Set Theory Test...

The function $$f(x)$$ satisfies the condition $$(x-2)f(x)+2f\left(\dfrac{1}{x}\right)=2$$ for all $$x\neq 0$$. Then the value of $$f(2)$$ is 

Let A,B are two sets such that n(A)=4 and n(B)=6. Then the least possible number of elements in the power set of $$(A\cup B)$$ is 

Left A = {1, 2, 3, 4, 5, 6} and B= {1, 2, 3, 4}  be two sets, then the number of functions that can be defined from A to B such that the element '2' in B has exactly 3 pre - images i A, is equal ot

Let  $$A , B$$  and  $$C$$  be pairwise independent events with  $$P ( C ) > 0$$  and  $$P ( A \cap B \cap C ) = 0$$  Then,  $$P \left( A ^ { C } \cap B ^ { C } / C \right)$$ is equal to 

The value of c for which the set $$\{(x, y)|x^2+y^2+2x\leq 1\}\cap \{(x, y)|x-y+c\geq 0\}$$ contains only one point in common is?

Let $$\displaystyle S=\left\{a\in N,a\le100\right\}$$ if the equation $$\displaystyle[{\tan}^{2}x]-\tan x-a=0$$ has real roots, then the number of elements $$S$$ is (when $$[.]$$ is greatest integer function)

If $$A=\left\{ 1,3,5,7,9,11,13,15,17 \right\} ,B=\left\{ 2,4,....,18 \right\} $$ and N is the universal set, then $$A'\cup \left( \left( A\cup B \right) \cap B' \right) $$

If $$A=\left\{ 1,2,4 \right\} ,B=\left\{ 2,4,5 \right\} $$ and $$C=\left\{ 2,5 \right\} $$, then $$\left( A-B \right) \times \left( B-C \right) =$$

If $$A=\left\{1, 2, 3, 4\right\}$$, then the number of subsets of $$A$$ that contain the element $$2$$ but not $$3$$, is 

Let $$p$$ and $$q$$ be two statements. amongst the following, the statement is equivalent to $$p\rightarrow q$$ is