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JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 8 April 2023, Shift 2, Maths Q2

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

Let

A = \left\{\theta \in (0, 2\pi) : \frac{1 + 2i\sin\theta}{1 - i\sin\theta} \text{ is purely imaginary}\right\}

. Then the sum of the elements in

A

is

(1) $2\pi$
(2) $3\pi$
(3) $4\pi$ Official answer
(4) $\pi$

Official answer

Option 3

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Complex Numbers - Polar Form
Idea tested: Purely Real and Imaginary Euler Conditions

Same idea in other shifts

Asked 2× in all

7 Apr 2025, Shift 1 · Q2Among the statements (S1) : The set $\{z \in \mathbb{C} - \{-i\} : |z| = 1$ and $\frac{z-i}{z+i}$ is purely real $\}$ contains exactly two…MediumTwo statements

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.