarrow 2\text{Xe} + \text{XeO}_3 + \frac{23}{2}\text{O}_2 + 12\text{HF}\)
∴ One mole of \(\text{XeF}_4\) gives 4 moles of HF on hydrolysis.
Method used for separation of mixture of products (B and C) obtained in the following reaction is: 
Let $ P(x_1, y_1) $ and $ Q(x_2, y_2) $ be two distinct points on the ellipse $$ \frac{x^2}{9} + \frac{y^2}{4} = 1 $$ such that $ y_1 > 0 $, and $ y_2 > 0 $. Let $ C $ denote the circle $ x^2 + y^2 = 9 $, and $ M $ be the point $ (3, 0) $. Suppose the line $ x = x_1 $ intersects $ C $ at $ R $, and the line $ x = x_2 $ intersects $ C $ at $ S $, such that the $ y $-coordinates of $ R $ and $ S $ are positive. Let $ \angle ROM = \frac{\pi}{6} $ and $ \angle SOM = \frac{\pi}{3} $, where $ O $ denotes the origin $ (0, 0) $. Let $ |XY| $ denote the length of the line segment $ XY $. Then which of the following statements is (are) TRUE?