If $S$ and $T$ are two sets such that $S$ has $21$ elements,$T$ has $32$ elements,and $S \cap T$ has $11$ elements,how many elements does $S \cup T$ have?

In a class,$50$ students play cricket,$20$ students play football and $10$ play both cricket and football. How many students play at least one of these two games?

$A$ 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 two sets,then $A \times B = B \times A$ if and only if

The interval for which ${\sin ^{ - 1}}\sqrt x + {\cos ^{ - 1}}\sqrt x = \frac{\pi }{2}$ holds is:

If $A$ and $B$ are two given sets,then $A \cap (A \cap B)^c$ is equal to