JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 5 April 2024, Shift 2, Maths Q5

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

Let

\alpha\beta \neq 0

and

A = \begin{bmatrix} \beta & \alpha & 3 \\ \alpha & \alpha & \beta \\ -\beta & \alpha & 2\alpha \end{bmatrix}

. If

B = \begin{bmatrix} 3\alpha & -9 & 3\alpha \\ -\alpha & 7 & -2\alpha \\ -2\alpha & 5 & -2\beta \end{bmatrix}

is the matrix of cofactors of the elements of

A

, then

\det(AB)

is equal to :

(1)125
(2)64
(3)216Official answer
(4)343

Official answer

Option 3

NTA final key.

Chapter: Determinants
Topic: Matrix Inverse
Idea tested: Cofactor Matrix and Adjoint

Same idea in other shifts

Asked 6× in all

8 Apr 2026, Shift 2 · Q4Let $A = \begin{bmatrix} \alpha & 1 & 2 \\ 2 & 3 & 0 \\ 0 & 4 & 5 \end{bmatrix}$ and…HardSingle correct
26 Jul 2022, Shift 1 · Q4Let A be a $2 \times 2$ matrix with $\det\,(\mathrm{A}) = -1$ and…HardSingle correct
4 Aug 2021, Shift 1 · Q63Let $A=\begin{bmatrix}x&3&2\\1&y&4\\2&2&z\end{bmatrix}$ , $xyz=60$ and $8x+4y+3z=20$ . If $A(adj\ A)=k\,I$ , then $k$ is equal toMediumSingle correct
17 Mar 2021, Shift 1 · Q82If A $=\begin{bmatrix}2 & 3\\ 0 & -1\end{bmatrix}$ , then the value of $\det(A^{4})+\det\left(A^{10}-(\mathrm{Adj}(2A))^{10}\right)$ is…MediumNumerical value
2 Apr 2017 (offline) · Q64If $A=\begin{bmatrix}2&-3\\-4&1\end{bmatrix}$ , then $\mathrm{adj}(3A^2+12A)$ 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.