JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 February 2021, Shift 2, Maths Q62

Question 62 of 90 in this shift, Maths question 2 of 30, Section A.

Let

A=\{1, 2, 3, \ldots, 10\}

and

f : A \to A

be defined as

f(k)=\begin{cases} k+1 & \text{if } k \text{ is odd} \\ k & \text{if } k \text{ is even} \end{cases}

Then the number of possible functions

g : A \to A

such that

g \circ f = f

is :

(1) $5!$
(2) ${}^{10}C_5$
(3) $5^5$
(4) $10^5$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Relations and Functions
Topic: Permutations and Combinations
Idea tested: Total Number of Functions

Same idea in other shifts

Asked 5× in all

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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.