JEE Main 4 April 2025, Shift 2, Maths Q21

Question 21 of 75 in this shift, Maths question 21 of 25, Section B.

\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 ____________.

Official answer

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Roots of Unity
Idea tested: Cyclic Powers of Omega Modulo 3

Same idea in other shifts

Asked 2× in all

3 Aug 2021, Shift 1 · Q81If $x^2 - x + 1 = 0$ , then the value of $\sum_{n=1}^{5}\left(x^n + \frac{1}{x^n}\right)^2$ is ________.MediumNumerical 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.