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Saturday, 31 October

JEE Main · Maths · Integrals

Even and Odd Functions

JEE Main asked Even and Odd Functions 4 times in 4 of the 108 shifts Lumi analysed, in 2021, 2024 and 2026. It belongs to Definite Integral Properties, in Integrals (Maths). The longest wait between two years asking it was 3 years. In 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
4
in 4 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, 2024 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.07’210’220’230.05’240’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 2 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 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
  • 20241 of 18
  • 20230 of 12
  • 20220 of 24
  • 20212 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.

  • Integrate rational function then evaluate logs
  • Evaluate integral functions with even integrand

Difficulty

Easy 1Medium 1Hard 2

1 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. 6 Apr 2026, Shift 2 · Q20The value of the integral ∫−11(x3+∣x∣+1x2+2∣x∣+1)dx\int_{-1}^{1}\left(\frac{x^3+|x|+1}{x^2+2|x|+1}\right)dx is equal to :MediumSingle correct
  2. 31 Jan 2024, Shift 2 · Q12Let f,g:(0,∞)→Rf,g:(0,\infty)\to\mathbb{R} be two functions defined by f(x)=∫−xx(∣t∣−t2)e−t2dtf(x)=\int_{-x}^{x}\left(|t|-t^2\right)e^{-t^2}dt and…HardSingle correct
  3. 18 Mar 2021, Shift 1 · Q82Let f(x)f(x) and g(x)g(x) be two functions satisfying f(x2)+g(4−x)=4x3f(x^2)+g(4-x)=4x^3 and g(4−x)+g(x)=0g(4-x)+g(x)=0, then the value of ∫−44f(x2) dx\int_{-4}^{4}f(x^2)\,dx is…HardNumerical value
  4. 25 Jul 2021, Shift 2 · Q69The value of the integral ∫−11log⁡(x+x2+1)dx\int_{-1}^{1}\log\left(x+\sqrt{x^2+1}\right)dx is :EasySingle correct

Shifts: 18 Mar 2021, Shift 1, 25 Jul 2021, Shift 2, 31 Jan 2024, Shift 2, 6 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