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Saturday, 31 October

JEE Main · Maths · Limits and Derivatives

e-Power Shortcut for 1^infinity Forms

JEE Main asked e-Power Shortcut for 1^infinity Forms 6 times in 6 of the 108 shifts Lumi analysed, in 2020, 2021 and 2022. It belongs to L'Hopital's Rule, in Limits and Derivatives (Maths). The longest wait between two years asking it was 1 year. In 2020 and 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
6
in 6 shifts
Years
3 of 8
First asked
2020
last in 2022
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170.17’200.10’210.04’220’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 2 in 12 shifts · 2021: 3 in 24 shifts · 2022: 1 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

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

  • 20260 of 9
  • 20250 of 8
  • 20240 of 18
  • 20230 of 12
  • 20221 of 24
  • 20213 of 24
  • 20202 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.

  • Limit of one-to-infinity form
  • One-to-infinity form limit

Difficulty

Easy 2Medium 3Hard 1

1 of the 6 questions had a numerical answer.

Every question

All 6 questions

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

  1. 28 Jul 2022, Shift 1 · Q29lim⁡x→0((x+2cos⁡x)3+2(x+2cos⁡x)2+3sin⁡(x+2cos⁡x)(x+2)3+2(x+2)2+3sin⁡(x+2))100x\lim_{x\to0}\left(\frac{(x+2\cos x)^3+2(x+2\cos x)^2+3\sin(x+2\cos x)}{(x+2)^3+2(x+2)^2+3\sin(x+2)}\right)^{\frac{100}{x}} is equal to…HardNumerical value
  2. 25 Feb 2021, Shift 1 · Q66lim⁡n→∞(1+1+12+.......+1nn2)n\lim_{n \to \infty}\left(1 + \frac{1 + \frac{1}{2} + ....... + \frac{1}{n}}{n^2}\right)^n is equal to :MediumSingle correct
  3. 4 Aug 2021, Shift 2 · Q66The value of lim⁡x→2(2−cos⁡(2x2−5x+2))1(x2−4x+4)\lim_{x\to2}\left(2-\cos\left(2x^2-5x+2\right)\right)^{\frac{1}{\left(x^2-4x+4\right)}} is equal toMediumSingle correct
  4. 4 Aug 2021, Shift 1 · Q67lim⁡x→2(x3−x2−8x+13)1x3−3x2+4\lim_{x\to 2}\left(x^3-x^2-8x+13\right)^{\frac{1}{x^3-3x^2+4}}MediumSingle correct
  5. 2 Sep 2020, Shift 2 · Q59lim⁡x→0(tan⁡(π4+x))1/x\lim_{x \to 0}\left(\tan\left(\frac{\pi}{4}+x\right)\right)^{1/x} is equal to :EasySingle correct
  6. 8 Jan 2020, Shift 1 · Q57lim⁡x→0(3x2+27x2+2)1/x2\lim_{x\to 0}\left(\dfrac{3x^2+2}{7x^2+2}\right)^{1/x^2} is equal to :EasySingle correct

Shifts: 8 Jan 2020, Shift 1, 2 Sep 2020, Shift 2, 25 Feb 2021, Shift 1, 4 Aug 2021, Shift 2, 4 Aug 2021, Shift 1, 28 Jul 2022, 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