Let R 1 and R 2 be two relations defined as follows : R 1 = a , b ∈ R 2 : a 2 + b 2 ∈ Q and R 2 = a , b ∈ R 2 : a 2 + b 2 ∉ Q , where Q is the set of all rational numbers, then

Neither R 1 nor R 2 is transitive.

R 1 is transitive but R 2 is not transitive.

R 2 is transitive but R 1 is not transitive.

R 1 and R 2 are both transitive.

Let P S denote the power set of S = 1 , 2 , 3 , … , 10 . Define the relations R 1 and R 2 on P S as A R 1 B if A ∩ B c ∪ B ∩ A c = ϕ and A R 2 B if A ∪ B c = B ∪ A c , ∀ A , B ∈ P S . Then :

both R 1 and R 2 are equivalence relations

only R 1 is an equivalence relation

only R 2 is an equivalence relation

both R 1 and R 2 are not equivalence relations

Let R be a relation on ℝ , given by R = { a , b : 3 a - 3 b + 7 is an irrational number } . Then R is

Reflexive but neither symmetric nor transitive

Reflexive and transitive but not symmetric

Reflexive and symmetric but not transitive

Let R be a relation on N × N defined by a , b R c , d if and only if a d b - c = b c a - d . Then R is

symmetric but neither reflexive nor transitive

transitive but neither reflexive nor symmetric

reflexive and symmetric but not transitive

symmetric and transitive but not reflexive

The relation R = a , b : g c d a , b = 1 , 2 a ≠ b , a , b ∈ ℤ is:

neither symmetric nor transitive

EASY

JEE Main

IMPORTANT

Earn 100

In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement?

50% studentsanswered this correctly

Important Questions on Set Theory and Relations

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main 17 March 2021 Shift 2>Q 8

Let $S_{1}, S_{2}$ and $S_{3}$ be three sets defined as

$S_{1} = {z \in ℂ : | z - 1 | \leq \sqrt{2}},$

$S_{2} = {z \in ℂ : R e ((1 - i) z) \geq 1}$ and

$S_{3} = {z \in ℂ : I m (z) \leq 1} .$

Then, the set $S_{1} \cap S_{2} \cap S_{3}$

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main 18 March 2021 Shift 2>Q 9

Define a relation $R$ over a class of $n \times n$ real matrices $A$ and $B$ as " $A R B$ iff there exists a non-singular matrix $P$ such that $P A P^{- 1} = B$ ". Then which of the following is true ?

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 24 Feb 2021 Shift 1>Q 10

Let

A = {n \in N : n

is a

3 -

digit number

}

B = \{9 k + 2 : k \in N\}

and

C = \{9 k + l : k \in N\}

for some

l (0 < l < 9)

. If the sum of all the elements of the set

A \cap (B \cup C)

274 \times 400,

then

l

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 26 Feb 2021 Shift 1>Q 11

Let

R = {(P, Q) | P

and

Q

are at the same distance from the origin

}

be a relation, then the equivalence class of

(1, - 1)

is the set

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 2 September 2020 Shift 1>Q 12

R = \{(x, y) : x, y \in Z, x^{2} + 3 y^{2} \leq 8\}

is a relation on the set of integers

Z

, then the domain of

R^{- 1}

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 3 September 2020 Shift 1>Q 13

Consider the two sets:

A = {m \in R :

both the roots of

x^{2} - (m + 1) x + m + 4 = 0

are real

}

and

B = [- 3, 5)

Which of the following is not true?

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 3 September 2020 Shift 2>Q 14

Let

R_{1}

and

R_{2}

be two relations defined as follows :

$R_{1} = \{(a, b) \in R^{2} : a^{2} + b^{2} \in Q\}$ and $R_{2} = \{(a, b) \in R^{2} : a^{2} + b^{2} \notin Q\}$ , where $Q$ is the set of all rational numbers, then

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 4 September 2020 Shift 1>Q 15

A survey shows that

63 %

of the people in a city read newspaper

A

whereas

76 %

read news paper

B

. If

x %

of the people read both the newspapers, then a possible value of

x

can be:

In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement?

Important Questions on Set Theory and Relations

Learn and Prepare for any exam you want !