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

Suppose $A_1, A_2, A_3, \dots, A_{30}$ are $30$ sets each having $5$ elements and $B_1, B_2, \dots, B_n$ are $n$ sets each with $3$ elements. Let $\bigcup_{i=1}^{30} A_i = \bigcup_{j=1}^n B_j = S$ and each element of $S$ belongs to exactly $10$ of the $A_i$'s and exactly $9$ of the $B_j$'s. Then $n$ is equal to:

Let $A$ and $B$ be two non-empty subsets of a set $X$ such that $A$ is not a subset of $B$, then

The domain of the function $f(x) = \sqrt{x - x^2} + \sqrt{4 + x} + \sqrt{4 - x}$ is

If $A = \{1, 2, 3, 4, 5\}, B = \{2, 4, 6\}, C = \{3, 4, 6\},$ then $(A \cup B) \cap C$ is

If ${N_a} = \{ an : n \in N \} ,$ then ${N_3} \cap {N_4} = $