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

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 $............$.

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

An electronic assembly consists of two subsystems $A$ and $B$. Past testing procedures data show that probabilities of failure are $P(A \text{ fails}) = 0.2$, $P(B \text{ fails alone}) = 0.15$, and $P(A \cap B \text{ fail}) = 0.15$. Then the probability that $A$ fails alone is equal to

$A$ contractor has two teams of workers,team $A$ and team $B$. Team $A$ can complete a project $P$ in $12$ days and team $B$ can complete $P$ in $36$ days. Team $A$ starts working on $P$ and team $B$ joins team $A$ after four days. Team $A$ is withdrawn after another two days and team $B$ is asked to double its efficiency. The number of additional days required for team $B$ to complete $P$ is

The lengths of the sides and the diagonal of an isosceles trapezium form a two-element set $\{a, b\}$. If $a > b$,then $a / b$ equals