Let $S = \{1, 2, 3, \dots, 100\}$. The number of non-empty subsets $A$ of $S$ such that the product of elements in $A$ is even 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

The probability that at least one of the events $A$ and $B$ occurs is $0.6$. If $A$ and $B$ occur simultaneously with probability $0.2$,then $P(A') + P(B')$ is equal to

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

Sets $A$ and $B$ have $3$ and $6$ elements respectively. What can be the minimum number of elements in $A \cup B$?

In a class of $55$ students,the number of students studying different subjects are $23$ in Mathematics,$24$ in Physics,$19$ in Chemistry,$12$ in Mathematics and Physics,$9$ in Mathematics and Chemistry,$7$ in Physics and Chemistry,and $4$ in all the three subjects. The total number of students who have taken exactly one subject is