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JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 8 April 2025, Shift 2, Maths Q5

Question 5 of 75 in this shift, Maths question 5 of 25, Section A.

Let

\alpha

be a solution of

x^2 + x + 1 = 0

, and for some

a

and

b

in

\mathbb{R}

,

\begin{bmatrix} 4 & a & b \end{bmatrix}\begin{bmatrix} 1 & 16 & 13 \\ -1 & -1 & 2 \\ -2 & -14 & -8 \end{bmatrix} = \begin{bmatrix} 0 & 0 & 0 \end{bmatrix}

. If

\frac{4}{\alpha^4} + \frac{m}{\alpha^a} + \frac{n}{\alpha^b} = 3

, then

m + n

is equal to ________

(1)8
(2)11Official answer
(3)7
(4)3

Official answer

Option 2

NTA final key.

Chapter: Matrices
Topic: Roots of Unity
Idea tested: Periodicity of Omega Powers

Same idea in other shifts

Asked 3× in all

27 Jan 2024, Shift 1 · Q21If $\alpha$ 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…MediumNumerical value
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.