JEE Main 2021 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 3 August 2021, Shift 1, Maths Q81

Question 81 of 90 in this shift, Maths question 21 of 30, Section B.

x^2 - x + 1 = 0

, then the value of

\sum_{n=1}^{5}\left(x^n + \frac{1}{x^n}\right)^2

is ________.

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

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

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.