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

If a set $A$ has $5$ elements,then the number of ways of selecting two subsets $P$ and $Q$ from $A$ such that $P$ and $Q$ are mutually disjoint,is

The number of polynomials $p(x)$ with integer coefficients such that the curve $y=p(x)$ passes through $(2,2)$ and $(4,5)$ is

If $P(x) = x^5 + ax^4 + bx^3 + cx^2 + dx + e$ is a polynomial such that $P(0) = 1, P(1) = 2, P(2) = 5, P(3) = 10$ and $P(4) = 17$,then $P(5) =$

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

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: