JEE Main 2026 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 5 April 2026, Shift 1, Maths Q3

Question 3 of 75 in this shift, Maths question 3 of 25, Section A.

Let 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}

A^T\begin{bmatrix}0\\0\\1\end{bmatrix}=\begin{bmatrix}3\\1\\1\end{bmatrix}

A\begin{bmatrix}1\\0\\1\end{bmatrix}=\begin{bmatrix}3\\4\\4\end{bmatrix}

and

A\begin{bmatrix}0\\0\\1\end{bmatrix}=\begin{bmatrix}1\\3\\1\end{bmatrix}

. If

\det(A) = 1

, then

\det(\mathrm{adj}(A^2 + A))

is equal to:

(1)16
(2)25
(3)49
(4)64Official answer

Official answer

Option 4

NTA final key.

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

Same idea in other shifts

Asked 6× in all

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
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

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 42 of the 174 JEE Main shifts held from 2017 to 2026.