Learn

Saturday, 31 October

JEE Main · Maths · Integrals

Periodic Function Property

JEE Main asked Periodic Function Property 6 times in 6 of the 108 shifts Lumi analysed, in 2021, 2022 and 2026. It belongs to Definite Integral Properties, in Integrals (Maths). The longest wait between two years asking it was 4 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
3 of 8
First asked
2021
last in 2026
Pattern
Frequent
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170’200.03’210.14’220’230’240’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 4 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 in 8 shifts · 2026: 1 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20261 of 9
  • 20250 of 8
  • 20240 of 18
  • 20230 of 12
  • 20224 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

Single correct is the usual form. Skill tested: multi-step.

  • Definite integral over multiple periods
  • Integral of piecewise floor-based function

Difficulty

Easy 1Medium 1Hard 4

Every question was multiple choice.

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. 2 Apr 2026, Shift 2 · Q17The value of ∫020π(sin⁡4x+cos⁡4x)dx\int_0^{20\pi} (\sin^4 x + \cos^4 x)dx is equal to:EasySingle correct
  2. 28 Jun 2022, Shift 2 · Q8Let f:R→Rf : \mathbf{R} \to \mathbf{R} be a continuous function satisfying f(x)+f(x+k)=nf(x)+f(x+k)=n, for all x∈Rx \in \mathbf{R} where k>0k>0 and n is a…HardSingle correct
  3. 30 Jul 2022, Shift 2 · Q71Let Ak=∫kπ(k+1)πe−xsin⁡x dxA_k = \int_{k\pi}^{(k+1)\pi} e^{-x} \sin x\, dx , k=0,1,2,...,20k = 0, 1, 2, ..., 20. Then ∑k=020∣Ak∣\sum_{k=0}^{20} |A_k| is equal toHardSingle correct
  4. 26 Jul 2022, Shift 2 · Q9∫020π(∣sin⁡x∣+∣cos⁡x∣)2dx\int_0^{20\pi}\left(|\sin x|+|\cos x|\right)^2dx is equal toMediumSingle correct
  5. 25 Jul 2022, Shift 1 · Q9For any real number xx, let [x][x] denote the largest integer less than equal to xx. Let ff be a real valued function defined on the…HardSingle correct
  6. 22 Jul 2021, Shift 2 · Q76If ∫0100πsin⁡2xe(xπ−[xπ])dx=απ31+4π2\int_0^{100\pi}\frac{\sin^2x}{e^{\left(\frac{x}{\pi}-\left[\frac{x}{\pi}\right]\right)}}dx=\frac{\alpha\pi^3}{1+4\pi^2},…HardSingle correct

Shifts: 22 Jul 2021, Shift 2, 28 Jun 2022, Shift 2, 25 Jul 2022, Shift 1, 26 Jul 2022, Shift 2, 30 Jul 2022, Shift 2, 2 Apr 2026, Shift 2.

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