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Saturday, 31 October

JEE Main · Maths · Application of Derivatives

Higher-Order Derivative Roots

JEE Main asked Higher-Order Derivative Roots 4 times in 4 of the 108 shifts Lumi analysed, in 2021, 2022 and 2024. It belongs to Rolle's Theorem, in Application of Derivatives (Maths). The longest wait between two years asking it was 2 years. In 2024 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
2021
last in 2024
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

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

00.050.10’170’200.03’210.04’220’230.09’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 1 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
  • 20221 of 24
  • 20211 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: application.

  • Least number of zeros of higher derivative
  • Count roots of derivative of symmetric function

Difficulty

Easy 0Medium 2Hard 2

2 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. 30 Jan 2024, Shift 1 · Q9Let g:R→Rg:\mathbf{R}\to\mathbf{R} be a non constant twice differentiable function such that…HardSingle correct
  2. 4 Apr 2024, Shift 2 · Q25Let f:R→Rf:\mathbb{R}\to\mathbb{R} be a thrice differentiable function such that f(0)=0,f(1)=1,f(2)=−1,f(3)=2f(0)=0, f(1)=1, f(2)=-1, f(3)=2 and f(4)=−2f(4)=-2. Then, the…HardNumerical value
  3. 28 Jul 2022, Shift 1 · Q23Let f:[0,1]→Rf:[0,1]\to\mathbf{R} be a twice differentiable function in (0,1)(0,1) such that f(0)=3f(0)=3 and f(1)=5f(1)=5. If the line y=2x+3y=2x+3 intersects…MediumNumerical value
  4. 31 Aug 2021, Shift 2 · Q68Let ff be any continuous function on [0,2][0, 2] and twice differentiable on (0,2)(0, 2). If f(0)=0f(0) = 0, f(1)=1f(1) = 1 and f(2)=2f(2) = 2, then :MediumSingle correct

Shifts: 31 Aug 2021, Shift 2, 28 Jul 2022, Shift 1, 30 Jan 2024, Shift 1, 4 Apr 2024, Shift 2.

Same topic

Other ideas in Rolle's Theorem

Rolle's Theorem has 5 ideas JEE Main has asked; 2 of them came up in more than one question.

Topic analysisChapter analysisStudy this chapterAll repeated ideas