Domain of the function $f(x) = {\left[ {{{\log }_{10}}\left( {\frac{{5x - {x^2}}}{4}} \right)} \right]^{1/2}}$ is

Let $U = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \}$,$A = \{ 1, 2, 5 \}$,and $B = \{ 6, 7 \}$. Then $A \cap B'$ is:

The range of $f(x) = \frac{x^2 + 34x - 71}{x^2 + 2x - 7}$ is

Domain of the function $\frac{\sqrt{1 + x} - \sqrt{1 - x}}{x}$ is

In a class of $55$ students,the number of students studying different subjects are $23$ in Mathematics,$24$ in Physics,$19$ in Chemistry,$12$ in Mathematics and Physics,$9$ in Mathematics and Chemistry,$7$ in Physics and Chemistry and $4$ in all the three subjects. The number of students who have taken exactly one subject is

Which of the following pairs of sets are disjoint?
$(i)$ ${1, 2, 3, 4}$ and ${x : x in mathbb{N}, 4 leq x leq 6}$
$(ii)$ ${a, e, i, o, u}$ and ${c, d, e, f}$
$(iii)$ ${x : x \text{ is an even integer}}$ and ${x : x \text{ is an odd integer}}$