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Saturday, 31 October

JEE Main · Maths · Limits and Derivatives

Choosing Series Expansion over L'Hopital

JEE Main asked Choosing Series Expansion over L'Hopital 10 times in 10 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2023, 2024, 2025 and 2026. It belongs to L'Hopital's Rule, in Limits and Derivatives (Maths). The longest wait between two years asking it was 1 year. In 2021, 2022 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
10
in 10 shifts
Years
7 of 8
First asked
2020
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022, 2023, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170.08’200.07’210.07’220.07’230.09’240.13’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 2 in 24 shifts · 2022: 2 in 24 shifts · 2023: 1 in 12 shifts · 2024: 2 in 18 shifts · 2025: 1 in 8 shifts · 2026: 1 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20261 of 9
  • 20251 of 8
  • 20242 of 18
  • 20231 of 12
  • 20222 of 24
  • 20212 of 24
  • 20201 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: calculation.

  • Unknown constants from finite limit
  • Limit of indeterminate trig expression

Difficulty

Easy 0Medium 8Hard 2

3 of the 10 questions had a numerical answer.

Every question

All 10 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 6 Apr 2026, Shift 1 · Q17The value of lim⁡x→0(x2sin⁡2xx2−sin⁡2x)\lim_{x\to 0}\left(\frac{x^2\sin^2 x}{x^2-\sin^2 x}\right) is:MediumSingle correct
  2. 8 Apr 2025, Shift 2 · Q16Given below are two statements: Statement I :…MediumTwo statements
  3. 31 Jan 2024, Shift 2 · Q25If lim⁡x→0ax2ex−blog⁡e(1+x)+cxe−xx2sin⁡x=1\lim_{x\to0}\frac{ax^2e^x-b\log_e(1+x)+cxe^{-x}}{x^2\sin x}=1, then 16(a2+b2+c2)16(a^2+b^2+c^2) is equal to ________.HardNumerical value
  4. 8 Apr 2024, Shift 1 · Q26The value of lim⁡x→02(1−cos⁡xcos⁡2xcos⁡3x3⋯cos⁡10x10x2)\lim_{x\to0}2\left(\frac{1-\cos x\sqrt{\cos2x}\sqrt[3]{\cos3x}\cdots\sqrt[10]{\cos10x}}{x^2}\right) is ____________.MediumNumerical value
  5. 13 Apr 2023, Shift 2 · Q9If lim⁡x→0eax−cos⁡(bx)−cxe−cx21−cos⁡(2x)=17\lim_{x\to0}\dfrac{e^{ax}-\cos(bx)-\dfrac{cxe^{-cx}}{2}}{1-\cos(2x)}=17, then 5a2+b25a^2+b^2 is equal toHardSingle correct
  6. 26 Jun 2022, Shift 2 · Q4lim⁡x→0cos⁡(sin⁡x)−cos⁡xx4\lim_{x \to 0} \frac{\cos(\sin x) - \cos x}{x^4} is equal to :MediumSingle correct
  7. 26 Jul 2022, Shift 2 · Q7Let β=lim⁡x→0αx−(e3x−1)αx(e3x−1)\beta=\lim_{x\to 0}\frac{\alpha x-(e^{3x}-1)}{\alpha x(e^{3x}-1)} for some α∈R\alpha\in\mathbb{R}. Then the value of α+β\alpha+\beta…MediumSingle correct
  8. 18 Mar 2021, Shift 1 · Q72If lim⁡x→0sin⁡−1x−tan⁡−1x3x3\lim_{x\to0}\dfrac{\sin^{-1}x-\tan^{-1}x}{3x^3} is equal to L, then the value of (6L+1)(6L+1) is :MediumSingle correct
  9. 27 Aug 2021, Shift 1 · Q65If α\alpha, β\beta are the distinct roots of x2+bx+c=0x^2+bx+c=0, then lim⁡x→βe2(x2+bx+c)−1−2(x2+bx+c)(x−β)2\lim_{x\to\beta}\frac{e^{2(x^2+bx+c)}-1-2(x^2+bx+c)}{(x-\beta)^2} is…MediumSingle correct
  10. 3 Sep 2020, Shift 1 · Q74If lim⁡x→0{1x8(1−cos⁡x22−cos⁡x24\lim_{x\to0}\left\{\frac{1}{x^8}\left(1-\cos\frac{x^2}{2}-\cos\frac{x^2}{4}\right.\right.…MediumNumerical value

Shifts: 3 Sep 2020, Shift 1, 18 Mar 2021, Shift 1, 27 Aug 2021, Shift 1, 26 Jun 2022, Shift 2, 26 Jul 2022, Shift 2, 13 Apr 2023, Shift 2, 31 Jan 2024, Shift 2, 8 Apr 2024, Shift 1, 8 Apr 2025, Shift 2, 6 Apr 2026, Shift 1.

Same topic

Other ideas in L'Hopital's Rule

L'Hopital's Rule has 18 ideas JEE Main has asked; 9 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas