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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 26 June 2022, Shift 1, Maths Q2

Question 2 of 90 in this shift, Maths question 2 of 30, Section A.

Let A={z∈C:∣z+1z−1∣<1}A = \left\{z \in \mathbf{C} : \left|\frac{z+1}{z-1}\right| < 1\right\} and B={z∈C:arg⁡(z−1z+1)=2π3}B = \left\{z \in \mathbf{C} : \arg\left(\frac{z-1}{z+1}\right) = \frac{2\pi}{3}\right\}. Then A∩BA \cap B is :
  1. (1)a portion of a circle centred at (0,−13)\left(0, -\frac{1}{\sqrt{3}}\right) that lies in the second and third quadrants only
  2. (2)a portion of a circle centred at (0,−13)\left(0, -\frac{1}{\sqrt{3}}\right) that lies in the second quadrant onlyOfficial answer
  3. (3)an empty set
  4. (4)a portion of a circle of radius 23\frac{2}{\sqrt{3}} that lies in the third quadrant only

Official answer

Option 2

NTA final key.

Chapter
Complex Numbers and Quadratic Equations
Topic
Complex Numbers - Polar Form
Idea tested
Locus of Argument Ratio (Circular Arc)

Same idea in other shifts

Asked 6× in all
  1. 4 Apr 2026, Shift 1 · Q3Let zz be a complex number such that ∣z+2∣=∣z−2∣|z+2|=|z-2| and arg⁡(z+3z−i)=π4\arg\left(\frac{z+3}{z-i}\right)=\frac{\pi}{4}. Then ∣z∣2|z|^2 is equal to:MediumSingle correct
  2. 29 Jun 2022, Shift 2 · Q2Let arg⁡(z)\arg(z) represent the principal argument of the complex number zz. Then, ∣z∣=3|z| = 3 and arg⁡(z−1)−arg⁡(z+1)=π4\arg(z - 1) - \arg(z + 1) = \frac{\pi}{4}…MediumSingle correct
  3. 26 Aug 2021, Shift 1 · Q62The equation arg⁡(z−1z+1)=π4\arg\left(\frac{z-1}{z+1}\right) = \frac{\pi}{4} represents a circle with :MediumSingle correct
  4. 31 Aug 2021, Shift 1 · Q82A point zz moves in the complex plane such that arg⁡(z−2z+2)=π4\arg\left(\frac{z-2}{z+2}\right)=\frac{\pi}{4}, then the minimum value of…HardNumerical value
  5. 31 Aug 2021, Shift 2 · Q62If zz is a complex number such that z−iz−1\frac{z-i}{z-1} is purely imaginary, then the minimum value of ∣z−(3+3i)∣|z-(3+3i)| is :MediumSingle 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 108 of the 174 JEE Main shifts held from 2017 to 2026.