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Friday, 9 October

JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 30 January 2024, Shift 2, Maths Q7

Question 7 of 90 in this shift, Maths question 7 of 30, Section A.

Let f:R−{0}→Rf: \mathbb{R} - \{0\} \to \mathbb{R} be a function satisfying f(xy)=f(x)f(y)f\left(\frac{x}{y}\right) = \frac{f(x)}{f(y)} for all x,y,f(y)≠0x, y, f(y) \neq 0. If f′(1)=2024f'(1) = 2024, then
  1. (1)xf′(x)−2024f(x)=0xf'(x) - 2024 f(x) = 0Official answer
  2. (2)xf′(x)+2024f(x)=0xf'(x) + 2024 f(x) = 0
  3. (3)xf′(x)−2023f(x)=0xf'(x) - 2023 f(x) = 0
  4. (4)xf′(x)+f(x)=2024xf'(x) + f(x) = 2024

Official answer

Option 1

NTA final key.

Chapter
Continuity and Differentiability
Topic
Continuity and Differentiability
Idea tested
Differentiability via Functional Equations

Same idea in other shifts

Asked 3× in all
  1. 5 Apr 2026, Shift 1 · Q19Let f:R→Rf: \mathbb{R} \to \mathbb{R} be a differentiable function such that f(x+y3)=f(x)+f(y)3f\left(\frac{x+y}{3}\right) = \frac{f(x)+f(y)}{3} for all…MediumSingle correct
  2. 2 Apr 2025, Shift 1 · Q14Let f:R→Rf:\mathbf{R}\to\mathbf{R} be a twice differentiable function such that…HardSingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.