JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 9 April 2024, Shift 2, Maths Q9

Question 9 of 90 in this shift, Maths question 9 of 30, Section A.

\lim_{x\to\frac{\pi}{2}}\left(\frac{\int_{x^3}^{(\pi/2)^3}\left(\sin\left(2t^{1/3}\right)+\cos\left(t^{1/3}\right)\right)dt}{\left(x-\frac{\pi}{2}\right)^2}\right)

is equal to

(1) $\frac{3\pi^2}{2}$
(2) $\frac{5\pi^2}{9}$
(3) $\frac{9\pi^2}{8}$ Official answer
(4) $\frac{11\pi^2}{10}$

Official answer

Option 3

NTA final key.

Chapter: Integrals
Topic: Leibniz Rule
Idea tested: Limit Evaluation

Same topic in other shifts

All Leibniz Rule questions

4 Apr 2026, Shift 2 · Q25Let $f$ be a twice differentiable function such that $f(x)=\int_0^x\tan(t-x)\,dt-\int_0^x f(t)\tan t\,dt$ ,…HardNumerical value
5 Apr 2026, Shift 2 · Q19Let $f:[1,\infty)\to\mathbf{R}$ be a differentiable function defined as $f(x)=\int_1^x f(t)\,dt+(1-x)(\log_e x-1)+e$ . Then the value of…HardSingle correct
2 Apr 2025, Shift 2 · Q20Let $f : [1, \infty) \to [2, \infty)$ be a differentiable function. If $10\int_1^x f(t)\,\mathrm{d}t = 5xf(x) - x^5 - 9$ for all…MediumSingle 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.