Q26. If 7 * 24 = 25 and 12 * 16 = 20, then what is 16 * 63 equal to?

The problem defines a custom operation '*'. We need to identify the underlying mathematical pattern. Given: 1. 7 * 24 = 25 2. 12 * 16 = 20 Observe that the numbers in each equation form Pythagorean triplets: - For 7, 24, 25: 7^2 + 24^2 = 49 + 576 = 625.

And 25^2 = 625. So, 25 = sqrt(7^2 + 24^2). - For 12, 16, 20: 12^2 + 16^2 = 144 + 256 = 400. And 20^2 = 400. So, 20 = sqrt(12^2 + 16^2). The pattern is that 'a * b' is equal to the hypotenuse of a right-angled triangle with sides 'a' and 'b', i.e., sqrt(a^2 + b^2).

Now, apply this pattern to find 16 * 63: 16 * 63 = sqrt(16^2 + 63^2) 16^2 = 256 63^2 = 3969 16 * 63 = sqrt(256 + 3969) = sqrt(4225) To find the square root of 4225: Since the number ends in 5, its square root must end in 5. The number 42 lies between 6^2 (36) and 7^2 (49).

So, the square root must be 65. (Check: 65^2 = 4225). Therefore, 16 * 63 = 65. This question tests pattern recognition and basic mathematical knowledge (Pythagorean triplets, squares, square roots), which are common in UPSC CSAT's logical reasoning and quantitative aptitude sections.