JEE Main 2021 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 25 February 2021, Shift 2, Maths Q84

Question 84 of 90 in this shift, Maths question 24 of 30, Section B.

\lim_{x\to 0} \frac{ax - (e^{4x} - 1)}{ax(e^{4x} - 1)}

exists and is equal to b, then the value of

a - 2b

is ________.

Official answer

NTA final key.

Chapter: Limits and Derivatives
Topic: L'Hopital's Rule
Idea tested: Determining Unknown Constants from Finite Limits

Same idea in other shifts

Asked 6× in all

2 Apr 2026, Shift 1 · Q16If $\lim_{x\to2}\frac{\sin\left(x^3-5x^2+ax+b\right)}{\left(\sqrt{x-1}-1\right)\log_e(x-1)}=m$ , then $a+b+m$ is equal to :HardSingle correct
2 Apr 2025, Shift 1 · Q7For $\alpha, \beta, \gamma\in\mathbf{R}$ , if $\lim_{x\to0}\frac{x^2\sin\alpha x+(\gamma-1)e^{x^2}}{\sin2x-\beta x}=3$ , then…MediumSingle correct
2 Apr 2025, Shift 2 · Q17If $\lim_{x\to0} \frac{\cos(2x) + a\cos(4x) - b}{x^4}$ is finite, then $(a+b)$ is equal to :MediumSingle correct
25 Jul 2022, Shift 1 · Q5If $\lim_{n\to\infty}\left(\sqrt{n^2-n-1}+n\alpha+\beta\right)=0$ , then $8(\alpha+\beta)$ is equal to :MediumSingle correct
29 Jul 2022, Shift 1 · Q5If $\lim_{x \to 0} \frac{\alpha e^x + \beta e^{-x} + \gamma \sin x}{x \sin^2 x} = \frac{2}{3}$ , where…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.