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Saturday, 31 October

JEE Main · Maths · Limits and Derivatives

Indeterminate Power Forms

JEE Main asked Indeterminate Power Forms 5 times in 5 of the 108 shifts Lumi analysed, in 2021, 2024 and 2025. It belongs to L'Hopital's Rule, in Limits and Derivatives (Maths). The longest wait between two years asking it was 3 years. In 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
5
in 5 shifts
Years
3 of 8
First asked
2021
last in 2025
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170’200.10’210’220’230.05’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 3 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 in 18 shifts · 2025: 1 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
  • 20251 of 8
  • 20241 of 18
  • 20230 of 12
  • 20220 of 24
  • 20213 of 24
  • 20200 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
  • Limit with indeterminate power form

Difficulty

Easy 1Medium 2Hard 2

1 of the 5 questions had a numerical answer.

Every question

All 5 questions

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

  1. 3 Apr 2025, Shift 2 · Q25If lim⁡x→0(tan⁡xx)1x2=p\lim_{x \to 0}\left(\frac{\tan x}{x}\right)^{\frac{1}{x^2}} = p, then 96log⁡ep96 \log_e p is equal to ___________.MediumNumerical value
  2. 9 Apr 2024, Shift 2 · Q5lim⁡x→0e−(1+2x)12xx\lim_{x\to0}\frac{e-(1+2x)^{\frac{1}{2x}}}{x} is equal toHardSingle correct
  3. 31 Aug 2021, Shift 2 · Q67If α=lim⁡x→π/4tan⁡3x−tan⁡xcos⁡(x+π4)\alpha = \lim_{x\to\pi/4}\frac{\tan^3 x-\tan x}{\cos\left(x+\frac{\pi}{4}\right)} and β=lim⁡x→0(cos⁡x)cot⁡x\beta = \lim_{x\to 0}(\cos x)^{\cot x} are…MediumSingle correct
  4. 3 Aug 2021, Shift 2 · Q68lim⁡x→0(1+x)1ex−1\lim_{x\to0}(1+x)^{\frac{1}{e^x-1}} is equal toEasySingle correct
  5. 3 Aug 2021, Shift 1 · Q65The value of the limit : lim⁡x→4(2x+25−x−17)18−23x/4\lim_{x \to 4} \left(2^x + 2^{5-x} - 17\right)^{\frac{1}{8 - 2^{3x/4}}} is equal toHardSingle correct

Shifts: 3 Aug 2021, Shift 2, 3 Aug 2021, Shift 1, 31 Aug 2021, Shift 2, 9 Apr 2024, Shift 2, 3 Apr 2025, Shift 2.

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