In a class of $300$ students,every student reads $5$ newspapers and every newspaper is read by $60$ students. Then the number of newspapers is

Let $A = \{1, 2, 3, 4, 5, 6, 7\}$ and $B = \{3, 6, 7, 9\}$. Then the number of elements in the set $\{ C \subseteq A : C \cap B \neq \phi \}$ is

Let $X$ be the set consisting of the first $2018$ terms of the arithmetic progression $1, 6, 11, \dots$ and $Y$ be the set consisting of the first $2018$ terms of the arithmetic progression $9, 16, 23, \dots$. Then,the number of elements in the set $X \cup Y$ is:

$205$ students take an examination,of whom $105$ pass in English,$70$ students pass in Mathematics,and $30$ students pass in both. How many students fail in both subjects?

Let $A$ denote the set of all $2$-digit numbers in base $10$ that are equal to four times the sum of the factorials of their digits. The sum of the numbers in $A$ is

$A$ number is chosen at random from the set $\{1, 2, 3, \ldots, 2000\}$. Let $p$ be the probability that the chosen number is a multiple of $3$ or a multiple of $7$. Then the value of $500p$ is . . . . . .