The domain of the real valued function $f(x) = \log_2 \log_3 \log_5(x^2 - 5x + 11)$ is

The domain of the function $f: R \rightarrow R$ defined by $f(x) = \sqrt{x^{2}-7x+12}$ is

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

The domain of definition of the function $y(x)$ given by $2^x + 2^y = 2$ is

The number of integral values of $\lambda$ for which the function $f(x) = \sqrt{\ln(2\lambda \cos x + 5)}$ is defined for all $x \in R$ is:

For the function $f(x) = \left[ \frac{1}{[x]} \right]$,where $[x]$ denotes the greatest integer less than or equal to $x$,which of the following statements is true?