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Friday, 9 October

JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 8 April 2024, Shift 1, Maths Q1

Question 1 of 90 in this shift, Maths question 1 of 30, Section A.

Let [t][t] be the greatest integer less than or equal to tt. Let AA be the set of all prime factors of 2310 and f:A→Zf: A \to \mathbb{Z} be the function f(x)=[log⁡2(x2+[x35])]f(x)=\left[\log_2\left(x^2+\left[\frac{x^3}{5}\right]\right)\right]. The number of one-to-one functions from AA to the range of ff is
  1. (1)2020
  2. (2)2424
  3. (3)120120Official answer
  4. (4)2525

Official answer

Option 3

NTA final key.

Chapter
Relations and Functions
Topic
Permutations and Combinations
Idea tested
Number of Injective Functions

Same idea in other shifts

Asked 3× in all
  1. 5 Apr 2026, Shift 1 · Q21Let A={1,2,3,4,5,6}A = \{1, 2, 3, 4, 5, 6\}. The number of one-one functions f:A→Af: A \to A such that f(1)≥3f(1) \geq 3, f(3)≤4f(3) \leq 4 and f(2)+f(3)=5f(2) + f(3) = 5,…MediumNumerical value
  2. 24 Jun 2022, Shift 1 · Q21The number of one-one functions f:{a,b,c,d}→{0,1,2,…,10}f:\{a, b, c, d\}\to\{0, 1, 2, \ldots, 10\} such that 2f(a)−f(b)+3f(c)+f(d)=02f(a)-f(b)+3f(c)+f(d)=0 is ______.HardNumerical 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 42 of the 174 JEE Main shifts held from 2017 to 2026.