If the domain of the function $f(x) = x^2 - 6x + 7$ is $(-\infty, \infty)$,then the range of the function is:

The domain of the function $f(x) = \log (\sqrt {x - 4} + \sqrt {6 - x} )$ is

Let $\bigcup_{i=1}^{50} X_{i} = \bigcup_{i=1}^{n} Y_{i} = T$,where each $X_{i}$ contains $10$ elements and each $Y_{i}$ contains $5$ elements. If each element of the set $T$ is an element of exactly $20$ of the sets $X_{i}$ and exactly $6$ of the sets $Y_{i}$,then $n$ is equal to:

Let $X = \{ 1, 2, 3, 4, 5 \}$ and $Y = \{ 1, 3, 5, 7, 9 \}$. Which of the following is/are relations from $X$ to $Y$?

Domain of $f(x) = (x^2 - 1)^{-1/2}$ is

In a group of $70$ people,$37$ like coffee,$52$ like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?