CAT (QA) PYQs

The number of the real roots of the equation $2\cos (x(x + 1)) = 2^x + 2^{-x}$ is

If $f(x) = \frac{5x + 2}{3x - 5}$ and $g(x) = x^2 - 2x - 1$, then the value of $g(f(f(3)))$ is

If $f(x + y) = f (x) f (y)$ and $f(5) = 4$, then $f (10) - f (-10)$ is equal to