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Saturday, 31 October

JEE Main · Maths · Application of Derivatives

First Derivative Test

JEE Main asked First Derivative Test 4 times in 4 of the 108 shifts Lumi analysed, in 2020, 2022 and 2024. It belongs to Maxima and Minima, in Application of Derivatives (Maths). The longest wait between two years asking it was 2 years. In 2022 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
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, 2022 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170.08’200’210.07’220’230.05’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 0 in 24 shifts · 2022: 2 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 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
  • 20241 of 18
  • 20230 of 12
  • 20222 of 24
  • 20210 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: multi-step.

  • Local minimum location constrained by rational inequality
  • Find cubic from conditions then local extremum

Difficulty

Easy 0Medium 3Hard 1

1 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. 9 Apr 2024, Shift 1 · Q27Let the set of all positive values of λ\lambda, for which the point of local minimum of the function (1+x(λ2−x2))(1+x(\lambda^2-x^2)) satisfies…MediumNumerical value
  2. 29 Jun 2022, Shift 2 · Q6Let f:R→Rf : \mathbb{R} \to \mathbb{R} be a function defined by f(x)=(x−3)n1(x−5)n2f(x) = (x - 3)^{n_1}(x - 5)^{n_2}, n1,n2∈Nn_1, n_2 \in \mathbb{N}. Then, which…MediumSingle correct
  3. 25 Jul 2022, Shift 1 · Q7The curve y(x)=ax3+bx2+cx+5y(x)=ax^3+bx^2+cx+5 touches the xx-axis at the point P(−2,0)\mathrm{P}(-2,0) and cuts the yy-axis at the point Q\mathrm{Q},…MediumSingle correct
  4. 6 Sep 2020, Shift 2 · Q60The set of all real values of λ\lambda for which the function f(x)=(1−cos⁡2x)⋅(λ+sin⁡x)f(x)=(1-\cos^2 x)\cdot(\lambda+\sin x),…HardSingle correct

Shifts: 6 Sep 2020, Shift 2, 29 Jun 2022, Shift 2, 25 Jul 2022, Shift 1, 9 Apr 2024, Shift 1.

Same topic

Other ideas in Maxima and Minima

Maxima and Minima has 31 ideas JEE Main has asked; 14 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas