JEE Main 2021 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 24 February 2021, Shift 1, Maths Q66

Question 66 of 90 in this shift, Maths question 6 of 30, Section A.

\lim_{x \to 0} \frac{\int_0^{x^2} (\sin\sqrt{t})\,dt}{x^3}

is equal to :

(1) $\frac{2}{3}$ Official answer
(2) $\frac{3}{2}$
(3) $\frac{1}{15}$
(4) $0$

Official answer

Option 1

NTA final key.

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

Same idea in other shifts

Asked 3× in all

4 Apr 2024, Shift 2 · Q9Let $f(x)=\int_0^x\left(t+\sin\left(1-e^t\right)\right)dt,\ x\in\mathbb{R}$ . Then, $\lim_{x\to0}\frac{f(x)}{x^3}$ is equal toHardSingle correct
9 Apr 2024, Shift 2 · Q9…HardSingle 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.