CTET Paper II (Mathematics and Science) 21 Jan 2024 Solved Paper

Concept:An obtuse scalene triangle has one angle greater than 90°, and all sides of different lengths. The side opposite the largest angle is the longest side.Explanation:For each option, find the third angle using the sum of angles = 180°. Check if any angle exceeds 90° and if the side lengths obey the angle‑side relationship.Option A: ∠R = 35°. Then ∠Q = 180° − (55° + 35°) = 90°. This is a right triangle, not obtuse. Incorrect.Option B: ∠R = 25°. Then ∠Q = 180° − (55° + 25°) = 100°. Obtuse at Q. Side opposite ∠Q is PR (largest). QR = 18 cm opposite ∠P = 55°. Since ∠R = 25° is smallest, side PQ should be smallest and less than 18 cm, but option gives PQ = 18 cm. Contradiction. Incorrect.Option C: ∠R = 15°. Then ∠Q = 180° − (55° + 15°) = 110°. Obtuse at Q. Side PR opposite 110° is longest. QR = 18 cm opposite 55°, so PR must be greater than 18 cm. Given PR > 18 cm, this holds. All angles are different (55°, 15°, 110°), so sides are different. Hence an obtuse scalene triangle. Correct.Option D: ∠R = 65°. Then ∠Q = 180° − (55° + 65°) = 60°. All angles less than 90°, no obtuse angle. Incorrect.Answer:The correct option is C.