$A$ bag contains $30$ balls numbered from $1$ to $30$. One ball is drawn randomly. The probability that the number on the ball is a multiple of $5$ or $7$ is:

Out of $800$ boys in a school,$224$ played cricket,$240$ played hockey,and $336$ played basketball. Of the total,$64$ played both basketball and hockey,$80$ played cricket and basketball,and $40$ played cricket and hockey. $24$ played all three games. The number of boys who did not play any game is:

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

If $A = \{x \in \mathbb{R} : |x - 2| > 1\}$,$B = \{x \in \mathbb{R} : \sqrt{x^2 - 3} > 1\}$,$C = \{x \in \mathbb{R} : |x - 4| \geq 2\}$,and $\mathbb{Z}$ is the set of all integers,then the number of subsets of the set $(A \cap B \cap C)^c \cap \mathbb{Z}$ is .... .

The sum of all integers from $1$ to $100$ that are divisible by $2$ or $5$ is...........

Let $A = \{n \in N : H.C.F.(n, 45) = 1\}$ and $B = \{2k : k \in \{1, 2, \ldots, 100\}\}$. Then the sum of all the elements of $A \cap B$ is