The reaction of HClO3 with HCl gives a paramagnetic gas, which upon reaction with O3 produces
The reaction of chloric acid (\( \text{HClO}_3 \)) with hydrogen chloride (\( \text{HCl} \)) results in the formation of chlorine dioxide (\( \text{ClO}_2 \)), which is a paramagnetic gas. This is because chlorine dioxide has an unpaired electron in its structure, making it paramagnetic. The reaction can be written as: \[ \text{HClO}_3 + \text{HCl} \rightarrow \text{ClO}_2 + \text{H}_2\text{O} \]
When chlorine dioxide (\( \text{ClO}_2 \)) reacts with ozone (\( \text{O}_3 \)), it forms dichlorine hexaoxide (\( \text{Cl}_2\text{O}_6 \)). The reaction can be written as: \[ 2 \text{ClO}_2 + \text{O}_3 \rightarrow \text{Cl}_2\text{O}_6 \] This reaction shows that \( \text{ClO}_2 \) reacts with ozone to form the compound \( \text{Cl}_2\text{O}_6 \).
Based on the reactions described above, the correct compound formed after the reaction of the paramagnetic gas with \( \text{O}_3 \) is \( \text{Cl}_2\text{O}_6 \), which corresponds to option C.
The correct option is C: \( \text{Cl}_2\text{O}_6 \).
Given below are two statements. 
In the light of the above statements, choose the correct answer from the options given below:
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?