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JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 4 April 2024, Shift 2, Maths Q9

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

Let

f(x)=\int_0^x\left(t+\sin\left(1-e^t\right)\right)dt,\ x\in\mathbb{R}

. Then,

\lim_{x\to0}\frac{f(x)}{x^3}

is equal to

(1) $\frac{2}{3}$
(2) $-\frac{2}{3}$
(3) $\frac{1}{6}$
(4) $-\frac{1}{6}$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Limits and Derivatives
Topic: Leibniz Rule
Idea tested: Limit Evaluation

Same idea in other shifts

Asked 3× in all

9 Apr 2024, Shift 2 · Q9…HardSingle correct
24 Feb 2021, Shift 1 · Q66 $\lim_{x \to 0} \frac{\int_0^{x^2} (\sin\sqrt{t})\,dt}{x^3}$ is equal to :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 108 of the 174 JEE Main shifts held from 2017 to 2026.