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Saturday, 31 October

JEE Main · Maths · Integrals

Algebraic Reduction Formulas

JEE Main asked Algebraic Reduction Formulas 3 times in 3 of the 108 shifts Lumi analysed, in 2021, 2022 and 2023. It belongs to Integration by Parts, in Integrals (Maths). The longest wait between two years asking it was 1 year.

Updated 2026-10-24

Times asked
3
in 3 shifts
Years
3 of 8
First asked
2021
last in 2023
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022 and 2023. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170’200.03’210.04’220.07’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 1 in 24 shifts · 2023: 1 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
  • 20231 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

Numerical value is the usual form. Skill tested: multi-step.

  • Relation between parametric integrals via parts
  • Reduction relation for parametric integral

Difficulty

Easy 0Medium 1Hard 2

2 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. 11 Apr 2023, Shift 1 · Q26For m,n>0m, n > 0, let α(m,n)=∫02tm(1+3t)n dt\alpha(m, n) = \int_0^2 t^m(1+3t)^n\,dt. If 11 α(10,6)+18 α(11,5)=p (14)611\,\alpha(10, 6) + 18\,\alpha(11, 5) = p\,(14)^6, then pp is equal…HardNumerical value
  2. 28 Jul 2022, Shift 2 · Q69Let In(x)=∫0x1(t2+5)ndt, n=1,2,3,....I_n(x)=\int_0^x\frac{1}{(t^2+5)^n}dt,\ n=1,2,3,.... Then :HardSingle correct
  3. 17 Mar 2021, Shift 2 · Q81Let In=∫1ex19(log⁡∣x∣)ndxI_n=\int_1^e x^{19}(\log|x|)^n dx, where n∈Nn\in\mathbf{N}. If (20)I10=αI9+βI8(20)I_{10}=\alpha I_9+\beta I_8, for natural numbers α\alpha and…MediumNumerical value

Shifts: 17 Mar 2021, Shift 2, 28 Jul 2022, Shift 2, 11 Apr 2023, Shift 1.

Same topic

Other ideas in Integration by Parts

Integration by Parts has 9 ideas JEE Main has asked; 4 of them came up in more than one question.

Topic analysisChapter analysisStudy this chapterAll repeated ideas