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

\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

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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.