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Saturday, 31 October

JEE Main · Maths · Complex Numbers and Quadratic Equations

Nature of Roots

JEE Main asked Nature of Roots 9 times in 9 of the 108 shifts Lumi analysed, in 2020, 2021 and 2024. It belongs to Quadratic Roots, in Complex Numbers and Quadratic Equations (Maths). The longest wait between two years asking it was 3 years. In 2020, 2021 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
9
in 9 shifts
Years
3 of 8
First asked
2020
last in 2024
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170.17’200.17’210’220’230.09’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 2 in 12 shifts · 2021: 5 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
  • 20215 of 24
  • 20202 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.

  • Range of x from discriminant condition
  • Least parameter value for real roots

Difficulty

Easy 1Medium 4Hard 4

5 of the 9 questions had a numerical answer.

Every question

All 9 questions

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 2 · Q24Let a,b,ca, b, c be the lengths of three sides of a triangle satisfying the condition (a2+b2)x2−2b(a+c)x+(b2+c2)=0(a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0. If the set of all…HardNumerical value
  2. 4 Apr 2024, Shift 2 · Q22Let S={sin⁡22θ:(sin⁡4θ+cos⁡4θ)x2+(sin⁡2θ)x+(sin⁡6θ+cos⁡6θ)=0 has real roots}S=\{\sin^2 2\theta:(\sin^4\theta+\cos^4\theta)x^2+(\sin2\theta)x+(\sin^6\theta+\cos^6\theta)=0\ \text{has real roots}\}. If α\alpha…HardNumerical value
  3. 25 Feb 2021, Shift 1 · Q76The coefficients a, b and c of the quadratic equation, ax2+bx+c=0ax^2 + bx + c = 0 are obtained by throwing a dice three times. The probability…MediumSingle correct
  4. 24 Feb 2021, Shift 1 · Q81If the least and the largest real values of α\alpha, for which the equation z+α∣z−1∣+2i=0z + \alpha|z - 1| + 2i = 0 (z∈Cz \in C and i=−1i = \sqrt{-1})…HardNumerical value
  5. 27 Aug 2021, Shift 2 · Q62The set of all values of k>−1k > -1, for which the equation…HardSingle correct
  6. 27 Aug 2021, Shift 1 · Q61If x2+9y2−4x+3=0x^2+9y^2-4x+3=0, x,y∈Rx, y \in \mathbb{R}, then xx and yy respectively lie in the intervals :MediumSingle correct
  7. 26 Aug 2021, Shift 1 · Q83The sum of all integral values of k (k ≠\neq 0) for which the equation 2x−1−1x−2=2k\frac{2}{x-1}-\frac{1}{x-2}=\frac{2}{k} in xx has no real…MediumNumerical value
  8. 3 Sep 2020, Shift 1 · Q51Consider the two sets : A={m∈RA=\{m\in\mathbf{R} : both the roots of x2−(m+1)x+m+4=0x^2-(m+1)x+m+4=0 are real}\} and B=[−3,5)B=[-3,5). Which of the following is…MediumSingle correct
  9. 8 Jan 2020, Shift 1 · Q71The least positive value of 'a' for which the equation, 2x2+(a−10)x+332=2a2x^2+(a-10)x+\frac{33}{2}=2a has real roots is ______.EasyNumerical value

Shifts: 8 Jan 2020, Shift 1, 3 Sep 2020, Shift 1, 24 Feb 2021, Shift 1, 25 Feb 2021, Shift 1, 26 Aug 2021, Shift 1, 27 Aug 2021, Shift 2, 27 Aug 2021, Shift 1, 31 Jan 2024, Shift 2, 4 Apr 2024, Shift 2.

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