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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 27 July 2022, Shift 2, Maths Q2

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

Let S be the set of all (α,β)(\alpha, \beta), π<α,β<2π\pi < \alpha, \beta < 2\pi, for which the complex number 1−isin⁡α1+2isin⁡α\frac{1 - i\sin\alpha}{1 + 2i\sin\alpha} is purely imaginary and 1+icos⁡β1−2icos⁡β\frac{1 + i\cos\beta}{1 - 2i\cos\beta} is purely real. Let Zαβ=sin⁡2α+icos⁡2βZ_{\alpha\beta} = \sin 2\alpha + i\cos 2\beta, (α,β)∈S(\alpha, \beta) \in S. Then ∑(α,β)∈S(iZαβ+1iZ‾αβ)\sum_{(\alpha, \beta) \in S}\left(i Z_{\alpha\beta} + \frac{1}{i\overline{Z}_{\alpha\beta}}\right) is equal to :
  1. (1)33
  2. (2)3i3i
  3. (3)11Official answer
  4. (4)2−i2 - i

Official answer

Option 3

NTA final key.

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