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Saturday, 31 October

JEE Main · Maths · Integrals

Removing 'x' using King's Property

JEE Main asked Removing 'x' using King's Property 2 times in 2 of the 108 shifts Lumi analysed, in 2024 and 2025. It belongs to Definite Integral Properties, in Integrals (Maths). The longest wait between two years asking it was 1 year.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2024
last in 2025
Pattern
New since 2024
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170’200’210’220’230.05’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 0 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
  • 20220 of 24
  • 20210 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: multi-step.

  • Definite integral using king's property

Difficulty

Easy 0Medium 1Hard 1

1 of the 2 questions had a numerical answer.

Every question

All 2 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 1 · Q18The integral ∫0π(x+3)sin⁡x1+3cos⁡2x dx\int_0^{\pi} \frac{(x+3)\sin x}{1+3\cos^2 x}\,dx is equal toMediumSingle correct
  2. 31 Jan 2024, Shift 2 · Q26∣120π3∫0πx2sin⁡xcos⁡xsin⁡4x+cos⁡4xdx∣\left|\frac{120}{\pi^3}\int_0^{\pi}\frac{x^2\sin x\cos x}{\sin^4x+\cos^4x}dx\right| is equal to ____________.HardNumerical value

Shifts: 31 Jan 2024, Shift 2, 7 Apr 2025, Shift 1.

Same topic

Other ideas in Definite Integral Properties

Definite Integral Properties has 19 ideas JEE Main has asked; 13 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas