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:

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:

If $A = \{5^{n} - 4n - 1 : n \in N\}$ and $B = \{16(n - 1) : n \in N\}$,then:

In a class of $60$ students,$25$ students play cricket and $20$ students play tennis,and $10$ students play both the games. The number of students who play neither is:

Let $S = \{1, 2, 3, \ldots, 2022\}$. The probability that a randomly chosen number $n$ from the set $S$ satisfies $\operatorname{HCF}(n, 2022) = 1$ is:

There is a group of $265$ persons who like either singing,dancing,or painting. In this group,$200$ like singing,$110$ like dancing,and $55$ like painting. If $60$ persons like both singing and dancing,$30$ like both singing and painting,and $10$ like all three activities,then the number of persons who like only dancing and painting is: