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Saturday, 31 October

JEE Main · Maths · Trigonometric Functions

Graphical Root Counting for Mixed Equations

JEE Main asked Graphical Root Counting for Mixed Equations 4 times in 4 of the 108 shifts Lumi analysed, in 2021, 2022, 2024 and 2025. It belongs to General Solutions, in Trigonometric Functions (Maths). The longest wait between two years asking it was 2 years.

Updated 2026-10-24

Times asked
4
in 4 shifts
Years
4 of 8
First asked
2021
last in 2025
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022, 2024 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.03’210.04’220’230.05’240.13’250’26

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: 1 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
  • 20241 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: data or graph.

  • Count solutions of trig equation in interval
  • Count solutions of mixed trig equation

Difficulty

Easy 0Medium 3Hard 1

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. 3 Apr 2025, Shift 1 · Q10The number of solutions of the equation 2x+3tan⁡x=π2x + 3\tan x = \pi, x∈[−2π,2π]−{±π2,±3π2}x \in [-2\pi, 2\pi] - \left\{\pm\frac{\pi}{2}, \pm\frac{3\pi}{2}\right\} is:MediumSingle correct
  2. 5 Apr 2024, Shift 2 · Q21The number of solutions of sin⁡2x+(2+2x−x2)sin⁡x−3(x−1)2=0\sin^2 x + (2+2x-x^2)\sin x - 3(x-1)^2 = 0, where −π≤x≤π-\pi \leq x \leq \pi, is ________.HardNumerical value
  3. 29 Jun 2022, Shift 1 · Q25The number of solutions of the equation 2θ−cos⁡2θ+2=02\theta - \cos^2\theta + \sqrt{2} = 0 in R\mathbf{R} is equal to ____________.MediumNumerical value
  4. 17 Mar 2021, Shift 2 · Q79The number of solutions of the equation x+2tan⁡x=π2x+2\tan x=\frac{\pi}{2} in the interval [0,2π][0, 2\pi] is :MediumSingle correct

Shifts: 17 Mar 2021, Shift 2, 29 Jun 2022, Shift 1, 5 Apr 2024, Shift 2, 3 Apr 2025, Shift 1.

Same topic

Other ideas in General Solutions

General Solutions has 23 ideas JEE Main has asked; 6 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas