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Saturday, 31 October

JEE Main · Maths · Complex Numbers and Quadratic Equations

Newton's Sums

JEE Main asked Newton's Sums 16 times in 16 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2023, 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 1 year. In 2021, 2022, 2023, 2024 and 2025 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
16
in 16 shifts
Years
7 of 8
First asked
2020
last in 2026
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, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170.08’200.14’210.07’220.21’230.14’240.25’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 4 in 24 shifts · 2022: 2 in 24 shifts · 2023: 3 in 12 shifts · 2024: 3 in 18 shifts · 2025: 2 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
  • 20252 of 8
  • 20243 of 18
  • 20233 of 12
  • 20222 of 24
  • 20214 of 24
  • 20201 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
  • Sum of powers of quadratic roots

Difficulty

Easy 3Medium 11Hard 2

7 of the 16 questions had a numerical answer.

Every question

All 16 questions

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

  1. 6 Apr 2026, Shift 2 · Q3Let S={z∈C:z2+6 iz−3=0}S=\{z\in\mathbb{C}: z^2+\sqrt{6}\,iz-3=0\}. Then ∑z∈Sz8\sum_{z\in S} z^8 is equal to :MediumSingle correct
  2. 3 Apr 2025, Shift 1 · Q3Let α\alpha and β\beta be the roots of x2+3x−16=0x^2 + \sqrt{3}x - 16 = 0, and γ\gamma and δ\delta be the roots of x2+3x−1=0x^2 + 3x - 1 = 0. If…MediumSingle correct
  3. 2 Apr 2025, Shift 1 · Q17Let Pn=αn+βnP_n=\alpha^n+\beta^n, n∈Nn\in\mathbf{N}. If P10=123P_{10}=123, P9=76P_9=76, P8=47P_8=47 and P1=1P_1=1, then the quadratic equation having roots…MediumSingle correct
  4. 9 Apr 2024, Shift 2 · Q3Let α,β; α>β\alpha, \beta;\ \alpha>\beta, be the roots of the equation x2−2x−3=0x^2-\sqrt{2}x-\sqrt{3}=0. Let Pn=αn−βn, n∈NP_n=\alpha^n-\beta^n,\ n\in\mathbb{N}.…MediumSingle correct
  5. 6 Apr 2024, Shift 2 · Q21Let α,β\alpha,\beta be roots of x2+2x−8=0x^2+\sqrt{2}x-8=0. If Un=αn+βnU_n=\alpha^n+\beta^n, then U10+2U92U8\frac{U_{10}+\sqrt{2}U_9}{2U_8} is equal to ________.EasyNumerical value
  6. 6 Apr 2024, Shift 1 · Q4Let α,β\alpha, \beta be the distinct roots of the equation x2−(t2−5t+6)x+1=0x^2-(t^2-5t+6)x+1=0, t∈Rt \in \mathbb{R} and an=αn+βna_n=\alpha^n+\beta^n. Then the…HardSingle correct
  7. 13 Apr 2023, Shift 2 · Q3Let α,β\alpha, \beta be the roots of the equation x2−2x+2=0x^2-\sqrt{2}x+2=0. Then α14+β14\alpha^{14}+\beta^{14} is equal toMediumSingle correct
  8. 12 Apr 2023, Shift 1 · Q2Let α,β\alpha, \beta be the roots of the quadratic equation x2+6x+3=0x^2+\sqrt{6}x+3=0. Then…HardSingle correct
  9. 11 Apr 2023, Shift 1 · Q24If aa and bb are the roots of the equation x2−7x−1=0x^2 - 7x - 1 = 0, then the value of…MediumNumerical value
  10. 26 Jun 2022, Shift 1 · Q21The sum of the cubes of all the roots of the equation x4−3x3−2x2+3x+1=0x^4 - 3x^3 - 2x^2 + 3x + 1 = 0 is ________.MediumNumerical value
  11. 29 Jul 2022, Shift 2 · Q22Let α,β (α>β)\alpha,\beta\ (\alpha>\beta) be the roots of the quadratic equation x2−x−4=0x^2-x-4=0. If Pn=αn−βnP_n=\alpha^n-\beta^n, n∈Nn\in\mathbb{N}, then…MediumNumerical value
  12. 25 Jul 2021, Shift 2 · Q84If a+b+c=1a+b+c=1, ab+bc+ca=2ab+bc+ca=2 and abc=3abc=3, then the value of a4+b4+c4a^4+b^4+c^4 is equal to __________.MediumNumerical value
  13. 25 Jul 2021, Shift 1 · Q90If α,β\alpha,\beta are roots of the equation x2+5(2)x+10=0x^2+5(\sqrt2)x+10=0, α>β\alpha>\beta and Pn=αn−βnP_n=\alpha^n-\beta^n for each positive integer n,…MediumNumerical value
  14. 26 Feb 2021, Shift 2 · Q87Let α\alpha and β\beta be two real numbers such that α+β=1\alpha+\beta=1 and αβ=−1\alpha\beta=-1. Let pn=(α)n+(β)np_n=(\alpha)^n+(\beta)^n, pn−1=11p_{n-1}=11…EasyNumerical value
  15. 25 Feb 2021, Shift 2 · Q66Let α\alpha and β\beta be the roots of x2−6x−2=0x^2 - 6x - 2 = 0. If an=αn−βna_n = \alpha^n - \beta^n for n≥1n \geq 1, then the value of…MediumSingle correct
  16. 2 Sep 2020, Shift 1 · Q52Let α\alpha and β\beta be the roots of the equation, 5x2+6x−2=05x^{2}+6x-2=0. If Sn=αn+βnS_n=\alpha^{n}+\beta^{n}, n=1,2,3,…n=1, 2, 3, \ldots, then :EasySingle correct

Shifts: 2 Sep 2020, Shift 1, 25 Feb 2021, Shift 2, 26 Feb 2021, Shift 2, 25 Jul 2021, Shift 2, 25 Jul 2021, Shift 1, 26 Jun 2022, Shift 1, 29 Jul 2022, Shift 2, 11 Apr 2023, Shift 1, 12 Apr 2023, Shift 1, 13 Apr 2023, Shift 2, 6 Apr 2024, Shift 2, 6 Apr 2024, Shift 1, 9 Apr 2024, Shift 2, 2 Apr 2025, Shift 1, 3 Apr 2025, Shift 1, 6 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