JEE Main 2026 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 8 April 2026, Shift 2, Maths Q4

Question 4 of 75 in this shift, Maths question 4 of 25, Section A.

Let

A = \begin{bmatrix} \alpha & 1 & 2 \\ 2 & 3 & 0 \\ 0 & 4 & 5 \end{bmatrix}

and

B = \begin{bmatrix} 1 & 0 & 0 \\ 0 & -5\alpha & 0 \\ 0 & 4\alpha & -2\alpha \end{bmatrix} + \mathrm{adj}(A)

. If

\det(B) = 66

, then

\det(\mathrm{adj}(A))

equals :

(1)289
(2)361
(3)441Official answer
(4)529

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

5 Apr 2024, Shift 2 · Q5Let $\alpha\beta \neq 0$ and…MediumSingle 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.