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\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) $\frac{3\pi}{4}$
(2) $\frac{3\pi}{8}$
(3) $\frac{3\pi^2}{4}$
(4) $\frac{3\pi^2}{8}$ 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 topic in other shifts

All L'Hopital's Rule questions

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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.