Relations Test ...

The number of ordered pairs $$\left( m,n \right)$$, where $$ m, n \in \left\{ 1,2,3,\dots ,50 \right\}$$, such that $$ { 6 }^{ m }+{ 9 }^{ n }$$ is a multiple of $$5$$ is

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

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 $$S$$ be a relation on $$\mathbb{R}^{+}$$ defined by $$xSy\Leftrightarrow { x }^{ 2 }-{ y }^{ 2 }=2\left( y-x \right)$$, then $$S$$ is

If $${C}_{r}$$ stands for $${ _{  }^{ n }{ C } }_{ r }$$ then $$\left( { C }_{ 0 }+{ C }_{ 1 } \right) +\left( { C }_{ 1 }+{ C }_{ 2 } \right) +....\left( { C }_{ n-1 }+{ C }_{ n } \right) \quad $$ is equal to

Let $$\rho$$ be a relation defined on$$N$$, the set of natural numbers, as
$$\rho =\left\{ \left( x,y \right) \in N\times N:2x+y=41 \right\} $$ then

For real values of x ,the range of $$\frac {x^2+2x+1}{X^2+2x-1}$$ is

Let $$R$$ be a relation defined as $$aRb$$ if $$1 + ab > 0$$, then the relation $$R$$ is

Let $$A=\left\{ a,b,c \right\} $$ and $$B=\left\{ 1,2 \right\} $$. Consider a relation $$R$$ defined from set $$A$$ to set $$B$$. Then $$R$$ is equal to set