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Friday, 9 October

JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 29 June 2022, Shift 1, Maths Q21

Question 21 of 90 in this shift, Maths question 21 of 30, Section B.

Let S={z∈C:∣z−2∣≤1,z(1+i)+zˉ(1−i)≤2}S = \{z \in \mathbf{C} : |z - 2| \le 1, z(1 + i) + \bar{z}(1 - i) \le 2\}. Let ∣z−4i∣|z - 4i| attains minimum and maximum values, respectively, at z1∈Sz_1 \in S and z2∈Sz_2 \in S. If 5(∣z1∣2+∣z2∣2)=α+β55(|z_1|^2 + |z_2|^2) = \alpha + \beta\sqrt{5}, where α\alpha and β\beta are integers, then the value of α+β\alpha + \beta is equal to ____________.

Official answer

26

NTA final key (2022 Session 1).

Chapter
Complex Numbers and Quadratic Equations
Topic
No close match in our taxonomy
Idea tested
No close match in our taxonomy

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.