Let $A = \{x : |x^{2} - 10| \le 6\}$ and $B = \{x : |x - 2| > 1\}$. Then:

The number of $4$-digit numbers that are less than or equal to $2800$ and are either divisible by $3$ or by $11$ is equal to $............$.

In a class of $30$ pupils,$12$ take needle work,$16$ take physics,and $18$ take history. If all the $30$ students take at least one subject and no one takes all three,then the number of pupils taking exactly $2$ subjects is:

In a school,$20$ teachers teach either Mathematics or Physics. If $12$ teachers teach Mathematics and $4$ teachers teach both subjects,then the number of teachers teaching only Physics is:

$A$ number $n$ is chosen at random from $S=\{1, 2, 3, \ldots, 50\}$. Let $A=\{n \in S: n+\frac{50}{n} > 27\}$, $B=\{n \in S: n \text{ is a prime}\}$ and $C=\{n \in S: n \text{ is a square}\}$. Then, the correct order of their probabilities is:

The number of $3$-digit numbers that are divisible by either $2$ or $3$ but not divisible by $7$ is $.........$.