JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 13 April 2023, Shift 1, Maths Q3

Question 3 of 90 in this shift, Maths question 3 of 30, Section A.

Let

B=\begin{bmatrix}1&3&\alpha\\1&2&3\\\alpha&\alpha&4\end{bmatrix}

\alpha>2

be the adjoint of a matrix

A

and

|A|=2

. Then

\begin{bmatrix}\alpha&-2\alpha&\alpha\end{bmatrix}B\begin{bmatrix}\alpha\\-2\alpha\\\alpha\end{bmatrix}

is equal to

(1) $0$
(2) $-16$ Official answer
(3) $16$
(4) $32$

Official answer

Option 2

NTA final key.

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

Same idea in other shifts

Asked 16× 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 108 of the 174 JEE Main shifts held from 2017 to 2026.