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Saturday, 31 October

JEE Main · Maths · Application of Derivatives

Determining Coefficients from Extrema

JEE Main asked Determining Coefficients from Extrema 5 times in 5 of the 108 shifts Lumi analysed, in 2020, 2021 and 2025. It belongs to Maxima and Minima, in Application of Derivatives (Maths). The longest wait between two years asking it was 4 years. In 2020 and 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
5
in 5 shifts
Years
3 of 8
First asked
2020
last in 2025
Pattern
Frequent
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170.17’200.07’210’220’230’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 2 in 12 shifts · 2021: 2 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 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
  • 20240 of 18
  • 20230 of 12
  • 20220 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

Numerical value is the usual form. Skill tested: multi-step.

  • Determine polynomial from extrema and limit
  • Determine polynomial from extrema

Difficulty

Easy 0Medium 5Hard 0

3 of the 5 questions had a numerical answer.

Every question

All 5 questions

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

  1. 7 Apr 2025, Shift 2 · Q18Let f:R→Rf:\mathbf{R}\to\mathbf{R} be a polynomial function of degree four having extreme values at x=4x=4 and x=5x=5. If…MediumSingle correct
  2. 18 Mar 2021, Shift 2 · Q85Let P(x)P(x) be a real polynomial of degree 3 which vanishes at x=−3x=-3. Let P(x)P(x) have local minima at x=1x=1, local maxima at x=−1x=-1 and…MediumNumerical value
  3. 31 Aug 2021, Shift 2 · Q85Let f(x)f(x) be a cubic polynomial with f(1)=−10f(1) = -10, f(−1)=6f(-1) = 6, and has a local minima at x=1x = 1, and f′(x)f'(x) has a local minima at…MediumNumerical value
  4. 2 Sep 2020, Shift 1 · Q61If p(x)p(x) be a polynomial of degree three that has a local maximum value 8 at x=1x=1 and a local minimum value 4 at x=2x=2; then p(0)p(0) is…MediumSingle correct
  5. 8 Jan 2020, Shift 2 · Q73Let f(x)f(x) be a polynomial of degree 3 such that f(−1)=10f(-1) = 10, f(1)=−6f(1) = -6, f(x)f(x) has a critical point at x=−1x = -1 and f′(x)f'(x) has a…MediumNumerical value

Shifts: 8 Jan 2020, Shift 2, 2 Sep 2020, Shift 1, 18 Mar 2021, Shift 2, 31 Aug 2021, Shift 2, 7 Apr 2025, Shift 2.

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