If $[x]^2-5[x]+6=0$,where $[x]$ denotes the greatest integer function,then

The function $f(x) = \sin x - \cos x$ is ........

The number of positive integral values of $K$ for which the equation $K = |x + |2x - 1|| - |x - |2x - 1||$ has exactly three real solutions is

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

Let the function $g : (-\infty, \infty) \to \left( - \frac{\pi}{2}, \frac{\pi}{2} \right)$ be given by $g(u) = 2 \tan^{-1}(e^u) - \frac{\pi}{2}$. Then,$g$ is -

How many positive real numbers $x$ satisfy the equation $x^3-3|x|+2=0$?