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Saturday, 31 October

JEE Main · Maths · Differential Equations

Recognizing Exact Differentials in Homogeneous Forms

JEE Main asked Recognizing Exact Differentials in Homogeneous Forms 2 times in 2 of the 108 shifts Lumi analysed, in 2022 and 2024. It belongs to Homogeneous Equations, in Differential Equations (Maths). The longest wait between two years asking it was 2 years.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2022
last in 2024
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2022 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170’200’210.04’220’230.05’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 1 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 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
  • 20241 of 18
  • 20230 of 12
  • 20221 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.

  • Solve initial value differential equation
  • Differential equation representing a circle

Difficulty

Easy 0Medium 0Hard 2

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. 8 Apr 2024, Shift 2 · Q27Let α∣x∣=∣y∣exy−β\alpha|x| = |y|e^{xy-\beta}, α,β∈N\alpha, \beta \in \mathbb{N} be the solution of the differential equation…HardNumerical value
  2. 27 Jun 2022, Shift 1 · Q4Let dydx=ax−by+abx+cy+a\frac{dy}{dx} = \frac{ax-by+a}{bx+cy+a}, where a, b, c are constants, represent a circle passing through the point (2,5)(2, 5). Then…HardSingle correct

Shifts: 27 Jun 2022, Shift 1, 8 Apr 2024, Shift 2.

Same topic

Other ideas in Homogeneous Equations

Homogeneous Equations has 9 ideas JEE Main has asked; 5 of them came up in more than one question.

Topic analysisChapter analysisStudy this chapterAll repeated ideas