In a hostel,$60 \%$ of the students read Hindi newspaper,$40 \%$ read English newspaper and $20 \%$ read both Hindi and English newspapers. $A$ student is selected at random. Find the probability that she reads neither Hindi nor English newspapers.

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

If $A$ and $B$ are two sets such that $n(A) = 70$,$n(B) = 60$,and $n(A \cup B) = 110$,then $n(A \cap B)$ is equal to:

Let $A = \{x : x \in R, |x| < 1\};$ $B = \{x : x \in R, |x - 1| \ge 1\}$ and $A \cup B = R - D,$ then the set $D$ is

Of the members of three athletic teams in a school,$21$ are in the cricket team,$26$ are in the hockey team,and $29$ are in the football team. Among them,$14$ play hockey and cricket,$15$ play hockey and football,and $12$ play football and cricket. Eight play all the three games. The total number of members in the three athletic teams is:

Let $A = \{a_1, a_2, a_3, \dots, a_n\}$ be a set containing $n$ elements. Two subsets $P$ and $Q$ of $A$ are formed independently. The number of ways in which these subsets can be formed such that $(P - Q)$ contains exactly $2$ elements is: