JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 3 August 2021, Shift 1, Maths Q78

Question 78 of 90 in this shift, Maths question 18 of 30, Section A.

Let

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)

(1) $\frac{1}{10}$
(2) $\frac{3}{20}$
(3) $\frac{1}{20}$
(4) $\frac{1}{15}$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Probability
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
28 Jun 2022, Shift 2 · Q29Let $S=\{1, 2, 3, 4\}$ . Then the number of elements in the set…HardNumerical value
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.