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Saturday, 31 October

JEE Main · Maths · Complex Numbers and Quadratic Equations

Roots of Modulus Quadratics

JEE Main asked Roots of Modulus Quadratics 12 times in 12 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2023, 2024 and 2025. It belongs to Quadratic Roots, in Complex Numbers and Quadratic Equations (Maths). The longest wait between two years asking it was 1 year. In 2020, 2021, 2023 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
12
in 12 shifts
Years
6 of 8
First asked
2020
last in 2025
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022, 2023, 2024 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170.17’200.07’210.04’220.21’230.14’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 2 in 12 shifts · 2021: 2 in 24 shifts · 2022: 1 in 24 shifts · 2023: 3 in 12 shifts · 2024: 3 in 18 shifts · 2025: 1 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
  • 20251 of 8
  • 20243 of 18
  • 20233 of 12
  • 20221 of 24
  • 20212 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.

  • Count real roots of modulus equation
  • Value from roots of linked quadratics

Difficulty

Easy 2Medium 8Hard 2

6 of the 12 questions had a numerical answer.

Every question

All 12 questions

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

  1. 8 Apr 2025, Shift 2 · Q2The sum of the squares of the roots of ∣x−2∣2+∣x−2∣−2=0|x-2|^2 + |x-2| - 2 = 0 and the squares of the roots of x2−2∣x−3∣−5=0x^2 - 2|x-3| - 5 = 0, isMediumSingle correct
  2. 30 Jan 2024, Shift 2 · Q22The number of real solutions of the equation x(x2+3∣x∣+5∣x−1∣+6∣x−2∣)=0x\left(x^2 + 3|x| + 5|x-1| + 6|x-2|\right) = 0 is ________.MediumNumerical value
  3. 8 Apr 2024, Shift 2 · Q21The number of distinct real roots of the equation ∣x+1∣ ∣x+3∣−4∣x+2∣+5=0|x+1|\,|x+3| - 4|x+2| + 5 = 0, is ________MediumNumerical value
  4. 5 Apr 2024, Shift 1 · Q22The number of distinct real roots of the equation ∣x∣∣x+2∣−5∣x+1∣−1=0|x||x+2|-5|x+1|-1=0 is ________.MediumNumerical value
  5. 15 Apr 2023, Shift 1 · Q2The number of real roots of the equation x∣x∣−5∣x+2∣+6=0x|x|-5|x+2|+6=0, isMediumSingle correct
  6. 13 Apr 2023, Shift 1 · Q2The set of all a∈Ra \in \mathbb{R} for which the equation x∣x−1∣+∣x+2∣+a=0x|x-1|+|x+2|+a=0 has exactly one real root, isHardSingle correct
  7. 8 Apr 2023, Shift 2 · Q22Let mm and nn be the numbers of real roots of the quadratic equations x2−12x+[x]+31=0x^2 - 12x + [x] + 31 = 0 and x2−5∣x+2∣−4=0x^2 - 5|x + 2| - 4 = 0…HardNumerical value
  8. 30 Jul 2022, Shift 2 · Q81The number of solutions of the equation ∣x2+3x+2∣+∣x+5∣−2=0|x^2 + 3x + 2| + |x + 5| - 2 = 0, x∈Rx \in \mathbb{R}, is ________.MediumNumerical value
  9. 25 Jul 2021, Shift 2 · Q74The number of real solutions of the equation, x2−∣x∣−12=0x^2-|x|-12=0 is :EasySingle correct
  10. 24 Feb 2021, Shift 2 · Q90The number of the real roots of the equation (x+1)2+∣x−5∣=274(x+1)^2+|x-5|=\frac{27}{4} is ________.MediumNumerical value
  11. 5 Sep 2020, Shift 1 · Q53The product of the roots of the equation 9x2−18∣x∣+5=09x^2-18|x|+5=0, is :EasySingle correct
  12. 8 Jan 2020, Shift 2 · Q53Let S be the set of all real roots of the equation, 3x(3x−1)+2=∣3x−1∣+∣3x−2∣3^x(3^x - 1) + 2 = |3^x - 1| + |3^x - 2|. Then S :MediumSingle correct

Shifts: 8 Jan 2020, Shift 2, 5 Sep 2020, Shift 1, 24 Feb 2021, Shift 2, 25 Jul 2021, Shift 2, 30 Jul 2022, Shift 2, 8 Apr 2023, Shift 2, 13 Apr 2023, Shift 1, 15 Apr 2023, Shift 1, 30 Jan 2024, Shift 2, 5 Apr 2024, Shift 1, 8 Apr 2024, Shift 2, 8 Apr 2025, 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