JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 28 July 2022, Shift 1, Maths Q15

Question 15 of 90 in this shift, Maths question 15 of 30, Section A.

Let

S_1=\left\{z_1\in\mathbf{C}:|z_1-3|=\frac{1}{2}\right\}

and

S_2=\{z_2\in\mathbf{C}:|z_2-|z_2+1||=|z_2+|z_2-1||\}

. Then, for

z_1\in S_1

and

z_2\in S_2

, the least value of

|z_2-z_1|

is :

(1) $0$
(2) $\frac{1}{2}$
(3) $\frac{3}{2}$ Official answer
(4) $\frac{5}{2}$

Official answer

Option 3

NTA final key (2022 Session 2).

Chapter: Complex Numbers and Quadratic Equations
Topic: Complex Numbers - Polar Form
Idea tested: Polar Triangle Inequality Extrema

Same idea in other shifts

Asked 4× in all

2 Apr 2026, Shift 2 · Q2Let the circles $C_1: |z| = r$ and $C_2: |z - 3 - 4i| = 5, z \in \mathbb{C}_e$ be such that $C_2$ lies within $C_1$ . If $z_1$ moves on…MediumSingle correct
2 Apr 2025, Shift 1 · Q2Let $z$ be a complex number such that $|z|=1$ . If $\frac{2+k^2z}{k+\bar{z}}=kz$ , $k\in\mathbf{R}$ , then the maximum distance of $k+ik^2$ …HardSingle correct
9 Apr 2024, Shift 2 · Q2Let $z$ be a complex number such that the real part of $\frac{z-2i}{z+2i}$ is zero. Then, the maximum value of $|z-(6+8i)|$ is equal toMediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.