JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 28 June 2022, Shift 2, Maths Q29

Question 29 of 90 in this shift, Maths question 29 of 30, Section B.

Let

S=\{1, 2, 3, 4\}

. Then the number of elements in the set

\{f : S\times S\to S : f \text{ is onto and } f(a, b)=f(b, a) \geq a\ \forall\ (a, b) \in S\times S\}

is __________.

Official answer

NTA final key.

Chapter: Relations and Functions
Topic: Permutations and Combinations
Idea tested: Number of Surjective (Onto) Functions

Same idea in other shifts

Asked 6× in all

2 Apr 2026, Shift 1 · Q6The number of seven-digit numbers, that can be formed by using the digits $1, 2, 3, 5$ and $7$ such that each digit is used at least once,…MediumSingle correct
4 Apr 2026, Shift 1 · Q4The number of functions $f:\{1,2,3,4\}\to\{a,b,c\}$ , which are not onto, is:EasySingle correct
6 Apr 2023, Shift 1 · Q23The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is ____________MediumNumerical value
3 Aug 2021, Shift 1 · Q78Let $A = \{0, 1, 2, 3, 4, 5\}$ . Then the probability that a randomly selected onto function $f$ from A to A satisfies $f(1) + f(2) = f(3)$ …HardSingle correct
31 Aug 2021, Shift 2 · Q76Let $\mathrm{S} = \{1, 2, 3, 4, 5, 6\}$ . Then the probability that a randomly chosen onto function $\mathrm{g}$ from S to S satisfies…MediumSingle correct

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.