JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 2 April 2025, Shift 1, Maths Q15

Question 15 of 75 in this shift, Maths question 15 of 25, Section A.

Let

a\in\mathbf{R}

and A be a matrix of order

3\times3

such that

\det(A)=-4

and

A+I=\begin{bmatrix}1&a&1\\2&1&0\\a&1&2\end{bmatrix}

, where I is the identity matrix of order

3\times3

. If

\det((a+1)\operatorname{adj}((a-1)A))

2^m3^n

m, n\in\{0, 1, 2,\ldots, 20\}

, then

m+n

is equal to :

(1)14
(2)15
(3)16Official answer
(4)17

Official answer

Option 3

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

5 Apr 2026, Shift 1 · Q3Let A be a $3 \times 3$ matrix such that $A^T\begin{bmatrix}1\\0\\1\end{bmatrix}=\begin{bmatrix}5\\2\\2\end{bmatrix}$ ,…HardSingle 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.