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Saturday, 31 October

JEE Main · Maths · Limits and Derivatives

Determining Unknown Constants from Finite Limits

JEE Main asked Determining Unknown Constants from Finite Limits 6 times in 6 of the 108 shifts Lumi analysed, in 2021, 2022, 2025 and 2026. It belongs to L'Hopital's Rule, in Limits and Derivatives (Maths). The longest wait between two years asking it was 3 years. In 2022 and 2025 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
6
in 6 shifts
Years
4 of 8
First asked
2021
last in 2026
Pattern
Frequent
across the analysed shifts

Questions on this idea a shift, by year

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

00.150.30’170’200.03’210.07’220’230’240.25’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 2 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 2 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
  • 20252 of 8
  • 20240 of 18
  • 20230 of 12
  • 20222 of 24
  • 20211 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
  • Unknown constants for finite limit

Difficulty

Easy 0Medium 5Hard 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. 2 Apr 2026, Shift 1 · Q16If lim⁡x→2sin⁡(x3−5x2+ax+b)(x−1−1)log⁡e(x−1)=m\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+ma+b+m is equal to :HardSingle correct
  2. 2 Apr 2025, Shift 2 · Q17If lim⁡x→0cos⁡(2x)+acos⁡(4x)−bx4\lim_{x\to0} \frac{\cos(2x) + a\cos(4x) - b}{x^4} is finite, then (a+b)(a+b) is equal to :MediumSingle correct
  3. 2 Apr 2025, Shift 1 · Q7For α,β,γ∈R\alpha, \beta, \gamma\in\mathbf{R}, if lim⁡x→0x2sin⁡αx+(γ−1)ex2sin⁡2x−βx=3\lim_{x\to0}\frac{x^2\sin\alpha x+(\gamma-1)e^{x^2}}{\sin2x-\beta x}=3, then…MediumSingle correct
  4. 29 Jul 2022, Shift 1 · Q5If lim⁡x→0αex+βe−x+γsin⁡xxsin⁡2x=23\lim_{x \to 0} \frac{\alpha e^x + \beta e^{-x} + \gamma \sin x}{x \sin^2 x} = \frac{2}{3}, where…MediumSingle correct
  5. 25 Jul 2022, Shift 1 · Q5If lim⁡n→∞(n2−n−1+nα+β)=0\lim_{n\to\infty}\left(\sqrt{n^2-n-1}+n\alpha+\beta\right)=0, then 8(α+β)8(\alpha+\beta) is equal to :MediumSingle correct
  6. 25 Feb 2021, Shift 2 · Q84If lim⁡x→0ax−(e4x−1)ax(e4x−1)\lim_{x\to 0} \frac{ax - (e^{4x} - 1)}{ax(e^{4x} - 1)} exists and is equal to b, then the value of a−2ba - 2b is ________.MediumNumerical value

Shifts: 25 Feb 2021, Shift 2, 25 Jul 2022, Shift 1, 29 Jul 2022, Shift 1, 2 Apr 2025, Shift 2, 2 Apr 2025, Shift 1, 2 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