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.

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 topic in other shifts

All Roots of Unity questions

3 Apr 2025, Shift 2 · Q5If $z_1, z_2, z_3 \in \mathbb{C}$ are the vertices of an equilateral triangle, whose centroid is $z_0$ , then…MediumSingle correct
4 Apr 2025, Shift 2 · Q21If $\alpha$ is a root of the equation $x^2+x+1=0$ and $\sum_{k=1}^{n}\left(\alpha^k+\frac{1}{\alpha^k}\right)^2=20$ , then n is equal to…MediumNumerical value
8 Apr 2025, Shift 2 · Q5Let $\alpha$ be a solution of $x^2 + x + 1 = 0$ , and for some $a$ and $b$ in $\mathbb{R}$ ,…MediumSingle correct
25 Jul 2022, Shift 1 · Q2If $\alpha,\ \beta,\ \gamma,\ \delta$ are the roots of the equation $x^4+x^3+x^2+x+1=0$ , then…MediumSingle correct
18 Mar 2021, Shift 1 · Q81Let $z_1, z_2$ be the roots of the equation $z^2+az+12=0$ and $z_1, z_2$ form an equilateral triangle with origin. Then, the value of…MediumNumerical value
2 Apr 2017 (offline) · Q63Let $\omega$ be a complex number such that $2\omega+1=z$ where $z=\sqrt{-3}$ . If…MediumSingle correct

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.