JEE Main 2021 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 3 August 2021, Shift 2, Maths Q68

Question 68 of 90 in this shift, Maths question 8 of 30, Section A.

\lim_{x\to0}(1+x)^{\frac{1}{e^x-1}}

is equal to

(1) $0$
(2) $1$
(3) $e$ Official answer
(4) $e^e$

Official answer

Option 3

NTA final key.

Chapter: Limits and Derivatives
Topic: L'Hopital's Rule
Idea tested: Indeterminate Power Forms

Same idea in other shifts

Asked 3× in all

3 Apr 2025, Shift 2 · Q25If $\lim_{x \to 0}\left(\frac{\tan x}{x}\right)^{\frac{1}{x^2}} = p$ , then $96 \log_e p$ is equal to ___________.MediumNumerical value
9 Apr 2024, Shift 2 · Q5 $\lim_{x\to0}\frac{e-(1+2x)^{\frac{1}{2x}}}{x}$ is equal toHardSingle 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.