UPSC Prelims 2025 CSAT, question 16

Solution.

Answer: (c) 65

1. Observe the Pythagorean relation $a * b = \sqrt{a^2 + b^2}$: $7 * 24 = \sqrt{7^2 + 24^2} = \sqrt{49 + 576} = \sqrt{625} = 25$, and $12 * 16 = \sqrt{12^2 + 16^2} = \sqrt{144 + 256} = \sqrt{400} = 20$.
2. Applying the same operation to $16 * 63$ gives $\sqrt{16^2 + 63^2} = \sqrt{256 + 3969} = \sqrt{4225} = 65$.