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Saturday, 31 October

JEE Main · Maths · Integrals

Fractional Part Function Integrals

JEE Main asked Fractional Part Function Integrals 3 times in 3 of the 108 shifts Lumi analysed, in 2020 and 2021. It belongs to Definite Integral Properties, in Integrals (Maths). The longest wait between two years asking it was 1 year. In 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
3
in 3 shifts
Years
2 of 8
First asked
2020
last in 2021
Pattern
Gone quiet
across the analysed shifts

Questions on this idea a shift, by year

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

00.050.10’170.08’200.07’210’220’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 2 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 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
  • 20250 of 8
  • 20240 of 18
  • 20230 of 12
  • 20220 of 24
  • 20212 of 24
  • 20201 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 with fractional part function
  • Definite integral with greatest integer function

Difficulty

Easy 1Medium 2Hard 0

1 of the 3 questions had a numerical answer.

Every question

All 3 questions

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

  1. 26 Feb 2021, Shift 1 · Q80The value of ∑n=1100∫n−1nex−[x] dx\sum_{n=1}^{100}\int_{n-1}^{n} e^{x-[x]}\,dx, where [x][x] is the greatest integer ≤x\le x, is :EasySingle correct
  2. 4 Aug 2021, Shift 2 · Q71If u+v+w=91u+v+w=91, and 2u=3v=4w2u=3v=4w, then the value of ∫u−v+w2u+v+4we(x−[x]) dx\int_{u-v+w}^{2u+v+4w}e^{(x-[x])}\,dx, where [x][x] denotes the greatest integer…MediumSingle correct
  3. 4 Sep 2020, Shift 2 · Q73Let {x}\{x\} and [x][x] denote the fractional part of xx and the greatest integer ≤x\leq x respectively of a real number xx. If…MediumNumerical value

Shifts: 4 Sep 2020, Shift 2, 26 Feb 2021, Shift 1, 4 Aug 2021, 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