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Saturday, 31 October

JEE Main · Maths · Continuity and Differentiability

Continuity at a Point

JEE Main asked Continuity at a Point 8 times in 8 of the 108 shifts Lumi analysed, in 2020, 2021, 2022 and 2024. It belongs to Continuity and Differentiability (Maths). The longest wait between two years asking it was 2 years. In 2020, 2021, 2022 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
8
in 8 shifts
Years
4 of 8
First asked
2020
last in 2024
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170.17’200.07’210.07’220’230.09’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 2 in 12 shifts · 2021: 2 in 24 shifts · 2022: 2 in 24 shifts · 2023: 0 in 12 shifts · 2024: 2 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
  • 20242 of 18
  • 20230 of 12
  • 20222 of 24
  • 20212 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: multi-step.

  • Unknown constants from continuity of piecewise function
  • Parameters from continuity of piecewise function

Difficulty

Easy 0Medium 6Hard 2

1 of the 8 questions had a numerical answer.

Every question

All 8 questions

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

  1. 4 Apr 2024, Shift 2 · Q8If the function f(x)={72x−9x−8x+12−1+cos⁡x,x≠0alog⁡e2log⁡e3,x=0f(x)=\begin{cases}\dfrac{72^x-9^x-8^x+1}{\sqrt2-\sqrt{1+\cos x}}, & x\ne 0\\ a\log_e 2\log_e 3, & x=0\end{cases} is…HardSingle correct
  2. 4 Apr 2024, Shift 1 · Q6Let f:R→Rf: \mathbf{R} \to \mathbf{R} be a function given by…MediumSingle correct
  3. 30 Jul 2022, Shift 2 · Q69Let…HardSingle correct
  4. 27 Jul 2022, Shift 2 · Q5If for p≠q≠0p \neq q \neq 0, the function f(x)=p(729+x)7−3729+qx3−9f(x) = \frac{\sqrt[7]{p(729 + x)} - 3}{\sqrt[3]{729 + qx} - 9} is continuous at x=0x = 0, then :MediumSingle correct
  5. 25 Jul 2021, Shift 1 · Q65Let f:R→Rf:\mathbf{R}\to\mathbf{R} be defined as…MediumSingle correct
  6. 26 Aug 2021, Shift 1 · Q82Let a, b ∈\in R\mathbf{R}, b ≠\neq 0. Define a function…MediumNumerical value
  7. 2 Sep 2020, Shift 1 · Q59If a function f(x)f(x) defined by…MediumSingle correct
  8. 9 Jan 2020, Shift 1 · Q58If…MediumSingle correct

Shifts: 9 Jan 2020, Shift 1, 2 Sep 2020, Shift 1, 25 Jul 2021, Shift 1, 26 Aug 2021, Shift 1, 27 Jul 2022, Shift 2, 30 Jul 2022, Shift 2, 4 Apr 2024, Shift 2, 4 Apr 2024, Shift 1.

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