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Saturday, 31 October

JEE Main · Maths · Integrals

Exponential Factor Manipulation

JEE Main asked Exponential Factor Manipulation 4 times in 4 of the 108 shifts Lumi analysed, in 2022, 2023, 2024 and 2026. It belongs to Integration by Substitution, in Integrals (Maths). The longest wait between two years asking it was 2 years.

Updated 2026-10-24

Times asked
4
in 4 shifts
Years
4 of 8
First asked
2022
last in 2026
Pattern
Frequent
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2022, 2023, 2024 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200’210.04’220.07’230.05’240’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 1 in 24 shifts · 2023: 1 in 12 shifts · 2024: 1 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
  • 20241 of 18
  • 20231 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

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

  • Definite integral with parameter from ap and minimum
  • Integrate given slope then evaluate point

Difficulty

Easy 0Medium 0Hard 4

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. 5 Apr 2026, Shift 2 · Q18Let (21−a+21+a)(2^{1-a}+2^{1+a}), f(a)f(a), (3a+3−a)(3^a+3^{-a}) be in A.P. and α\alpha be the minimum value of f(a)f(a). Then the value of the integral…HardSingle correct
  2. 8 Apr 2024, Shift 2 · Q11Let ∫αlog⁡e4dxex−1=π6\int_{\alpha}^{\log_e 4} \frac{dx}{\sqrt{e^x - 1}} = \frac{\pi}{6}. Then eαe^{\alpha} and e−αe^{-\alpha} are the roots of the…HardSingle correct
  3. 10 Apr 2023, Shift 2 · Q10For α,β,γ,δ∈N\alpha, \beta, \gamma, \delta \in \mathbb{N}, if…HardSingle correct
  4. 25 Jul 2022, Shift 1 · Q10The slope of the tangent to a curve C:y=y(x)C:y=y(x) at any point (x,y)(x,y) on it is…HardSingle correct

Shifts: 25 Jul 2022, Shift 1, 10 Apr 2023, Shift 2, 8 Apr 2024, Shift 2, 5 Apr 2026, Shift 2.

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