Let N be the set of natural numbers and a relation R on N be defined by R = x , y ∈ N × N : x 3 - 3 x 2 y - x y 2 + 3 y 3 = 0 . Then the relation R is

reflexive but neither symmetric nor transitive

symmetric but neither reflexive nor transitive

reflexive and symmetric, but not 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

MEDIUM

JEE Main

IMPORTANT

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Out of all the patients in a hospital $89 %$ are found to be suffering from heart ailment and $98 %$ are suffering from lungs infection. If $K %$ of them are suffering from both ailments, then $K$ can not belong to the set:

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Important Questions on Set Theory and Relations

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 27 August 2021 Shift 1>Q 2

A = {x \in R : | x - 2 | > 1}, B = \{x \in R : \sqrt{x^{2} - 3} > 1\}, C = {x \in R : | x - 4 | ⩾ 2}

and

Z

is the set of all integers, then the number of subsets of the set

(A \cap B \cap C)^{c} \cap Z

is _________.

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 31 August 2021 Shift 1>Q 3

Which of the following is not correct for relation

R

on the set of real numbers?

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 27 July 2021 Shift 2>Q 4

Let

N

be the set of natural numbers and a relation

R

N

be defined by

R = \{(x, y) \in N \times N : x^{3} - 3 x^{2} y - x y^{2} + 3 y^{3} = 0\}

. Then the relation

R

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 27 July 2021 Shift 2>Q 5

Let

A = \{n \in N ∣ n^{2} \leq n + 10, 000\}, B = \{3 k + 1 ∣ k \in N\}

and

C = \{2 k ∣ k \in N\},

then the sum of all the elements of the set

A \cap (B - C)

is equal to ________.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main 16 March 2021 Shift 2>Q 6

Let

A = \{2, 3, 4, 5, \dots ., 30\}

and

' ≃'

be an equivalence relation on

A \times A,

defined by

(a, b) ≃ (c, d),

if and only if

a d = b c

. Then the number of ordered pairs which satisfy this equivalence relation with ordered pair

(4, 3)

is equal to :

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main 17 March 2021 Shift 1>Q 7

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?

Question Image

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 ?

Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If K% of them are suffering from both ailments, then K can not belong to the set:

Important Questions on Set Theory and Relations

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Out of all the patients in a hospital $89 %$ are found to be suffering from heart ailment and $98 %$ are suffering from lungs infection. If $K %$ of them are suffering from both ailments, then $K$ can not belong to the set: