CAT (QA) PYQs

For real values of $x$, the range of the function $f(x)=\frac{2x-3}{2x^2+4x-6}$ is

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

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