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

If $f(x) = \frac{x - |x|}{|x|}$,then $f(-1) = $

Let $A, B, C$ be three sets such that $n(A \cap B) = n(B \cap C) = n(C \cap A) = n(A \cap B \cap C) = 2$. Then $n((A \times B) \cap (B \times C))$ is equal to -

Find the cardinal number of the following set $\{x: x\}$ is a natural number $\leq 30$ and is divisible by $7$ or $\{11\}$

Let $P(n) : 3^n < n!$ for $n \in N$. If this statement is true for all $n \geq \lambda$,then the smallest value of $\lambda$ is:

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