CAT (QA) PYQs

If $x$ and $y$ are non-negative integers such that $x+9=z, y+1=z$ and $x+y<z+5$, then the maximum possible value of $2 x+y$ ?

If the sum of squares of two numbers is $97$, then which one of the following cannot be their product?

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