The domain of the function $f(x) = \sqrt{2 - x} - \frac{1}{\sqrt{9 - x^2}}$ is:

Let $A = \{1, 2, 3, 4, 5\}$ and $B = \{2, 3, 6, 7\}$. Then the number of elements in $(A \times B) \cap (B \times A)$ is

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

There are $80$ families in a small extension area. $20$ percent of these families own a car each. $50$ percent of the remaining families own a motor cycle each. How many families in that extension do not own any vehicle?

$2n (A \setminus B) = n (B \setminus A)$ and $5n (A \cap B) = n (A) + 3n (B)$,where $P \setminus Q = P \cap Q^C$. If $n (A \cup B) \leq 10$,then the value of $\frac{n(A) \cdot n(B) \cdot n(A \cap B)}{8}$ is:

In a certain office,$72 \%$ of the workers prefer cold drink and $44 \%$ prefer tea. If each of them prefers cold drink or tea and $40$ like both,then the total number of workers in the office is