If $A, B, C$ are three sets such that $A \cup B = A \cup C$ and $A \cap B = A \cap C$,then

Let $A = \{x \in (0, \pi) - \{\frac{\pi}{2}\} : \log_{(2/\pi)}|\sin x| + \log_{(2/\pi)}|\cos x| = 2\}$ and $B = \{x \geq 0 : \sqrt{x}(\sqrt{x} - 4) - 3|\sqrt{x} - 2| + 6 = 0\}$. Then $n(A \cup B)$ is equal to:

If $A=\{x \in R: \sqrt{x^2-8x+15} \in R\}$ and $B=\{x \in R: \frac{x-3}{2x-5} < \frac{x-6}{2x-11}\}$,then $A \cap B=$

If $U$ is the universal set and $A \cup B \cup C = U$,then ${(A - B) \cup (B - C) \cup (C - A)}'$ is equal to:

Let $A$ be the set of first $101$ terms of an $A$.$P$.,whose first term is $1$ and the common difference is $5$,and let $B$ be the set of first $71$ terms of an $A$.$P$.,whose first term is $9$ and the common difference is $7$. Then,the number of elements in $A \cap B$ which are divisible by $3$ is:

Let $A$ and $B$ be finite sets and $P_A$ and $P_B$ respectively denote their power sets. If $P_B$ has $112$ elements more than those in $P_A$,then the number of injective functions from $A$ to $B$ is