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

If $A = \{ 2, 4, 5 \}$ and $B = \{ 7, 8, 9 \}$,then $n(A \times B)$ is equal to

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

In a town of $10,000$ families,it was found that $40\%$ of families buy newspaper $A$,$20\%$ buy newspaper $B$,$10\%$ buy newspaper $C$,$5\%$ buy $A$ and $B$,$3\%$ buy $B$ and $C$,and $4\%$ buy $A$ and $C$. If $2\%$ of families buy all three newspapers,then the number of families that buy newspaper $A$ only is:

If $f: R \to R$,then the range of the function $f(x) = \frac{x^2}{x^2 + 1}$ is

The relation $R$ defined on the set of natural numbers as $\{(a, b) : a\}$ differs from $b$ by $\{3\}$,is given by