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Saturday, 31 October

JEE Main · Maths · Complex Numbers and Quadratic Equations

Polar Triangle Inequality Extrema

JEE Main asked Polar Triangle Inequality Extrema 8 times in 8 of the 108 shifts Lumi analysed, in 2021, 2022, 2024, 2025 and 2026. It belongs to Complex Numbers - Polar Form, in Complex Numbers and Quadratic Equations (Maths). The longest wait between two years asking it was 2 years. In 2022 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
8
in 8 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.

00.10.20’170’200.03’210.11’220’230.09’240.13’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 3 in 24 shifts · 2023: 0 in 12 shifts · 2024: 2 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
  • 20242 of 18
  • 20230 of 12
  • 20223 of 24
  • 20211 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.

  • Max/min distance between points on circles
  • Max distance from circle given complex condition

Difficulty

Easy 0Medium 4Hard 4

2 of the 8 questions had a numerical answer.

Every question

All 8 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 · Q2Let the circles C1:∣z∣=rC_1: |z| = r and C2:∣z−3−4i∣=5,z∈CeC_2: |z - 3 - 4i| = 5, z \in \mathbb{C}_e be such that C2C_2 lies within C1C_1. If z1z_1 moves on…MediumSingle correct
  2. 2 Apr 2025, Shift 1 · Q2Let zz be a complex number such that ∣z∣=1|z|=1. If 2+k2zk+zˉ=kz\frac{2+k^2z}{k+\bar{z}}=kz, k∈Rk\in\mathbf{R}, then the maximum distance of k+ik2k+ik^2…HardSingle correct
  3. 1 Feb 2024, Shift 1 · Q22Let P={z∈C:∣z+2−3i∣≤1}P=\{z\in\mathbb{C}:|z+2-3i|\leq1\} and Q={z∈C:z(1+i)+zˉ(1−i)≤−8}Q=\{z\in\mathbb{C}:z(1+i)+\bar{z}(1-i)\leq-8\}. Let in P∩QP\cap Q, ∣z−3+2i∣|z-3+2i| be maximum and…HardNumerical value
  4. 9 Apr 2024, Shift 2 · Q2Let zz be a complex number such that the real part of z−2iz+2i\frac{z-2i}{z+2i} is zero. Then, the maximum value of ∣z−(6+8i)∣|z-(6+8i)| is equal toMediumSingle correct
  5. 29 Jul 2022, Shift 2 · Q1If z≠0z\neq 0 be a complex number such that ∣z−1z∣=2\left|z-\frac{1}{z}\right|=2, then the maximum value of ∣z∣|z| is :MediumSingle correct
  6. 28 Jul 2022, Shift 1 · Q15Let S1={z1∈C:∣z1−3∣=12}S_1=\left\{z_1\in\mathbf{C}:|z_1-3|=\frac{1}{2}\right\} and S2={z2∈C:∣z2−∣z2+1∣∣=∣z2+∣z2−1∣∣}S_2=\{z_2\in\mathbf{C}:|z_2-|z_2+1||=|z_2+|z_2-1||\}. Then, for…HardSingle correct
  7. 25 Jul 2022, Shift 2 · Q1For z∈Cz \in \mathbb{C} if the minimum value of (∣z−32∣+∣z−p2i∣)\left(\left|z-3\sqrt{2}\right|+\left|z-p\sqrt{2}i\right|\right) is 525\sqrt{2}, then a…MediumSingle correct
  8. 26 Feb 2021, Shift 2 · Q82Let zz be those complex numbers which satisfy ∣z+5∣≤4|z+5| \le 4 and z(1+i)+z‾(1−i)≥−10z(1+i)+\overline{z}(1-i) \ge -10, i=−1i=\sqrt{-1}. If the maximum value…HardNumerical value

Shifts: 26 Feb 2021, Shift 2, 25 Jul 2022, Shift 2, 28 Jul 2022, Shift 1, 29 Jul 2022, Shift 2, 1 Feb 2024, Shift 1, 9 Apr 2024, Shift 2, 2 Apr 2025, Shift 1, 2 Apr 2026, Shift 2.

Same topic

Other ideas in Complex Numbers - Polar Form

Complex Numbers - Polar Form has 20 ideas JEE Main has asked; 9 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas