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Saturday, 31 October

JEE Main · Maths · Complex Numbers and Quadratic Equations

Always Negative Condition

JEE Main asked Always Negative Condition once in the 108 shifts Lumi analysed, on 31 Jan 2024, Shift 1. It belongs to Quadratic Roots, in Complex Numbers and Quadratic Equations (Maths).

Updated 2026-10-24

Times asked
1
in 1 shift
Years
1 of 8
First asked
2024
the only year
Pattern
New since 2024
asked once so far

Questions on this idea a shift, by year

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

00.050.10’170’200’210’220’230.05’240’250’26

Raw count: 2017: 0 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
  • 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: application.

  • Count parameter values for always-negative quadratic

Difficulty

Easy 1Medium 0Hard 0

The question was multiple choice.

Every question

The question

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 31 Jan 2024, Shift 1 · Q2Let S be the set of postive integral values of aa for which ax2+2(a+1)x+9a+4x2−8x+32<0, ∀x∈R\frac{ax^2+2(a+1)x+9a+4}{x^2-8x+32}<0,\ \forall x\in\mathbb{R}. Then, the…EasySingle correct

Shift: 31 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