JEE Main 2021 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 25 February 2021, Shift 2, Maths Q78

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

Let

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 number of one-one functions from the set A to the set

A \times B

. Then :

(1) $2y = 91x$ Official answer
(2) $2y = 273x$
(3) $y = 91x$
(4) $y = 273x$

Official answer

Option 1

NTA final key.

Chapter: Relations and Functions
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
28 Jun 2022, Shift 2 · Q17The probability that a randomly chosen one-one function from the set $\{a, b, c, d\}$ to the set $\{1, 2, 3, 4, 5\}$ satisfies…HardSingle 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.