The number of integers from $1$ to $1000$ which are divisible by $2$ or $3$ is

Let $E$ denote the set of letters of the English alphabet,$V = \{a, e, i, o, u\}$ and $C$ be the complement of $V$ in $E$. Then,the number of four-letter words (where repetitions of letters are allowed) having at least one letter from $V$ and at least one letter from $C$ is

If $A$ and $B$ are events of a random experiment such that $P(A \cup B) = \frac{3}{4}$,$P(A \cap B) = \frac{1}{4}$,and $P(\bar{A}) = \frac{2}{3}$,then find $P(\bar{A} \cap B)$.

Let $A = \{n \in [100, 700] \cap \mathbb{N} : n \text{ is neither a multiple of } 3 \text{ nor a multiple of } 4\}$. Then the number of elements in $A$ is

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

The sum of the integers from $1$ to $100$ which are not divisible by $3$ or $5$ is