Relations Test ...

If $A$ is a finite set having $n$ elements, then the number of relations which can be defined in $A$ is

Let X be the set of all citizens of India. Elements x, y in X are said to be related if the difference of their age is 5 years. Which one of the following is correct ?

Let R be a relation from A = {1, 2, 3, 4} to B = {1, 3, 5} such that
R = [(a, b) : a < b, where a $\varepsilon$ A and b $\varepsilon$ B].
What is RoR$^{-1}$ equal to?

Find the correct co-related number.
$5:36::6:?$ 

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 :

How many ordered pairs of (m, n) integers satisfy $\displaystyle\frac{m}{12}=\frac{12}{n}$?

If ${ y }^{ 2 }={ x }^{ 2 }-x+1$ and $\quad { I }_{ n }=\int { \cfrac { { x }^{ n } }{ y }  } dx$ and $A{ I }_{ 3 }+B{ I }_{ 2 }+C{ I }_{ 1 }={ x }^{ 2 }y$ then ordered triplet $A,B,C$ is

The number of ordered pairs $(x, y)$ of real numbers that satisfy the simultaneous equations.
$x + y^{2} = x^{2} + y = 12$ is.

$R$ is a relation on $N$ given by $R = \left \{(x, y)|4x + 3y = 20\right \}$. Which of the following doesnot belong to $R$?

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