
Step 1: Observe the word "ARCH" in Figure B. Four circular cutouts have been made within the letters. These cutouts contain unique sections of the letters.
Step 2: Compare the cutouts from Figure B with the given options (\( P, Q, R, S \)). The correct group should exactly match the missing sections in terms of alignment, shape, and letter strokes.
Step 3: After careful observation, the group labeled \( R \) contains the four exact cutouts extracted from "ARCH". The patterns within the circles align with the letter fragments in Figure B. Thus, the correct answer is option C (\( R \)).





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?