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

If $A \subseteq Z$ and the function $f: A \rightarrow R$ is defined by $f(x) = \frac{1}{\sqrt{64 - (0.5)^{24 + x - x^2}}}$,then the sum of all absolute values of elements of $A$ is

Define a function $f(x) = \frac{16x^2 - 96x + 153}{x - 3}$ for all real $x \neq 3$. The least positive value of $f(x)$ is

If $R$ is the set of all real numbers and $f: R \rightarrow R$ is defined by $f(x) = 3x^2 + 1$, then the set $f^{-1}([1, 6])$ is

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

If $f:R \to S$ defined by $f(x) = \sin x - \sqrt{3} \cos x + 1$ is onto,then the interval of $S$ is