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Saturday, 31 October

JEE Main · Maths · Application of Derivatives

Analyzing Polynomial Roots via Extrema

JEE Main asked Analyzing Polynomial Roots via Extrema 6 times in 6 of the 108 shifts Lumi analysed, in 2020, 2021, 2022 and 2025. It belongs to Maxima and Minima, in Application of Derivatives (Maths). The longest wait between two years asking it was 3 years. In 2022 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
6
in 6 shifts
Years
4 of 8
First asked
2020
last in 2025
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170.08’200.03’210.11’220’230’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 1 in 24 shifts · 2022: 3 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
  • 20223 of 24
  • 20211 of 24
  • 20201 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.

  • Count real roots of polynomial equation
  • Number of real roots after finding parameter from limit

Difficulty

Easy 0Medium 4Hard 2

3 of the 6 questions had a numerical answer.

Every question

All 6 questions

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

  1. 4 Apr 2025, Shift 2 · Q16Let ff be a differentiable function on R\mathbf{R} such that f(2)=1f(2)=1, f′(2)=4f'(2)=4. Let…HardSingle correct
  2. 27 Jun 2022, Shift 1 · Q6The number of distinct real roots of x4−4x+1=0x^4-4x+1=0 is :MediumSingle correct
  3. 30 Jul 2022, Shift 2 · Q83The number of integral values of bb for which 2x3−3x2−12x+b=02x^3 - 3x^2 - 12x + b = 0 has three distinct real roots is ________.MediumNumerical value
  4. 26 Jul 2022, Shift 1 · Q24The number of distinct real roots of the equation x5(x3−x2−x+1)+x (3x3−4x2−2x+4)−1=0x^5(x^3 - x^2 - x + 1) + x\ (3x^3 - 4x^2 - 2x + 4) - 1 = 0 is ___________.HardNumerical value
  5. 27 Aug 2021, Shift 1 · Q85The number of distinct real roots of the equation 3x4+4x3−12x2+4=03x^4+4x^3-12x^2+4=0 is __________.MediumNumerical value
  6. 3 Sep 2020, Shift 2 · Q58Suppose f(x)f(x) is a polynomial of degree four, having critical points at −1-1, 0, 1. If T={x∈R∣f(x)=f(0)}T = \{x \in \mathbf{R} \mid f(x) = f(0)\}, then…MediumSingle correct

Shifts: 3 Sep 2020, Shift 2, 27 Aug 2021, Shift 1, 27 Jun 2022, Shift 1, 26 Jul 2022, Shift 1, 30 Jul 2022, Shift 2, 4 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