In a group of $50$ people, $35$ speak Hindi, $25$ speak both Hindi and English, and all the people speak Hindi or English or both. The number of people who speak English only is

If two sets $A$ and $B$ have $99$ elements in common,then the number of elements common to each of the sets $A \times B$ and $B \times A$ is:

If $X = \{ 4^n - 3n - 1 : n \in N \}$ and $Y = \{ 9(n - 1) : n \in N \}$,then $X \cup Y$ = . . . . .

$A$ survey shows that $73 \%$ of the persons working in an office like coffee,whereas $65 \%$ like tea. If $x$ denotes the percentage of them who like both coffee and tea,then $x$ cannot be

If $A$ and $B$ are any two non-empty sets and $A$ is a proper subset of $B$. If $n(A) = 4$,then the minimum possible value of $n(A \Delta B)$ is (where $\Delta$ denotes the symmetric difference of set $A$ and set $B$).

If $A$ and $B$ are two sets,then $A \cup B = A \cap B$ if and only if: