The correct option is (C): \(Cl _2 O _6\)
When chloric acid (\(HClO_3\)) reacts with hydrochloric acid (\(HCl\)), it forms chlorine dioxide (\(ClO_2\)), which is a paramagnetic gas. The balanced reaction is:
\[ HClO_3 + HCl \rightarrow ClO_2 + Cl_2 + H_2O \]
Chlorine dioxide (\(ClO_2\)) can react further with ozone (\(O_3\)). The reaction of \(ClO_2\) with \(O_3\) can produce dichlorine hexoxide (\(Cl_2O_6\)).
The balanced chemical equation for the reaction of chlorine dioxide with ozone is:
\[ 2ClO_2 + 2O_3 \rightarrow Cl_2O_6 + 2O_2 \]
So, the paramagnetic gas \(ClO_2\) reacts with ozone to produce dichlorine hexoxide (\(Cl_2O_6\)).
The correct Answer is option is (C):\(Cl_2O_6\)
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?