Relations and F...

Events A and B associated with an experiment  are said to be independent iff

If $$f(x)=1+x+\dfrac { { x }^{ 2 } }{ 2 } +......+\dfrac { { x }^{ 100 } }{ 100 } ,$$ then I'(1) is equal to 

If $$h=\left\{ ((x,y),(x-y, x+y))/ x,y \epsilon  N \right\}  $$ is a relation on NxN, then domain of h

If y = f (x) = $$\dfrac{ax -+ b}{cx - a}$$, then x is equal to 

If $$f\left(x\right)+2f\left(1-x\right)={ x }^{ 2 }+2$$ ,  $$ \forall  x\in R$$,then$$ f\left (x\right)=$$ 

If the Period  of $$f(x)=\dfrac { cos\left( sin\left( nx \right)  \right)  }{ tan\left( \dfrac { x }{ n }  \right)  } ,n\epsilon N$$ is $$6\pi $$ , then n is equal to 

If $$A = \left \{1, 2, 3, 4, 5\right \}$$ then

If $$A=\left\{1,2,4  \right\}$$, $$B=\left\{1,4,6,9  \right\}$$ and $$R$$ is a relation from $$A$$ to $$B$$ defined by $$x$$ is greater than $$y$$. The rangle of $$R$$ is :

$$f(x)$$ is a linear function. If $$f(x)=-1$$ and $$f(2)=14$$ find the value of $$f(15)$$

If  $$f ( x ) = \log _ { a } x$$  and  $$F ( x ) = a ^ { x } ,$$  then  $$F [ f ( x ) ]$$  is