UPSC NDA I 2021 Mathematics Solved Paper

Concept
Cosine rule:
cos‌θ=‌

a2+b2−c2

2ab

Where a,b and c are the sides of the triangle and θ is the angle between the sides a and b.
Calculation:
Let m=n=1 unit
Then √m2+n2+mn=√3 unit√m2+n2+mn=√3
Using cosine rule;
cos‌θ=‌

12+12−√32

2×1×1

⇒cos‌θ=−1∕2
∴θ=120∘
Now, the sum of the acute angles of the triangle =180∘−120∘=60∘