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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 25 June 2022, Shift 1, Maths Q20

Question 20 of 90 in this shift, Maths question 20 of 30, Section A.

Let a circle C in complex plane pass through the points z1=3+4iz_1=3+4i, z2=4+3iz_2=4+3i and z3=5iz_3=5i. If z(≠z1)z(\neq z_1) is a point on C such that the line through zz and z1z_1 is perpendicular to the line through z2z_2 and z3z_3, then arg⁡(z)\arg(z) is equal to :
  1. (1)tan⁡−1(25)−π\tan^{-1}\left(\frac{2}{\sqrt{5}}\right)-\pi
  2. (2)tan⁡−1(247)−π\tan^{-1}\left(\frac{24}{7}\right)-\piOfficial answer
  3. (3)tan⁡−1(3)−π\tan^{-1}(3)-\pi
  4. (4)tan⁡−1(34)−π\tan^{-1}\left(\frac{3}{4}\right)-\pi

Official answer

Option 2

NTA final key.

Same idea in other shifts

Asked 2× in all
  1. 5 Sep 2020, Shift 1 · Q52If the four complex numbers zz, z‾\overline{z}, z‾−2Re(z‾)\overline{z}-2\mathrm{Re}(\overline{z}) and z−2Re(z)z-2\mathrm{Re}(z) represent the vertices…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.