JEE Main 2020 · MathsMultiple choiceSingle correctMediumConceptual

JEE Main 3 September 2020, Shift 2, Maths Q51

Question 51 of 75 in this shift, Maths question 1 of 25.

Let

R_1

and

R_2

be two relations defined as follows :

R_1 = \{(a, b) \in \mathbf{R}^2 : a^2 + b^2 \in Q\}

and

R_2 = \{(a, b) \in \mathbf{R}^2 : a^2 + b^2 \notin Q\}

, where Q is the set of all rational numbers. Then :

(1) $R_1$ and $R_2$ are both transitive.
(2) $R_1$ is transitive but $R_2$ is not transitive.
(3) $R_2$ is transitive but $R_1$ is not transitive.
(4)Neither $R_1$ nor $R_2$ is transitive.Official answer

Official answer

Option 4

NTA final key (Sep 2020).

Chapter: Relations and Functions
Topic: Sets and Relations
Idea tested: Relation Types

Same idea in other shifts

Asked 12× in all

4 Apr 2025, Shift 2 · Q2Let $A=\{-3,-2,-1,0,1,2,3\}$ and R be a relation on A defined by $xRy$ if and only if $2x-y\in\{0,1\}$ . Let $l$ be the number of elements…MediumSingle correct
8 Apr 2025, Shift 2 · Q1Let $A = \{0, 1, 2, 3, 4, 5\}$ . Let $R$ be a relation on $A$ defined by $(x, y) \in R$ if and only if $\max\{x, y\} \in \{3, 4\}$ . Then…MediumOther
4 Apr 2024, Shift 2 · Q1Let a relation R on $\mathbb{N}\times\mathbb{N}$ be defined as: $(x_1,y_1)\ \mathrm{R}\ (x_2,y_2)$ if and only if $x_1\le x_2$ or…MediumTwo statements
6 Apr 2024, Shift 1 · Q1Let the relations $R_1$ and $R_2$ on the set $X = \{1, 2, 3, \ldots., 20\}$ be given by $R_1 = \{(x, y): 2x - 3y = 2\}$ and…MediumSingle correct
8 Apr 2024, Shift 2 · Q1Let $A = \{2, 3, 6, 8, 9, 11\}$ and $B = \{1, 4, 5, 10, 15\}$ . Let R be a relation on $A \times B$ defined by $(a, b)R(c, d)$ if and only…HardSingle correct
27 Jan 2024, Shift 1 · Q1Let $S=\{1,2,3,\ldots,10\}$ . Suppose M is the set of all the subsets of S, then the relation $R=\{(A,B): A\cap B\neq\phi;\ A,B\in M\}$ is :EasySingle correct
29 Jan 2024, Shift 1 · Q2Let R be a relation on $\mathbb{Z}\times\mathbb{Z}$ defined by $(a, b)\,R\,(c, d)$ if and only if $ad-bc$ is divisible by 5. Then R isMediumSingle correct
31 Jan 2024, Shift 2 · Q21Let $A=\{1,2,3,\ldots,100\}$ . Let $R$ be a relation on $A$ defined by $(x,y)\in R$ if and only if $2x=3y$ . Let $R_1$ be a symmetric…MediumNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.