UPSC NDA I 2025 Mathematics Paper

We are given the triangle with angles:
‌∠B=x=30∘
‌∠A=3x=90∘
‌∠C=180∘−120∘=60∘
Step 1: Check if the sum of the angles is 180∘ :
∠A+∠B+∠C=90∘+30∘+60∘=180∘
This confirms that the angles satisfy the angle sum property of a triangle.
Statement I. The triangle is right-angled.
Since ∠A=90∘, the triangle is right-angled.
Statement III: III. The angles A,C and B of the triangle are in AP.
The angles 30∘60∘, and 90∘ are in Arithmetic Progression because:
60∘−30∘=30∘‌ and ‌90∘−60∘=30∘
This confirms that the angles are in AP .
Statement II is not correct because there is no mention of a side being 3 times the other.
∴ The correct answer is Option (I) and (III) are correct.