If $A$ and $B$ are subsets of universal set $X$ such that $n(X)=200, n(A)=90, n(B)=80$ and $n(A' \cap B')=40$,then $n(A \cap B')=$

If a number is chosen at random from the first $200$ positive integers,what is the probability that it is divisible by $6$ or $8$?

If $n(U) = 600$,$n(A) = 100$,$n(B) = 200$,and $n(A \cap B) = 50$,then $n(\bar{A} \cap \bar{B})$ is: ($U$ is the universal set and $A$ and $B$ are subsets of $U$)

The number of elements in the set $\{ n \in \mathbb{N} : 10 \leq n \leq 100 \text{ and } 3^n - 3 \text{ is a multiple of } 7 \}$ is $........$.

In a class of $60$ students,$40$ opted for $NCC$,$30$ opted for $NSS$ and $20$ opted for both $NCC$ and $NSS$. If one of these students is selected at random,then the probability that the student selected has opted neither for $NCC$ nor for $NSS$ is

Let $A, B, C$ be three non-void subsets of set $S$. Let $(A \cap C) \cup (B \cap C^{\prime}) = \phi$, where $C^{\prime}$ denotes the complement of set $C$ in $S$. Then: