The domain of the function $\log _{10}(x^2-5x+6)$ is

If $f:[2, \infty) \rightarrow B$ defined by $f(x)=x^2-4x+5$ is a bijection,then $B$ is equal to

Let the range of the function $f(x) = \frac{1}{2 + \sin 3x + \cos 3x}, x \in \mathbb{R}$ be $[a, b]$. If $\alpha$ and $\beta$ are respectively the $A.M.$ and the $G.M.$ of $a$ and $b$,then $\frac{\alpha}{\beta}$ is equal to:

If $[x]$ denotes the greatest integer $\leq x$,then the range of the real-valued function $f(x) = \frac{1}{\sqrt{x-[x]}}$ is

If the domain of the function $\log _e\left(\frac{6 x^2+5 x+1}{2 x-1}\right)+\cos ^{-1}\left(\frac{2 x^2-3 x+4}{3 x-5}\right)$ is $(\alpha, \beta) \cup(\gamma, \delta]$,then $18\left(\alpha^2+\beta^2+\gamma^2+\delta^2\right)$ is equal to $....$.

The domain of the function $f(x) = \frac{1}{\sqrt{|x|-x}}$ is