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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, 2021 and 2022. It belongs to Monotonicity, in Application of Derivatives (Maths). The longest wait between two years asking it was 1 year. 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
2020
last in 2022
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

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

00.050.10’170.08’200.07’210.04’220’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 2 in 24 shifts · 2022: 1 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 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
  • 20240 of 18
  • 20230 of 12
  • 20221 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: multi-step.

  • Identify incorrect statement on function behaviour
  • Monotonicity of oscillating piecewise function

Difficulty

Easy 0Medium 2Hard 2

Every question was multiple choice.

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. 24 Jun 2022, Shift 1 · Q10For the function f(x)=4log⁡e(x−1)−2x2+4x+5, x>1f(x)=4\log_e(x-1)-2x^2+4x+5,\ x>1, which one of the following is NOT correct ?HardSingle correct
  2. 17 Mar 2021, Shift 2 · Q69Consider the function f:R→Rf:\mathbf{R}\to\mathbf{R} defined by…HardSingle correct
  3. 24 Feb 2021, Shift 1 · Q67The function f(x)=4x3−3x26−2sin⁡x+(2x−1)cos⁡xf(x) = \frac{4x^3 - 3x^2}{6} - 2\sin x + (2x - 1)\cos x :MediumSingle correct
  4. 2 Sep 2020, Shift 2 · Q61Let f:(−1,∞)→Rf:(-1,\infty)\to\mathbf{R} be defined by f(0)=1f(0)=1 and f(x)=1xlog⁡e(1+x)f(x)=\frac{1}{x}\log_e(1+x), x≠0x\neq 0. Then the function ff :MediumSingle correct

Shifts: 2 Sep 2020, Shift 2, 24 Feb 2021, Shift 1, 17 Mar 2021, Shift 2, 24 Jun 2022, Shift 1.

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