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Saturday, 31 October

JEE Main · Maths · Differential Equations

LDEs Formed via Leibniz Integral Rule

JEE Main asked LDEs Formed via Leibniz Integral Rule 3 times in 3 of the 108 shifts Lumi analysed, in 2021, 2022 and 2026. It belongs to Linear Differential Equations, in Differential Equations (Maths). The longest wait between two years asking it was 4 years.

Updated 2026-10-24

Times asked
3
in 3 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.

00.10.20’170’200.03’210.04’220’230’240’250.11’26

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: 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
  • 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

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

  • Solve integral equation after functional equation
  • Minimum of function defined by integral equation

Difficulty

Easy 0Medium 1Hard 2

Every question was multiple choice.

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. 6 Apr 2026, Shift 2 · Q18Let f:R→Rf:\mathbf{R}\to\mathbf{R} be such that f(xy)=f(x)f(y)f(xy)=f(x)f(y), for all x,y∈Rx,y\in\mathbf{R} and f(0)≠0f(0)\neq0. Let g:[1,∞)→Rg:[1,\infty)\to\mathbf{R}…HardSingle correct
  2. 28 Jul 2022, Shift 1 · Q20The minimum value of the twice differentiable function f(x)=∫0xex−tf′(t) dt−(x2−x+1)ex, x∈Rf(x)=\int_0^x e^{x-t}f'(t)\,dt-(x^2-x+1)e^x,\ x\in\mathbf{R}, is :HardSingle correct
  3. 26 Feb 2021, Shift 2 · Q67Let f(x)=∫0xetf(t) dt+exf(x)=\int_0^x e^t f(t)\,dt + e^x be a differentiable function for all x∈Rx \in \mathbf{R}. Then f(x)f(x) equals :MediumSingle correct

Shifts: 26 Feb 2021, Shift 2, 28 Jul 2022, Shift 1, 6 Apr 2026, Shift 2.

Same topic

Other ideas in Linear Differential Equations

Linear Differential Equations has 18 ideas JEE Main has asked; 14 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas