JEE Main 2024 · MathsNumerical answerNumerical valueHardApplication

JEE Main 30 January 2024, Shift 1, Maths Q21

Question 21 of 90 in this shift, Maths question 21 of 30, Section B.

Let

A=\{1,2,3,\ldots,7\}

and let

P(A)

denote the power set of

A

. If the number of functions

f:A\to P(A)

such that

a\in f(a),\ \forall a\in A

m^n

m

and

n\in N

and

m

is least, then

m+n

is equal to __________.

Official answer

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

11 Apr 2023, Shift 2 · Q22Let $A = \{1, 2, 3, 4, 5\}$ and $B = \{1, 2, 3, 4, 5, 6\}$ . Then the number of functions $f : A \to B$ satisfying $f(1) + f(2) = f(4) - 1$ …MediumNumerical value
25 Jul 2022, Shift 1 · Q1The total number of functions, $f:\{1,2,3,4\}\rightarrow\{1,2,3,4,5,6\}$ such that $f(1)+f(2)=f(3)$ , is equal to :MediumSingle correct
27 Jul 2022, Shift 2 · Q22The number of functions f, from the set $A = \{x \in \mathbf{N} : x^2 - 10x + 9 \leq 0\}$ to the set $B = \{n^2 : n \in \mathbf{N}\}$ such…MediumNumerical value
26 Feb 2021, Shift 2 · Q62Let $A=\{1, 2, 3, \ldots, 10\}$ and $f : A \to A$ be defined as…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.