Relations and F...

If $$ f(2x+3y,2x-7y)=20x$$,then $$ f(x,y)$$ equal to

If $$f(x) = \cos (\log x)$$, then $$f(x)\, f(y)\, -\, \displaystyle \frac{1}{2}\, [f\left(\dfrac{x}{y}\right)\, +\, f(xy)]$$ is equal to :

Let $$A$$ and $$B$$ be two finite sets having $$m$$ and $$n$$ elements respectively. Then the total number of mapping from $$A$$ to $$B$$ is:

$$A$$ and $$B$$ are two sets having $$3$$ and $$4$$ elements respectively and having $$2$$ elements in common. The number of relations which can be defined from $$A$$ to $$B$$ is

If $$A=\left\{ 1,2,3 \right\} , B=\left\{ 1,4,6,9 \right\} $$ and $$R$$ is a relation from $$A$$ to $$B$$ defined by '$$x$$ is greater than $$y$$'. Then range of $$R$$ is

Let $$g\left( x \right)=1+x-\left[ x \right] $$ and $$f\left( x \right)=\begin{cases} \begin{matrix} -1 & x<0 \end{matrix} \\ \begin{matrix} 0 & x=0 \end{matrix} \\ \begin{matrix} 1 & x>0 \end{matrix} \end{cases}$$. Then for all $$x,f\left[ g\left( x \right) \right] $$ is equal to

If $$A = \left\{1,2,3\right\}$$, $$B = \left\{1,4,6,9\right\}$$ and $$R$$ is relation from $$A$$ to $$B$$ defined by $$'x'$$ is greater than $$'y'$$. Then range of $$R$$ is

Given the relation $$R = \left\{(1,2), (2,3)\right\}$$ on the set $$A = \left\{1,2,3\right\}$$, the minimum number of ordered pairs which when added to $$R$$ make it an equivalence relation is

If $$A = \left\{2,3\right\}$$ and $$B = \left\{1,2\right\}$$, then $$A \times B$$ is equal to 

Let $$n(A) = n$$. Then the number of all relations on $$A$$ is