JEE Main 2024 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 1 February 2024, Shift 2, Maths Q3

Question 3 of 90 in this shift, Maths question 3 of 30, Section A. NTA dropped this question from the final key; it is left out of every count on this site.

z

is a complex number such that

|z|\geq 1

, then the minimum value of

\left|z+\frac{1}{2}(3+4i)\right|

is :

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

Official answer

Dropped by NTA (marks given to all)

NTA final key: NTA final key: Drop (question dropped).

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

Same idea in other shifts

Asked 8× 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
1 Feb 2024, Shift 1 · Q22Let $P=\{z\in\mathbb{C}:|z+2-3i|\leq1\}$ and $Q=\{z\in\mathbb{C}:z(1+i)+\bar{z}(1-i)\leq-8\}$ . Let in $P\cap Q$ , $|z-3+2i|$ be maximum and…HardNumerical value
25 Jul 2022, Shift 2 · Q1For $z \in \mathbb{C}$ if the minimum value of $\left(\left|z-3\sqrt{2}\right|+\left|z-p\sqrt{2}i\right|\right)$ is $5\sqrt{2}$ , then a…MediumSingle correct
28 Jul 2022, Shift 1 · Q15Let $S_1=\left\{z_1\in\mathbf{C}:|z_1-3|=\frac{1}{2}\right\}$ and $S_2=\{z_2\in\mathbf{C}:|z_2-|z_2+1||=|z_2+|z_2-1||\}$ . Then, for…HardSingle correct
29 Jul 2022, Shift 2 · Q1If $z\neq 0$ be a complex number such that $\left|z-\frac{1}{z}\right|=2$ , then the maximum value of $|z|$ is :MediumSingle correct
26 Feb 2021, Shift 2 · Q82Let $z$ be those complex numbers which satisfy $|z+5| \le 4$ and $z(1+i)+\overline{z}(1-i) \ge -10$ , $i=\sqrt{-1}$ . If the maximum value…HardNumerical value

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 108 of the 174 JEE Main shifts held from 2017 to 2026.