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Saturday, 31 October

JEE Main · Maths · Complex Numbers and Quadratic Equations

Integer Roots Condition

JEE Main asked Integer Roots Condition 2 times in 2 of the 108 shifts Lumi analysed, in 2017 and 2024. It belongs to Quadratic Roots, in Complex Numbers and Quadratic Equations (Maths). The longest wait between two years asking it was 7 years, across 2018 and 2019, which Lumi has no shifts for.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2017
last in 2024
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

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

00.510.86’170’200’210’220’230.05’240’250’26

Raw count: 2017: 1 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 0 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
  • 20220 of 24
  • 20210 of 24
  • 20200 of 12
  • 20171 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.

  • Integer roots of quadratic from series expression
  • Minimal parameter for natural roots

Difficulty

Easy 0Medium 1Hard 1

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. 30 Jan 2024, Shift 1 · Q22Let α,β∈N\alpha,\beta\in N be roots of the equation x2−70x+λ=0x^2-70x+\lambda=0, where λ2,λ3∉N\frac{\lambda}{2},\frac{\lambda}{3}\notin N. If λ\lambda…MediumNumerical value
  2. 2 Apr 2017 (offline) · Q62If, for a positive integer n, the quadratic equation, x(x+1)+(x+1)(x+2)+…+(x+n−1‾)(x+n)=10nx(x+1)+(x+1)(x+2)+\ldots+(x+\overline{n-1})(x+n)=10n has two consecutive integral…HardSingle correct

Shifts: 2 Apr 2017 (offline), 30 Jan 2024, Shift 1.

Same topic

Other ideas in Quadratic Roots

Quadratic Roots has 22 ideas JEE Main has asked; 13 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas