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Saturday, 31 October

JEE Main · Maths · Complex Numbers and Quadratic Equations

Symmetric Functions

JEE Main asked Symmetric Functions 12 times in 12 of the 108 shifts Lumi analysed, in 2021, 2022, 2024, 2025 and 2026. It belongs to Quadratic Roots, in Complex Numbers and Quadratic Equations (Maths). The longest wait between two years asking it was 2 years. In 2021 and 2022 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
12
in 12 shifts
Years
5 of 8
First asked
2021
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

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

00.150.30’170’200.07’210.25’220’230.05’240.13’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 2 in 24 shifts · 2022: 7 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 in 18 shifts · 2025: 1 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
  • 20251 of 8
  • 20241 of 18
  • 20230 of 12
  • 20227 of 24
  • 20212 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.

  • Value from roots of linked quadratics
  • Minimise symmetric function of roots

Difficulty

Easy 1Medium 9Hard 2

2 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. 2 Apr 2026, Shift 2 · Q1Let α,β\alpha, \beta be the roots of the equation x2−3x+r=0x^2 - 3x + r = 0, and α2,2β\frac{\alpha}{2}, 2\beta be the roots of the equation…MediumSingle correct
  2. 3 Apr 2025, Shift 1 · Q4Let z∈Cz \in \mathbb{C} be such that z2+3iz−2+i=2+3i\frac{z^2 + 3i}{z - 2 + i} = 2 + 3i. Then the sum of all possible values of z2z^2 isMediumSingle correct
  3. 31 Jan 2024, Shift 2 · Q3Let z1z_1 and z2z_2 be two complex numbers such that z1+z2=5z_1+z_2=5 and z13+z23=20+15iz_1^3+z_2^3=20+15i. Then, ∣z14+z24∣|z_1^4+z_2^4| equals -HardSingle correct
  4. 30 Jun 2022, Shift 1 · Q3Let S be the set of all integral values of α\alpha for which the sum of squares of two real roots of the quadratic equation…MediumSingle correct
  5. 29 Jun 2022, Shift 1 · Q8Let α\alpha and β\beta be the roots of the equation x2+(2i−1)=0x^2 + (2i - 1) = 0. Then, the value of ∣α8+β8∣|\alpha^8 + \beta^8| is equal to :MediumSingle correct
  6. 27 Jun 2022, Shift 2 · Q22Let α,β\alpha, \beta be the roots of the equation x2−4λx+5=0x^2-4\lambda x+5=0 and α,γ\alpha, \gamma be the roots of the equation…HardNumerical value
  7. 26 Jun 2022, Shift 2 · Q22Let pp and qq be two real numbers such that p+q=3p + q = 3 and p4+q4=369p^4 + q^4 = 369. Then (1p+1q)−2\left(\frac{1}{p} + \frac{1}{q}\right)^{-2} is…MediumNumerical value
  8. 25 Jun 2022, Shift 2 · Q2Let a,b∈Ra, b \in \mathbb{R} be such that the equation ax2−2bx+15=0ax^2 - 2bx + 15 = 0 has a repeated root α\alpha. If α\alpha and β\beta are the…MediumSingle correct
  9. 24 Jun 2022, Shift 1 · Q7If the sum of the squares of the reciprocals of the roots α\alpha and β\beta of the equation 3x2+λx−1=03x^2+\lambda x-1=0 is 15, then…MediumSingle correct
  10. 26 Jul 2022, Shift 2 · Q1The minimum value of the sum of the squares of the roots of x2+(3−a)x+1=2ax^2+(3-a)x+1=2a is:EasySingle correct
  11. 24 Feb 2021, Shift 2 · Q62Let a, b, c be in arithmetic progression. Let the centroid of the triangle with vertices (a, c), (2, b) and (a, b) be…MediumSingle correct
  12. 24 Feb 2021, Shift 1 · Q62Let p and q be two positive numbers such that p+q=2p + q = 2 and p4+q4=272p^4 + q^4 = 272. Then p and q are roots of the equation :MediumSingle correct

Shifts: 24 Feb 2021, Shift 2, 24 Feb 2021, Shift 1, 24 Jun 2022, Shift 1, 25 Jun 2022, Shift 2, 26 Jun 2022, Shift 2, 27 Jun 2022, Shift 2, 29 Jun 2022, Shift 1, 30 Jun 2022, Shift 1, 26 Jul 2022, Shift 2, 31 Jan 2024, Shift 2, 3 Apr 2025, Shift 1, 2 Apr 2026, 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