The set $A = \{ x: x \in R, x^2 = 16 \text{ and } 2x = 6 \}$ equals

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 ${x : x \text{ is an odd integer}}$

For $\theta > \frac{\pi}{3}$,the value of $f(\theta) = \sec^2 \theta + \cos^2 \theta$ always lies in the interval

If $A = \{a, b\}$,$B = \{2, 3, 5, 6, 7\}$ and $C = \{5, 6, 7, 8, 9\}$,find $A \times (B \cap C)$.

The range of $f(x) = \cos x - \sin x$ is

The domain of the function $f(x) = \sqrt{\log \frac{1}{|\sin x|}}$ is