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Saturday, 31 October

JEE Main · Maths · Limits and Derivatives

Simplifying with Standard Limits Before L'Hopital

JEE Main asked Simplifying with Standard Limits Before L'Hopital 13 times in 13 of the 108 shifts Lumi analysed, in 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, 2023, 2024, 2025 and 2026 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
13
in 13 shifts
Years
6 of 8
First asked
2021
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 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.

00.150.30’170’200.07’210.07’220.14’230.14’240.25’250.22’26

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

Shift by shift

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

  • 20262 of 9
  • 20252 of 8
  • 20243 of 18
  • 20232 of 12
  • 20222 of 24
  • 20212 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: multi-step.

  • Unknown constants from finite limit
  • Parameter values from trigonometric limit

Difficulty

Easy 0Medium 8Hard 5

4 of the 13 questions had a numerical answer.

Every question

All 13 questions

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

  1. 5 Apr 2026, Shift 2 · Q17Let f(x)=lim⁡y→0(1−cos⁡(xy))tan⁡(xy)y3f(x)=\lim_{y\to 0}\frac{(1-\cos(xy))\tan(xy)}{y^3}. Then the number of solutions of the equation f(x)=sin⁡xf(x)=\sin x, x∈Rx \in \mathbf{R}…MediumSingle correct
  2. 5 Apr 2026, Shift 1 · Q17The product of all possible values of α\alpha, for which…HardSingle correct
  3. 7 Apr 2025, Shift 2 · Q23For t>−1t>-1, let αt\alpha_t and βt\beta_t be the roots of the equation…HardNumerical value
  4. 7 Apr 2025, Shift 1 · Q16…MediumSingle correct
  5. 31 Jan 2024, Shift 1 · Q6lim⁡x→0e2∣sin⁡x∣−2∣sin⁡x∣−1x2\lim_{x\to0}\frac{e^{2|\sin x|}-2|\sin x|-1}{x^2}MediumSingle correct
  6. 8 Apr 2024, Shift 2 · Q25If α=lim⁡x→0+(etan⁡x−extan⁡x−x)\alpha = \lim_{x \to 0^+} \left(\frac{e^{\sqrt{\tan x}} - e^{\sqrt{x}}}{\sqrt{\tan x} - \sqrt{x}}\right) and…HardNumerical value
  7. 5 Apr 2024, Shift 2 · Q23Let a>0a > 0 be a root of the equation 2x2+x−2=02x^2+x-2=0. If…HardNumerical value
  8. 8 Apr 2023, Shift 2 · Q9If α>β>0\alpha > \beta > 0 are the roots of the equation ax2+bx+1=0ax^2 + bx + 1 = 0, and…HardSingle correct
  9. 8 Apr 2023, Shift 1 · Q10lim⁡x→0((1−cos⁡2(3x)cos⁡3(4x))(sin⁡3(4x)(log⁡e(2x+1))5))\lim_{x\to0}\left(\left(\frac{1-\cos^2(3x)}{\cos^3(4x)}\right)\left(\frac{\sin^3(4x)}{\left(\log_e(2x+1)\right)^5}\right)\right) is…MediumSingle correct
  10. 29 Jun 2022, Shift 2 · Q5The value of lim⁡x→1(x2−1)sin⁡2(πx)x4−2x3+2x−1\lim_{x \to 1} \frac{(x^2 - 1)\sin^2(\pi x)}{x^4 - 2x^3 + 2x - 1} is equal to:MediumSingle correct
  11. 28 Jun 2022, Shift 2 · Q24If lim⁡x→1sin⁡(3x2−4x+1)−x2+12x3−7x2+ax+b=−2\lim_{x\to1}\frac{\sin(3x^2-4x+1)-x^2+1}{2x^3-7x^2+ax+b}=-2, then the value of (a−b)(a-b) is equal to __________.MediumNumerical value
  12. 17 Mar 2021, Shift 2 · Q65The value of the limit lim⁡θ→0tan⁡(πcos⁡2θ)sin⁡(2πsin⁡2θ)\lim_{\theta\to 0}\frac{\tan(\pi\cos^2\theta)}{\sin(2\pi\sin^2\theta)} is equal to :MediumSingle correct
  13. 31 Aug 2021, Shift 1 · Q67lim⁡x→0sin⁡2(πcos⁡4x)x4\lim_{x\to0}\frac{\sin^2(\pi\cos^4x)}{x^4} is equal to :MediumSingle correct

Shifts: 17 Mar 2021, Shift 2, 31 Aug 2021, Shift 1, 28 Jun 2022, Shift 2, 29 Jun 2022, Shift 2, 8 Apr 2023, Shift 2, 8 Apr 2023, Shift 1, 31 Jan 2024, Shift 1, 5 Apr 2024, Shift 2, 8 Apr 2024, Shift 2, 7 Apr 2025, Shift 2, 7 Apr 2025, Shift 1, 5 Apr 2026, Shift 2, 5 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