JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 4 April 2024, Shift 1, Maths Q5

Question 5 of 90 in this shift, Maths question 5 of 30, Section A.

Let

\alpha \in (0, \infty)

and

A=\begin{bmatrix}1&2&\alpha\\1&0&1\\0&1&2\end{bmatrix}

. If

\det(\mathrm{adj}(2A-A^T)\cdot \mathrm{adj}(A-2A^T))=2^8

, then

(\det(A))^2

is equal to :

(1) $1$
(2) $16$ Official answer
(3) $36$
(4) $49$

Official answer

Option 2

NTA final key.

Chapter: Determinants
Topic: Matrix Inverse
Idea tested: Trap involving |adj(A)| vs |A^-1|

Same idea in other shifts

Asked 10× in all

5 Apr 2026, Shift 1 · Q3Let A be a $3 \times 3$ matrix such that $A^T\begin{bmatrix}1\\0\\1\end{bmatrix}=\begin{bmatrix}5\\2\\2\end{bmatrix}$ ,…HardSingle correct
2 Apr 2025, Shift 1 · Q15Let $a\in\mathbf{R}$ and A be a matrix of order $3\times3$ such that $\det(A)=-4$ and…MediumSingle correct
3 Apr 2025, Shift 1 · Q5Let $A$ be a matrix of order $3 \times 3$ and $|A| = 5$ . If $|2\,adj(3A\,adj(2A))| = 2^{\alpha}\cdot 3^{\beta}\cdot 5^{\gamma}$ ,…MediumSingle correct
10 Apr 2023, Shift 1 · Q4If $A$ is a $3\times3$ matrix and $|A|=2$ , then $\left|3\,adj\left(|3A|A^2\right)\right|$ is equal toMediumSingle correct
13 Apr 2023, Shift 2 · Q5Let for $A=\begin{bmatrix}1&2&3\\ \alpha&3&1\\ 1&1&2\end{bmatrix}$ , $|A|=2$ . If $|2\,\mathrm{adj}(2\,\mathrm{adj}(2A))|=32^n$ , then…MediumSingle correct
28 Jul 2022, Shift 1 · Q14Let the matrix $A=\begin{bmatrix}0&1&0\\0&0&1\\1&0&0\end{bmatrix}$ and the matrix $B_0=A^{49}+2A^{98}$ . If $B_n=\mathrm{Adj}(B_{n-1})$ for…HardSingle correct
24 Jun 2022, Shift 1 · Q9Let $S = \{\sqrt{n} : 1 \le n \le 50$ and n is odd $\}$ . Let $a \in S$ and…MediumSingle correct
26 Jun 2022, Shift 1 · Q3Let A be a $3 \times 3$ invertible matrix. If $|\mathrm{adj}\,(24A)| = |\mathrm{adj}\,(3\,\mathrm{adj}\,(2A))|$ , then $|A|^2$ is equal to :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.