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Saturday, 31 October

JEE Main · Maths · Continuity and Differentiability

Limits via Series Expansion for Continuity

JEE Main asked Limits via Series Expansion for Continuity 4 times in 4 of the 108 shifts Lumi analysed, in 2021, 2024 and 2025. It belongs to Continuity and Differentiability (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
4
in 4 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.

00.10.20’170’200.07’210’220’230.05’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 2 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
  • 20212 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: calculation.

  • Value for continuity from trig limit
  • Unknown constants from finite limit

Difficulty

Easy 0Medium 2Hard 2

2 of the 4 questions had a numerical answer.

Every question

All 4 questions

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

  1. 7 Apr 2025, Shift 2 · Q25If the function f(x)=tan⁡(tan⁡x)−sin⁡(sin⁡x)tan⁡x−sin⁡xf(x)=\frac{\tan(\tan x)-\sin(\sin x)}{\tan x-\sin x} is continuous at x=0x=0, then f(0)f(0) is equal to ________.HardNumerical value
  2. 5 Apr 2024, Shift 1 · Q7If the function f(x)=sin⁡3x+αsin⁡x−βcos⁡3xx3f(x)=\frac{\sin3x+\alpha\sin x-\beta\cos3x}{x^3}, x∈Rx\in\mathbb{R}, is continuous at x=0x=0, then f(0)f(0) is equal to :MediumSingle correct
  3. 17 Mar 2021, Shift 1 · Q84If the function f(x)=cos⁡(sin⁡x)−cos⁡xx4f(x)=\frac{\cos(\sin x)-\cos x}{x^{4}} is continuous at each point in its domain and f(0)=1kf(0)=\frac{1}{k}, then k is…MediumNumerical value
  4. 22 Jul 2021, Shift 2 · Q65Let f:R→Rf:\mathbf{R}\to\mathbf{R} be defined as…HardSingle correct

Shifts: 17 Mar 2021, Shift 1, 22 Jul 2021, Shift 2, 5 Apr 2024, Shift 1, 7 Apr 2025, Shift 2.

Same topic

Other ideas in Continuity and Differentiability

Continuity and Differentiability has 18 ideas JEE Main has asked; 13 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas