JEE Main 2020 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 8 January 2020, Shift 2, Maths Q58

Question 58 of 75 in this shift, Maths question 8 of 25, Section A.

\lim_{x \to 0} \frac{\int_0^x t \sin(10t)\,dt}{x}

is equal to :

(1) $-\frac{1}{5}$
(2) $\frac{1}{10}$
(3) $-\frac{1}{10}$
(4) $0$ Official answer

Official answer

Option 4

NTA final key (Jan 2020).

Chapter: Integrals
Topic: L'Hopital's Rule
Idea tested: L'Hopital with Leibniz Rule

Same idea in other shifts

Asked 3× in all

29 Jan 2024, Shift 1 · Q8…MediumSingle correct
30 Jan 2024, Shift 1 · Q8Let $f:\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\to\mathbf{R}$ be a differentiable function such that $f(0)=\frac{1}{2}$ . If…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.