Sets And Relations - Algebra - Mathematics Previous Year Questions

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

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

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

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

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

If \(A=\{3,5,7\}\) and \(B=\{1,2,3,5\}\), then \(A \times B \cap B \times A\) 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.

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

Which of the following is a singleton set?

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

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

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

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.

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

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

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

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