If $aN = \{ ax : x \in N \}$,then the set $3N \cap 7N$ is equal to .....$N$.

Two finite sets have $m$ and $n$ elements. The total number of subsets of the first set is $56$ more than the total number of subsets of the second set. The values of $m$ and $n$ are

The domain of the function $f(x) = \exp (\sqrt {5x - 3 - 2{x^2}} )$ is

In a class of $140$ students numbered $1$ to $140$,all even-numbered students opted for the Mathematics course,those whose number is divisible by $3$ opted for the Physics course,and those whose number is divisible by $5$ opted for the Chemistry course. The number of students who did not opt for any of the three courses is:

The domain of the function $f(x) = \frac{1}{\sqrt{|x| - x}}$ is

If $A = \{ 2, 4, 5 \}$ and $B = \{ 7, 8, 9 \}$,then $n(A \times B)$ is equal to