Which of the following relations on the set of real numbers $$\mathrm{R}$$ is an equivalence relation?

The shaded region in the Venn diagram represents

Two finite sets have '$$m$$' and '$$n$$' number of elements respectively. The total number of subsets of the first set is 112 more than the total number of subsets of the second set. Then the values of $$\mathrm{m}$$ and $$\mathrm{n}$$ are respectively.

$$ \text { If } a \mathcal{N}=\{a x: x \in \mathcal{N}\} \text {, then } 3 \mathcal{N} \cap 7 \mathcal{N} \text { is } $$

$$ \text { Let } \mathrm{A} \text { and } \mathrm{B} \text { be two sets then } A-(A \cap B) \text { is equal to } $$

A relation $$R$$ is defined from $$\{2,3,4\}$$ to $$\{3,6,7,10\}$$. If $$x R y \Leftrightarrow x$$ and $$y$$ are co prime numbers. Then range of $$R$$ is

$$\begin{aligned} &\begin{aligned} & \text { A, B, C are subsets of the Universal set U } \\ & \text { If } \mathrm{A}=\{x: x \text { is even number, } x \leq 20\} \\ & \mathrm{B}=\{x: x \text { is multiple of } 3, x \leq 15\} \\ & \mathrm{C}=\{x: x \text { is multiple of } 5, x \leq 20\} \\ & \mathrm{U}=\text { Set of whole numbers } \end{aligned}\\ &\text { then the Venn diagram representing } \mathrm{U}, \mathrm{A}, \mathrm{B} \text { and } \mathrm{C} \text { is } \end{aligned}$$

$$ \text { If } A=\{1,2,3,4,5\} \text { and } B=\{2,3,6,7\} \text { then number of elements in the set }(A \times B) \cap(B \times A) \text { is equal to } $$

Express the set $$A=\{1,7,17,31,49\}$$ in set builder form

If $$A=\{a, b, c\}, B=\{b, c, d\}$$ and $$C=\{a, d, c\}$$ then $$(A-B) \times(B \cap C)$$ is equal to

If $$n(A)=p$$ and $$n(B)=q$$, then the numbers of relations from the set $$A$$ to the set $$B$$ is

Which of the following is a singleton set?

Let $$X$$ and $$Y$$ be the set of all positive divisors of 400 and 1000 respectively (including 1 and the number). Then $$n(X \cap Y)$$ is equal to

In the set $$\mathrm{W}$$ of whole numbers an equivalence relation $$\mathrm{R}$$ is defined as follows $$\mathrm{aRb}$$ iff both $$\mathrm{a}$$ & $$\mathrm{~b}$$ leave the same reminder when divided by 5. The equivalence class of 1 is given by.

If $$A=\{3,5,7\}$$ and $$B=\{1,2,3,5\}$$, then $$A \times B \cap B \times A$$ is equal to

If A = {1, 2, 5, 6} and B = {1, 2, 3}, then (A $$\times$$ B) $$\cap$$ (B $$\times$$ A) is equal to

Total number of elements in the power set of A containing 15 elements is

In the group $$(G\,{ \otimes _{15}})$$, where $$G = \{ 3,6,9,12\} $$, $${ \otimes _{15}}$$ is multiplication modulo 15, the identity element is

A group (G *) has 10 elements. The minimum number of elements of G, which are their own inverses is

A graph G has m vertices of odd degree and ‘n’ vertices of even degree. Then which of the following statements is necessarily true?

Which of the following is not a group with respect to the given operation?