JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 28 June 2022, Shift 2, Maths Q17

Question 17 of 90 in this shift, Maths question 17 of 30, Section A.

The probability that a randomly chosen one-one function from the set

\{a, b, c, d\}

to the set

\{1, 2, 3, 4, 5\}

satisfies

f(a)+2f(b)-f(c)=f(d)

is :

(1) $\frac{1}{24}$
(2) $\frac{1}{40}$
(3) $\frac{1}{30}$
(4) $\frac{1}{20}$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Probability
Topic: Permutations and Combinations
Idea tested: Number of Injective Functions

Same idea in other shifts

Asked 7× in all

5 Apr 2026, Shift 1 · Q21Let $A = \{1, 2, 3, 4, 5, 6\}$ . The number of one-one functions $f: A \to A$ such that $f(1) \geq 3$ , $f(3) \leq 4$ and $f(2) + f(3) = 5$ ,…MediumNumerical value
5 Apr 2024, Shift 1 · Q1Let $A=\{1,3,7,9,11\}$ and $B=\{2,4,5,7,8,10,12\}$ . Then the total number of one-one maps $f:A\to B$ , such that $f(1)+f(3)=14$ , is :MediumSingle correct
8 Apr 2024, Shift 1 · Q1Let $[t]$ be the greatest integer less than or equal to $t$ . Let $A$ be the set of all prime factors of 2310 and $f: A \to \mathbb{Z}$ be…MediumSingle correct
24 Jun 2022, Shift 1 · Q21The number of one-one functions $f:\{a, b, c, d\}\to\{0, 1, 2, \ldots, 10\}$ such that $2f(a)-f(b)+3f(c)+f(d)=0$ is ______.HardNumerical value
25 Feb 2021, Shift 2 · Q78Let $x$ denote the total number of one-one functions from a set A with 3 elements to a set B with 5 elements and $y$ denote the total…EasySingle correct
22 Jul 2021, Shift 2 · Q81Let $\mathrm{A}=\{0, 1, 2, 3, 4, 5, 6, 7\}$ . Then the number of bijective functions $f:\mathrm{A}\to\mathrm{A}$ such that…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.