Sets and Relations PYQs - Last 10 Years

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Practice 38 COMEDK Mathematics questions from Sets and Relations. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Last 10 Years Sets and Relations Questions

Showing 38 of 38 filtered questions.

1Sets And Relations

If $A=\{x: x$ is the first three odd numbers $\}$
$B=\{2 x+3: 0 \leq x<5, x \in \mathbb{N}\}$, then which of the following is true

2Sets And Relations

The set expression $A \cup\left(B \cap\left(A^{\prime} \cup B^{\prime}\right)\right)$ is equivalent to

3Sets And Relations

Consider the following list of ordered pairs: $(1,0),(-2,-1),(7,-6),(-3,4)$ and $(0,2)$
Which of the following options correctly identifies only those pairs that are NOT elements of the relation $R=\{(x, y): y=1-|x| ; x, y \in \mathbb{Q}\}$...

4Sets And Relations

A student needs to buy notebooks $(n)$ for a semester. Double the number of notebooks plus 5 must strictly exceed 15 , but the number of notebooks plus 10 must be no more than 22 . What is the range of notebooks they can buy?

5Sets And Relations

\(\text { The range of the relation } R=\left\{(x, y): y=x+\frac{6}{x} \text {; where } x, y \in \mathbb{N} \text { and } x<6\right\} \text { is: }\)

6Sets And Relations

Let $A$ and $B$ be two subsets of $\xi=\{\mathbf{1}, \mathbf{2}, \mathbf{3},-------, \mathbf{4 4}, \mathbf{4 5}\}$ such that
$A=\{x: x$ is divisible by 3 and 4$\}$
$B=\{x: x$ is a perfect square number $\}$
Then $n(B-A)$ equals

7Sets And Relations

Given the sets $A=\{1,2,3\} ; B=\{2,3,5\}$ and $C=\{4,5,6\}$ identify which of the following statement is incorrect.

8Sets And Relations

If $n(A)=3$ and $n(B)=7$ and $A \subseteq B$ then the number of elements in $A \cap B$ is equal to

9Sets And Relations

Identify the correct statement

10Sets And Relations

Let R be a relation on natural numbers defined by $x+2 y=8, x, y \in N$. The domain of R is

11Sets And Relations

Two finite sets have $m$ and $n$ elements. The total number of proper subsets of the first set is 119 more than the total number of subsets of the second set. Find the value of $m-n$

12Sets And Relations

The relation $R=\{(1,1),(2,2),(3,3)\}$ on the set $\{1,2,3\}$ is

13Sets And Relations

If $P=\{5 m: m \in N\}$ and $Q=\left\{5^m: m \in N\right\}$, where $N$ is set of natural numbers, then

14Sets And Relations

The inequality representing the following graph is

15Sets And Relations

Let $A=\{x: x=4 n+1, n \in Z, 0 \leq n<4\}$
$$\begin{aligned} & B=\{x: x=15 n+4, n \in N, n \leq 3\} \\ & C=\{x: x \text { is a prime number }, x \in A \cup B\} \end{aligned}$$
Then the cardinal number of set C is

16Sets And Relations

If $A=\{1,2,4\} \quad B=\{2,4,5\} \quad C=\{2,5\}$ then $(A-B) \cap(B-C)=$

17Sets And Relations

For real numbers $x$ and $y, x R y \Leftrightarrow x-y+\sqrt{2}$ is an irrational number. Then the relation R is:

18Sets And Relations

$$\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{...

19Sets And Relations

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

20Sets And Relations

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

21Sets And Relations

The shaded region in the Venn diagram represents

22Sets And Relations

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

23Sets And Relations

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 ...

24Sets And Relations

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

25Sets And Relations

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

26Sets And Relations

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

27Sets And Relations

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

28Sets And Relations

Which of the following is a singleton set?

29Sets And Relations

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 give...

30Sets And Relations

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

31Sets And Relations

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

32Sets And Relations

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

33Sets And Relations

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

34Sets And Relations

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

35Sets And Relations

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

36Sets And Relations

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

37Sets And Relations

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

38Sets And Relations

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