Relations and F...

If $  A  $ is a finite set containing n distinct elements, then the number of relations on A is equal to

Let $$f\left( n \right) =1+\frac { 1 }{ 2 } +\frac { 1 }{ 3 } +....+\frac { 1 }{ n } .\quad Then\quad f\left( 1 \right) +f\left( 2 \right) +f\left( 3 \right) +......+f\left( n \right) \quad is\quad equal\quad to$$

If $$f(x + \frac 1 2) + f(x - \frac 1 2) = f(x)$$,$$\forall\  x\ \epsilon\  R$$, then $$f(x-3) + f(x + 3)$$ is equal to 

If $$f(x)=\cfrac { 1 }{ \sqrt { x+2\sqrt { 2x-4 }  }  } +\cfrac { 1 }{ \sqrt { x-2\sqrt { 2x-4 }  }  } $$ for x > 2, then $$f(11)=$$

If n(A)=5 then number of relation on 'A' is:

If $$p,q$$ be non-zero real numbers and $$f\left(x\right)\neq 0$$ in $$\left[0,2\right]$$ and $${\int}_{0}^{1}f\left(x\right).\left(x^{2}+px+q\right)dx={\int}_{0}^{2}f\left(x\right).\left(x^{2}+px+q\right)dx=0$$ then equation $$x^{2}+px+q=0$$ has

Let $$f(n)=2cosnx\forall n\epsilon N$$, then $$f(1)f(n+1)-f(n)$$ is equal to 

For each positive integer $$n$$, let $$f\left(n + 1 \right) = n \left(-1\right)^{ n+1 } 2f\left(n\right) and f\left(1\right) = f\left(2010\right)$$. Then $$ \sum _{ K=1 }^{ 2009 }{ f\left( K \right)  } $$ is equal to

A non-zero function $$f (x)$$ is symmetrical about the line $$y = x$$ then the value of $$\lambda$$ such that:
$${ f }^{ 2 }(x)=({ f }^{ -1 }x))^{ 2 }-\lambda xf(x){ f }^{ -1 }(x)+3{ x }^{ 2 }f(x)\forall x\in R$$ is

Let $$f:(0, \infty) \rightarrow R $$ and $$\int^{2x}_0 (1+t)f(t) dt =-2x^3-\dfrac{x^2}{2} +2x+K$$, where K is constant , then $$\Sigma^8_{r=1} f(r)$$ is equal to