CAT (QA) PYQs

For any real number x, let [x] be the largest integer less than or equal to x. If $\sum_{n=1}^{N} [\frac{1}{5} + \frac{n}{25}] = 25$ then N is

If $f(x + 2) = f(x) + f(x + 1)$ for all positive integers $x$, and $f(11) = 91$, $f(15) = 617$, then $f(10)$ equals

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