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 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

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

Earn 100

Let $N$ be the set of natural numbers and a relation $R$ on $N$ 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 $R$ is

44.44% 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 - 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 ________.

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

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:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 4 September 2020 Shift 2>Q 16

Let $\cup_{i = 1}^{50} X_{i} = \cup_{i = 1}^{n} Y_{i} = T$ , where each $X_{i}$ contains $10$ elements and each $Y_{i}$ contains $5$ elements. If each element of the set $T$ is an element of exactly $20$ of sets $X_{i}$ 's and exactly $6$ of sets $Y_{i}$ 's then $n$ is equal to :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 6 September 2020 Shift 1>Q 18

Set

A

has

m

elements and set

B

has

n

elements. If the total number of subsets of

A

112

more than the total number of subsets of

B

, then the value of

m \cdot n

is___.

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 7th January 2020 Shift 2>Q 19

Let

X = \{n \in N : 1 \leq n \leq 50\}

. If

A = \{n \in X : n is a multiple of 2\}

and

B = \{n \in X : n is a multiple of 7\}

, then the number of elements in the smallest subset of

X

, containing both

A

and

B

, is.

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 15th April 2018>Q 26

Consider the following two binary relations on the set

A = \{a, b, c\} : R_{1} = \{(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)\}

and

R_{2} = \{(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)\}

, then :

Let N be the set of natural numbers and a relation R on N be defined by R=x,y∈N×N:x3-3x2y-xy2+3y3=0. Then the relation R is

Important Questions on Set Theory and Relations

Learn and Prepare for any exam you want !

Let $N$ be the set of natural numbers and a relation $R$ on $N$ 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 $R$ is