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Saturday, 31 October

JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 29 January 2024, Shift 1, Maths Q8

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

lim⁡x→π2(1(x−π2)2∫x3(π2)3cos⁡(t13)dt)\lim_{x\to\frac{\pi}{2}}\left(\frac{1}{\left(x-\frac{\pi}{2}\right)^2}\int_{x^3}^{\left(\frac{\pi}{2}\right)^3}\cos\left(t^{\frac{1}{3}}\right)dt\right) is equal to
  1. (1)3π4\frac{3\pi}{4}
  2. (2)3π8\frac{3\pi}{8}
  3. (3)3π24\frac{3\pi^2}{4}
  4. (4)3π28\frac{3\pi^2}{8}Official answer

Official answer

Option 4

NTA final key.

Chapter
Limits and Derivatives
Topic
L'Hopital's Rule
Idea tested
L'Hopital with Leibniz Rule

Same idea in other shifts

Asked 3× in all
  1. 30 Jan 2024, Shift 1 · Q8Let 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…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.