In a group of $400$ people,$250$ can speak Hindi and $200$ can speak English. How many people can speak both Hindi and English?

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

In a class of $100$ students,$15$ students chose only physics (but not mathematics and chemistry),$3$ chose only chemistry (but not mathematics and physics),and $45$ chose only mathematics (but not physics and chemistry). Of the remaining students,it is found that $23$ have taken physics and chemistry,$20$ have taken physics and mathematics,and $12$ have taken mathematics and chemistry. The number of students who chose all the three subjects is

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

If $n(X)=700, n(A)=200, n(B)=300,$ and $n(A \cap B)=100$,where $X$ is the universal set and $A$ and $B$ are subsets of $X$,then $n(A' \cap B')=$

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