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Saturday, 31 October

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JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 30 January 2024, Shift 2, Maths Q2

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

If

z

is a complex number, then the number of common roots of the equations

z^{1985} + z^{100} + 1 = 0

and

z^3 + 2z^2 + 2z + 1 = 0

, is equal to

(1) $0$
(2) $1$
(3) $2$ Official answer
(4) $3$

Official answer

Option 3

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Roots of Unity
Idea tested: Roots of z^2 + z + 1 = 0

Same idea in other shifts

Asked 2× in all

26 Jun 2022, Shift 2 · Q23If $z^2 + z + 1 = 0$ , $z \in \mathbb{C}$ , then $\left|\sum_{n=1}^{15}\left(z^n + (-1)^n \frac{1}{z^n}\right)^2\right|$ is equal to ______.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.