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Saturday, 31 October

JEE Main · Maths · Integrals

Numerator-Denominator Derivative Matching

JEE Main asked Numerator-Denominator Derivative Matching 3 times in 3 of the 108 shifts Lumi analysed, in 2021 and 2024. It belongs to Integration by Substitution, in Integrals (Maths). The longest wait between two years asking it was 3 years. In 2024 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
2021
last in 2024
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170’200.03’210’220’230.09’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 2 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
  • 20242 of 18
  • 20230 of 12
  • 20220 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.

  • Integrate rational function of tan then evaluate logs
  • Integrate linear trig ratio by numerator-denominator matching

Difficulty

Easy 0Medium 3Hard 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. 9 Apr 2024, Shift 1 · Q8Let ∫2−tan⁡x3+tan⁡x dx=12(αx+log⁡e∣βsin⁡x+γcos⁡x∣)+C\int\frac{2-\tan x}{3+\tan x}\,dx=\frac{1}{2}\left(\alpha x+\log_e|\beta\sin x+\gamma\cos x|\right)+C, where C is the constant of…MediumSingle correct
  2. 5 Apr 2024, Shift 1 · Q11The integral ∫0π/4136sin⁡x3sin⁡x+5cos⁡x dx\int_0^{\pi/4}\frac{136\sin x}{3\sin x+5\cos x}\,dx is equal to :MediumSingle correct
  3. 27 Aug 2021, Shift 2 · Q84If ∫2ex+3e−x4ex+7e−x dx=114(ux+vlog⁡e(4ex+7e−x))+C\int \frac{2e^x + 3e^{-x}}{4e^x + 7e^{-x}}\, dx = \frac{1}{14}\left(ux + v \log_e(4e^x + 7e^{-x})\right) + C, where C is a constant…MediumNumerical value

Shifts: 27 Aug 2021, Shift 2, 5 Apr 2024, Shift 1, 9 Apr 2024, Shift 1.

Same topic

Other ideas in Integration by Substitution

Integration by Substitution has 27 ideas JEE Main has asked; 12 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas