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Saturday, 31 October

JEE Main 2024 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 30 January 2024, Shift 1, Maths Q8

Question 8 of 90 in this shift, Maths question 8 of 30, Section A.

Let f:[−π2,π2]→Rf:\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\to\mathbf{R} be a differentiable function such that f(0)=12f(0)=\frac{1}{2}. If lim⁡x→0x∫0xf(t)dtex2−1=α\lim_{x\to0}\frac{x\int_0^x f(t)dt}{e^{x^2}-1}=\alpha, then 8α28\alpha^2 is equal to :
  1. (1)11
  2. (2)22Official answer
  3. (3)44
  4. (4)1616

Official answer

Option 2

NTA final key.

Chapter
Integrals
Topic
L'Hopital's Rule
Idea tested
L'Hopital with Leibniz Rule

Same idea in other shifts

Asked 3× in all
  1. 29 Jan 2024, Shift 1 · Q8…MediumSingle correct
  2. 8 Jan 2020, Shift 2 · Q58lim⁡x→0∫0xtsin⁡(10t) dtx\lim_{x \to 0} \frac{\int_0^x t \sin(10t)\,dt}{x} is equal to :EasySingle 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.