JEE Main 2024 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 27 January 2024, Shift 1, Maths Q21

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

\alpha

satisfies the equation

x^2+x+1=0

and

(1+\alpha)^7=A+B\alpha+C\alpha^2

A, B, C\geq 0

, then

5(3A-2B-C)

is equal to ________.

Official answer

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Roots of Unity
Idea tested: Periodicity of Omega Powers

Same idea in other shifts

Asked 3× in all

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
8 Jan 2020, Shift 2 · Q52Let $\alpha = \frac{-1 + i\sqrt{3}}{2}$ . If $a = (1 + \alpha) \sum_{k=0}^{100} \alpha^{2k}$ and $b = \sum_{k=0}^{100} \alpha^{3k}$ , then a…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 108 of the 174 JEE Main shifts held from 2017 to 2026.