JEE Main 2025 · MathsMultiple choiceTwo statementsMediumConceptual

JEE Main 7 April 2025, Shift 1, Maths Q2

Question 2 of 75 in this shift, Maths question 2 of 25, Section A.

Among the statements (S1) : The set

\{z \in \mathbb{C} - \{-i\} : |z| = 1

and

\frac{z-i}{z+i}

is purely real

\}

contains exactly two elements, and (S2) : The set

\{z \in \mathbb{C} - \{-1\} : |z| = 1

and

\frac{z-1}{z+1}

is purely imaginary

\}

contains infinitely many elements.

(1)both are correct
(2)both are incorrect
(3)only (S1) is correct
(4)only (S2) is correctOfficial answer

Official answer

Option 4

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 4× in all

8 Apr 2024, Shift 2 · Q7The sum of all possible values of $\theta \in [-\pi, 2\pi]$ , for which $\frac{1 + i\cos\theta}{1 - 2i\cos\theta}$ is purely imaginary, is…MediumSingle correct
8 Apr 2023, Shift 2 · Q2Let $A = \left\{\theta \in (0, 2\pi) : \frac{1 + 2i\sin\theta}{1 - i\sin\theta} \text{ is purely imaginary}\right\}$ . Then the sum of the…MediumSingle correct
11 Apr 2023, Shift 2 · Q21Let $S = \left\{z \in \mathbb{C} - \{i, 2i\} : \frac{z^2 + 8iz - 15}{z^2 - 3iz - 2} \in \mathbb{R}\right\}$ . If…HardNumerical value

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.