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Saturday, 31 October

JEE Main · Maths · Application of Derivatives

Finding Intervals

JEE Main asked Finding Intervals 7 times in 7 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2024 and 2025. It belongs to Monotonicity, in Application of Derivatives (Maths). The longest wait between two years asking it was 2 years. In 2021 and 2022 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
7
in 7 shifts
Years
5 of 8
First asked
2020
last in 2025
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022, 2024 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170.08’200.07’210.07’220’230.05’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 2 in 24 shifts · 2022: 2 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
  • 20222 of 24
  • 20212 of 24
  • 20201 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: application.

  • Find intervals of monotonicity of rational function
  • Intervals where function is increasing

Difficulty

Easy 2Medium 4Hard 1

Every question was multiple choice.

Every question

All 7 questions

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

  1. 8 Apr 2025, Shift 2 · Q17Let the function f(x)=x3+3x+3f(x) = \frac{x}{3} + \frac{3}{x} + 3, x≠0x \neq 0 be strictly increasing in…EasySingle correct
  2. 1 Feb 2024, Shift 1 · Q7If 5f(x)+4f(1x)=x2−2, ∀ x≠05f(x)+4f\left(\frac{1}{x}\right)=x^2-2,\ \forall\ x\neq0 and y=9x2f(x)y=9x^2f(x), then yy is strictly increasing in :HardSingle correct
  3. 30 Jun 2022, Shift 1 · Q9Let f(x)=4x3−11x2+8x−5f(x) = 4x^3 - 11x^2 + 8x - 5, x∈Rx \in \mathbf{R}. Then ff :EasySingle correct
  4. 28 Jul 2022, Shift 2 · Q66The function f(x)=xex(1−x), x∈Rf(x)=xe^{x(1-x)},\ x\in\mathbb{R}, is :MediumSingle correct
  5. 16 Mar 2021, Shift 2 · Q64Let ff be a real valued function, defined on R−{−1,1}\mathbf R-\{-1,1\} and given by f(x)=3log⁡e∣x−1x+1∣−2x−1f(x)=3\log_e\left|\frac{x-1}{x+1}\right|-\frac{2}{x-1}.…MediumSingle correct
  6. 25 Jul 2021, Shift 1 · Q67Let f(x)=3sin⁡4x+10sin⁡3x+6sin⁡2x−3f(x)=3\sin^4x+10\sin^3x+6\sin^2x-3, x∈[−π6,π2]x\in\left[-\frac{\pi}{6},\frac{\pi}{2}\right]. Then, ff is :MediumSingle correct
  7. 3 Sep 2020, Shift 1 · Q59The function, f(x)=(3x−7)x2/3f(x)=(3x-7)x^{2/3}, x∈Rx\in\mathbf{R}, is increasing for all xx lying in :MediumSingle correct

Shifts: 3 Sep 2020, Shift 1, 16 Mar 2021, Shift 2, 25 Jul 2021, Shift 1, 30 Jun 2022, Shift 1, 28 Jul 2022, Shift 2, 1 Feb 2024, Shift 1, 8 Apr 2025, Shift 2.

Same topic

Other ideas in Monotonicity

Monotonicity has 12 ideas JEE Main has asked; 4 of them came up in more than one question.

Topic analysisChapter analysisStudy this chapterAll repeated ideas