Number of solutions of the equation $2^x + x = 2^{\sin x} + \sin x$ in $[0, 10\pi]$ is -

If $f(x)=ax+b$,where $a$ and $b$ are integers,$f(-1)=-5$ and $f(4)=3$,then $a$ and $b$ are respectively

Let $f(x) = \begin{cases} \frac{1}{2}, & \text{if } 0 \le x \le \frac{1}{2} \\ \frac{1}{3}, & \text{if } \frac{1}{2} < x \le 1 \end{cases}$,then $f$ is

Function $f(x) = {\left( {\left\{ x \right\} - \frac{1}{2}} \right)^2}$ is (where $\{.\}$ represents the fractional part function).

Let $g: (-\infty, \infty) \to (-\frac{\pi}{2}, \frac{\pi}{2})$ be defined by $g(x) = 2 \tan^{-1}(e^x) - \frac{\pi}{2}$. Then $g(x)$ is...

Which of the following is an even function?