Relations and F...

If $$f\left( x \right) = \cfrac{{{4^x}}}{{{4^x} + 2}}$$, then $$f\left( {\cfrac{1}{{97}}} \right) + f\left( {\cfrac{2}{{97}}} \right) + .... + f\left( {\cfrac{{96}}{{97}}} \right)$$ is equal to :

Let R be a relation from N to N defined by 
$$R = \left\{ {\left( {a,\,b} \right):a,\,b\, \in \,N\,\,and\,\,a = {b^2}} \right\}$$

If $$A = \{2, 3, 5\}$$ and $$B = \{5, 7\}$$, find the set with highest number of elements:

Let $$A = \left\{ {a,\,b,\,c} \right\}$$ and $$B = \left\{ {4,\,5} \right\}$$. Consider a relation defined from set A to set B, then R is equal to

Let $$A$$ and $$B$$ be two sets containing four and two elements respectively.Then the number of subset of the  set $$A \times B$$, each having at least three elements is 

If $$f:R \to R$$ is defined by $$f\left( x \right) = {x^2} - 3x + 2$$ and $$f\left( {{x^2} - 3x - 2} \right) = a{x^4} + b{x^3} + c{x^2} + dx + e$$ then $$a + b + c + d + e = $$

Let $$A = \left\{ {x,\,y,\,z} \right\}$$ and $$B = \left\{ {1,\,2} \right\}$$. The number relations from A to B is 

If $$f:R\rightarrow R$$ and $$g:R\rightarrow R$$ are defined by $$f\left( x \right) =x-\left[ x \right]$$ and $$ g\left( x \right) =\left[ x \right]$$  for $$x\in R$$,where $$[x]$$ is the greatest integer not exceeding $$x$$,then for every  $$x\in R$$,$$f(g(x))$$ is equal to

If $$A = \left \{1, 2, 3, 4\right \}$$ and $$I_{A}$$ be the identify relation on $$A$$, then

The number of pairs (a, b) of positive real numbers satisfying $$a^4+b^4 < 1$$ and $$a^2+b^2 > 1$$ is