JEE Main 2025 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 7 April 2025, Shift 1, Maths Q5

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

Let

A

be a

3 \times 3

matrix such that

|\mathrm{adj}(\mathrm{adj}(\mathrm{adj}\,A))| = 81

. If

S = \left\{n \in \mathbb{Z} : \left(|\mathrm{adj}(\mathrm{adj}\,A)|\right)^{\frac{(n-1)^2}{2}} = |A|^{(3n^2 - 5n - 4)}\right\}

, then

\sum_{n \in S} \left|A^{(n^2+n)}\right|

is equal to

(1) $732$ Official answer
(2) $750$
(3) $820$
(4) $866$

Official answer

Option 1

NTA final key.

Chapter: Matrices
Topic: Matrix Inverse
Idea tested: Inverse Relation to Double Adjoint

Same idea in other shifts

Asked 8× in all

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30 Jan 2024, Shift 2 · Q3Let $R = \begin{pmatrix} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{pmatrix}$ be a non-zero $3\times 3$ matrix, where…HardOther
31 Jan 2024, Shift 2 · Q22Let A be a $3\times3$ matrix and $\det(A)=2$ . If…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 42 of the 174 JEE Main shifts held from 2017 to 2026.