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Saturday, 31 October

JEE Main · Maths · Differential Equations

Standard Linear Form Identification

JEE Main asked Standard Linear Form Identification 4 times in 4 of the 108 shifts Lumi analysed, in 2020, 2021 and 2025. It belongs to Linear Differential Equations, in Differential Equations (Maths). The longest wait between two years asking it was 4 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
2020
last in 2025
Pattern
Frequent
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170.08’200.07’210’220’230’240.13’250’26

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: 1 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
  • 20251 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.

  • Solve initial value differential equation
  • Identify coefficient of linear de from solution

Difficulty

Easy 0Medium 2Hard 2

Every question was multiple choice.

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. 8 Apr 2025, Shift 2 · Q20Let f(x)=x−1f(x) = x - 1 and g(x)=exg(x) = e^x for x∈Rx \in \mathbb{R}. If…HardSingle correct
  2. 17 Mar 2021, Shift 2 · Q67If the curve y=y(x)y=y(x) is the solution of the differential equation 2(x2+x5/4)dy−y(x+x1/4)dx=2x9/4dx2(x^2+x^{5/4})dy-y(x+x^{1/4})dx=2x^{9/4}dx, x>0x>0 which passes…HardSingle correct
  3. 24 Feb 2021, Shift 2 · Q78If a curve y=f(x)y=f(x) passes through the point (1, 2) and satisfies xdydx+y=bx4x\frac{dy}{dx}+y=bx^4, then for what value of b,…MediumSingle correct
  4. 6 Sep 2020, Shift 2 · Q63If y=(2πx−1)cosec xy=\left(\frac{2}{\pi}x-1\right)\mathrm{cosec}\,x is the solution of the differential equation,…MediumSingle correct

Shifts: 6 Sep 2020, Shift 2, 24 Feb 2021, Shift 2, 17 Mar 2021, Shift 2, 8 Apr 2025, 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