EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 30 January 2023 Shift 1>Q 47

MEDIUM

JEE Main

IMPORTANT

Earn 100

The minimum number of elements that must be added to the relation $R = (a, b), (b, c)$ on the set ${a, b, c}$ so that it becomes symmetric and transitive is:

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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 - 31 January 2023 Shift 1>Q 48

Let

R

be a relation on

N \times N

defined by

(a, b) R (c, d)

if and only if

a d (b - c) = b c (a - d)

. Then

R

is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 31 January 2023 Shift 2>Q 49

Among the relations

S = \{(a, b) : a, b \in R - \{0\}, 2 + \frac{a}{b} > 0\}

and

T = \{(a, b) : a, b \in R, a^{2} - b^{2} \in Z\}

,

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 1 February 2023 Shift 1>Q 50

Let

R

be a relation on

ℝ

, given by

R = {(a, b) : 3 a - 3 b + \sqrt{7}

is an irrational number

}

. Then

R

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 1 February 2023 Shift 2>Q 51

Let

P (S)

denote the power set of

S = \{1, 2, 3, \dots, 10\}

. Define the relations

R_{1}

and

R_{2}

on

P (S)

as

A R_{1} B

if

(A \cap B^{c}) \cup (B \cap A^{c}) = ϕ

and

A R_{2} B

if

A \cup B^{c} = B \cup A^{c}, \forall A, B \in P (S)

. Then :