CAT (QA) PYQs

Let $a, b, x, y$ be real number such $a² + b² = 25, x² + y² = 169$, and $ax + by = 65.$ If $k = ay - bx,$ then

How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits?

$f(x) = \frac{x^2+2x-15}{x^2-7x-18}$ is negative if and only if