The probability that a relation R from $\{x, y\}$ to $\{x, y\}$ is both symmetric and transitive, is equal to

JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 29 June 2022, Shift 2, Maths Q16

Question 16 of 90 in this shift, Maths question 16 of 30, Section A.

The probability that a relation R from

\{x, y\}

\{x, y\}

is both symmetric and transitive, is equal to

(1) $\frac{5}{16}$ Official answer
(2) $\frac{9}{16}$
(3) $\frac{11}{16}$
(4) $\frac{13}{16}$

Official answer

Option 1

NTA final key.

Chapter: Probability
Topic: Sets and Relations
Idea tested: Counting Relations

Same idea in other shifts

Asked 14× in all

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7 Apr 2025, Shift 1 · Q24The number of relations on the set $A = \{1, 2, 3\}$ , containing at most 6 elements including $(1, 2)$ , which are reflexive and transitive…HardNumerical value
6 Apr 2024, Shift 2 · Q2Let $A=\{1,2,3,4,5\}$ . Let $R$ be a relation on $A$ defined by $xRy$ if and only if $4x\le 5y$ . Let $m$ be the number of elements in $R$ …MediumSingle correct
9 Apr 2024, Shift 1 · Q21Let $A=\{2,3,6,7\}$ and $B=\{4,5,6,8\}$ . Let R be a relation defined on $A\times B$ by $(a_1,b_1)\,R\,(a_2,b_2)$ if and only if…MediumNumerical value
1 Feb 2024, Shift 1 · Q21Let $A=\{1,2,3,\ldots,20\}$ . Let $R_1$ and $R_2$ two relation on A such that $R_1=\{(a,b): b$ is divisible by $a\}$ $R_2=\{(a,b): a$ is an…MediumNumerical value
30 Jan 2024, Shift 2 · Q21The number of symmetric relations defined on the set $\{1, 2, 3, 4\}$ which are not reflexive is ________.MediumNumerical value
6 Apr 2023, Shift 1 · Q21Let $A=\{1,2,3,4,\ldots,10\}$ and $B=\{0,1,2,3,4\}$ . The number of elements in the relation…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.