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 :