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Saturday, 31 October

JEE Main · Maths · Continuity and Differentiability

Continuity involving GIF and Fractional Part

JEE Main asked Continuity involving GIF and Fractional Part 17 times in 17 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2023, 2024 and 2026. It belongs to Continuity and Differentiability (Maths). The longest wait between two years asking it was 2 years. In 2020, 2021, 2022, 2023 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
17
in 17 shifts
Years
6 of 8
First asked
2020
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022, 2023, 2024 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170.17’200.07’210.21’220.21’230.14’240’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 2 in 12 shifts · 2021: 2 in 24 shifts · 2022: 6 in 24 shifts · 2023: 3 in 12 shifts · 2024: 3 in 18 shifts · 2025: 0 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
  • 20250 of 8
  • 20243 of 18
  • 20233 of 12
  • 20226 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.

  • Count discontinuities of greatest integer function
  • Continuity with fractional part function

Difficulty

Easy 0Medium 10Hard 7

8 of the 17 questions had a numerical answer.

Every question

All 17 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 2 · Q25The number of points in the interval [2,4][2, 4], at which the function f(x)=x2−x−1⌊x⌋−12f(x) = x^2 - x - \frac{1}{\lfloor x \rfloor - \frac{1}{2}}, where…MediumNumerical value
  2. 27 Jan 2024, Shift 1 · Q8Consider the function.…HardSingle correct
  3. 6 Apr 2024, Shift 2 · Q24Let [t][t] denote the greatest integer less than or equal to tt. Let f:[0,∞)→Rf:[0,\infty)\to\mathbb{R} be a function defined by…MediumNumerical value
  4. 5 Apr 2024, Shift 2 · Q10Let f:[−1,2]→Rf : [-1, 2] \to \mathbf{R} be given by f(x)=2x2+x+[x2]−[x]f(x) = 2x^2 + x + [x^2] - [x], where [t][t] denotes the greatest integer less than or equal…MediumSingle correct
  5. 12 Apr 2023, Shift 1 · Q25Let [x][x] be the greatest integer ≤x\le x. Then the number of points in the interval (−2,1)(-2,1), where the function…MediumNumerical value
  6. 11 Apr 2023, Shift 1 · Q7Let f(x)=[x2−x]+∣−x+[x]∣f(x) = [x^2 - x] + |-x + [x]|, where x∈Rx \in \mathbb{R} and [t][t] denotes the greatest integer less than or equal to tt. Then, ff isMediumSingle correct
  7. 6 Apr 2023, Shift 1 · Q25Let a∈Za\in\mathbb{Z} and [t][t] be the greatest integer ≤t\le t. Then the number of points, where the function f(x)=[a+13sin⁡x]f(x)=[a+13\sin x],…HardNumerical value
  8. 28 Jun 2022, Shift 1 · Q8Let f:R→Rf:\mathbb{R}\to\mathbb{R} be defined as…HardSingle correct
  9. 27 Jun 2022, Shift 2 · Q25Let [t][t] denote the greatest integer ≤t\leq t and {t}\{t\} denote the fractional part of tt. The integral value of α\alpha for which the…MediumNumerical value
  10. 27 Jun 2022, Shift 1 · Q5Let a be an integer such that lim⁡x→718−[1−x][x−3a]\lim_{x \to 7} \frac{18-[1-x]}{[x-3a]} exists, where [t][t] is greatest integer ⩽t\leqslant t. Then a is…MediumSingle correct
  11. 24 Jun 2022, Shift 2 · Q5Let…HardSingle correct
  12. 24 Jun 2022, Shift 1 · Q25The number of points where the function…HardNumerical value
  13. 29 Jul 2022, Shift 2 · Q26If [t][t] denotes the greatest integer ≤t\leq t, then the number of points, at which the function…HardNumerical value
  14. 16 Mar 2021, Shift 2 · Q69Let α∈R\alpha\in\mathbf R be such that the function…HardSingle correct
  15. 24 Feb 2021, Shift 1 · Q69If f:R→Rf : \mathbb{R} \to \mathbb{R} is a function defined by f(x)=[x−1]cos⁡(2x−12)πf(x) = [x - 1]\cos\left(\frac{2x - 1}{2}\right)\pi, where [⋅][\cdot] denotes…MediumSingle correct
  16. 5 Sep 2020, Shift 1 · Q73Let f(x)=x.[x2]f(x)=x.\left[\frac{x}{2}\right], for −10<x<10-10<x<10, where [t] denotes the greatest integer function. Then the number of points of…MediumNumerical value
  17. 9 Jan 2020, Shift 2 · Q58Let [t][t] denote the greatest integer ≤t\le t and lim⁡x→0x[4x]=A\lim_{x\to0}x\left[\frac{4}{x}\right]=A. Then the function, f(x)=[x2]sin⁡(πx)f(x)=[x^2]\sin(\pi x) is…MediumSingle correct

Shifts: 9 Jan 2020, Shift 2, 5 Sep 2020, Shift 1, 24 Feb 2021, Shift 1, 16 Mar 2021, Shift 2, 24 Jun 2022, Shift 2, 24 Jun 2022, Shift 1, 27 Jun 2022, Shift 2, 27 Jun 2022, Shift 1, 28 Jun 2022, Shift 1, 29 Jul 2022, Shift 2, 6 Apr 2023, Shift 1, 11 Apr 2023, Shift 1, 12 Apr 2023, Shift 1, 27 Jan 2024, Shift 1, 5 Apr 2024, Shift 2, 6 Apr 2024, Shift 2, 2 Apr 2026, 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