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

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 $f(x) = \log_{(10x^{2}-17x+7)}(18x^{2}-11x+1)$ is $(-\infty, a) \cup (b, c) \cup (d, \infty) - \{e\}$, then $90(a+b+c+d+e)$ equals:

Which of the following intervals is a possible domain of the function $f(x) = \log_{\{x\}}[x] + \log_{[x]}\{x\}$,where $[x]$ is the greatest integer not exceeding $x$ and $\{x\} = x - [x]$?

Domain of the real valued function $f(x) = \log(x^2 - 1) + x \operatorname{coth}^{-1} x$ is

For $f(x)=\sin \left(\frac{1}{|x| \sqrt{x^2-1}}\right)$,the domain and range of $f(x)$ in $R$ are: