Relations and F...

If $$ n (A) = 5 $$ and $$ n (B) = 7 , $$ then the number of relations on $$ A \times B $$ is :

The functions $$f, g$$ and $$h$$ satisfy the relations $$f^{ ' }\left( x \right) =g\left( x+1 \right) $$ and $$g^{ ' }\left( x \right) =h\left( x-1 \right) $$. Then, $$f^{ '' }\left( 2x \right) $$ is equal to

Let $$ \phi (x) = \dfrac {b(x-a)}{b-a} + \dfrac {a(x-b)}{a-b} , $$ where $$ x \epsilon R $$ and $$a$$ and $$b$$  are fixed real numbers with $$ a \ne b. $$ Then $$ \phi ( a + b) $$ is equal to :

If two sets $$A$$ and $$B$$ are having $$39$$ elements in common, then the number of elements common to each of the sets $$A\times B$$ and $$B\times A$$ are

Let $$n$$ be a fixed positive integer. Define a relation $$R$$ in the set $$Z$$ of integers by $$aRb$$ if and only if $$\dfrac {n}{a - b}$$. The relation $$R$$ is

A function $$f$$ satisfies the relation $$f\left( { n }^{ 2 } \right) =f\left( n \right) +6$$ for $$n\ge 2$$ and $$f\left( 2 \right) =8$$. Then, the value of $$f\left( 256 \right) $$ is

Number of distinct real roots of the equation $$f(x) = 0$$, is

Let $$ A = \{ 1,2,3,4 \} $$ and $$R$$ be a relation in $$A$$ given by $$ R = \{ (1,1) , (2,2) (3,3) , (4,4) , (1,2) , (3,1) , (1,3) \} $$ then $$R$$ is :

The graph of a constant function $$f(x)=k$$ is?

If $$f,g,h$$ are three functions from a set of positive real numbers into itself satisfying the condition,
$$f(x) \cdot g(x)=h \sqrt{x^2 + y^2}$$ such that $$x,y \epsilon (0,\infty)$$.then, $$\dfrac{f(x)}{g(x)}$$ is a?