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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumConceptual

JEE Main 31 August 2021, Shift 1, Maths Q61

Question 61 of 90 in this shift, Maths question 1 of 30, Section A.

Which of the following is not correct for relation R on the set of real numbers ?
  1. (1)(x,y)∈R⇔∣x−y∣≤1(x, y) \in R \Leftrightarrow |x-y| \leq 1 is reflexive and symmetric.
  2. (2)(x,y)∈R⇔∣x∣−∣y∣≤1(x, y) \in R \Leftrightarrow |x|-|y| \leq 1 is reflexive but not symmetric.
  3. (3)(x,y)∈R⇔0<∣x∣−∣y∣≤1(x, y) \in R \Leftrightarrow 0 < |x|-|y| \leq 1 is neither transitive nor symmetric.
  4. (4)(x,y)∈R⇔0<∣x−y∣≤1(x, y) \in R \Leftrightarrow 0 < |x-y| \leq 1 is symmetric and transitive.Official answer

Official answer

Option 4

NTA final key.

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

Same idea in other shifts

Asked 12× in all
  1. 4 Apr 2025, Shift 2 · Q2Let A={−3,−2,−1,0,1,2,3}A=\{-3,-2,-1,0,1,2,3\} and R be a relation on A defined by xRyxRy if and only if 2x−y∈{0,1}2x-y\in\{0,1\}. Let ll be the number of elements…MediumSingle correct
  2. 8 Apr 2025, Shift 2 · Q1Let A={0,1,2,3,4,5}A = \{0, 1, 2, 3, 4, 5\}. Let RR be a relation on AA defined by (x,y)∈R(x, y) \in R if and only if max⁡{x,y}∈{3,4}\max\{x, y\} \in \{3, 4\}. Then…MediumOther
  3. 4 Apr 2024, Shift 2 · Q1Let a relation R on N×N\mathbb{N}\times\mathbb{N} be defined as: (x1,y1) R (x2,y2)(x_1,y_1)\ \mathrm{R}\ (x_2,y_2) if and only if x1≤x2x_1\le x_2 or…MediumTwo statements
  4. 6 Apr 2024, Shift 1 · Q1Let the relations R1R_1 and R2R_2 on the set X={1,2,3,….,20}X = \{1, 2, 3, \ldots., 20\} be given by R1={(x,y):2x−3y=2}R_1 = \{(x, y): 2x - 3y = 2\} and…MediumSingle correct
  5. 8 Apr 2024, Shift 2 · Q1Let A={2,3,6,8,9,11}A = \{2, 3, 6, 8, 9, 11\} and B={1,4,5,10,15}B = \{1, 4, 5, 10, 15\}. Let R be a relation on A×BA \times B defined by (a,b)R(c,d)(a, b)R(c, d) if and only…HardSingle correct
  6. 27 Jan 2024, Shift 1 · Q1Let S={1,2,3,…,10}S=\{1,2,3,\ldots,10\}. Suppose M is the set of all the subsets of S, then the relation R={(A,B):A∩B≠ϕ; A,B∈M}R=\{(A,B): A\cap B\neq\phi;\ A,B\in M\} is :EasySingle correct
  7. 29 Jan 2024, Shift 1 · Q2Let R be a relation on Z×Z\mathbb{Z}\times\mathbb{Z} defined by (a,b) R (c,d)(a, b)\,R\,(c, d) if and only if ad−bcad-bc is divisible by 5. Then R isMediumSingle correct
  8. 31 Jan 2024, Shift 2 · Q21Let A={1,2,3,…,100}A=\{1,2,3,\ldots,100\}. Let RR be a relation on AA defined by (x,y)∈R(x,y)\in R if and only if 2x=3y2x=3y. Let R1R_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.