JEE Main 2017 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 2 April 2017 (offline), Maths Q64

Question 64 of 90 in this shift, Maths question 4 of 30.

A=\begin{bmatrix}2&-3\\-4&1\end{bmatrix}

, then

\mathrm{adj}(3A^2+12A)

is equal to :

(1) $\begin{bmatrix}51&63\\84&72\end{bmatrix}$ Official answer
(2) $\begin{bmatrix}51&84\\63&72\end{bmatrix}$
(3) $\begin{bmatrix}72&-63\\-84&51\end{bmatrix}$
(4) $\begin{bmatrix}72&-84\\-63&51\end{bmatrix}$

Official answer

Option 1

CBSE answer key (25/04/2017, used for result).

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
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

Question text from the official JEE Main paper published by NTA (CBSE ran the 2017 exam); 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.