1
JEE Main 2025 (Online) 23rd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $\mathrm{A}, \mathrm{B}, \operatorname{and}\left(\operatorname{adj}\left(\mathrm{A}^{-1}\right)+\operatorname{adj}\left(\mathrm{B}^{-1}\right)\right)$ are non-singular matrices of same order, then the inverse of $A\left(\operatorname{adj}\left(A^{-1}\right)+\operatorname{adj}\left(B^{-1}\right)\right)^{-1} B$, is equal to

A
$\frac{A B^{-1}}{|A|}+\frac{B A^{-1}}{|B|}$
B
$\operatorname{adj}\left(\mathrm{B}^{-1}\right)+\operatorname{adj}\left(\mathrm{A}^{-1}\right)$
C
$\mathrm{AB}^{-1}+\mathrm{A}^{-1} \mathrm{~B}$
D
$\frac{1}{|A B|}(\operatorname{adj}(B)+\operatorname{adj}(A))$
2
JEE Main 2025 (Online) 22nd January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the system of linear equations :

$$\begin{aligned} & x+y+2 z=6 \\ & 2 x+3 y+\mathrm{az}=\mathrm{a}+1 \\ & -x-3 y+\mathrm{b} z=2 \mathrm{~b} \end{aligned}$$

where $a, b \in \mathbf{R}$, has infinitely many solutions, then $7 a+3 b$ is equal to :

A
12
B
9
C
22
D
16
3
JEE Main 2025 (Online) 22nd January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

For a $3 \times 3$ matrix $M$, let trace $(M)$ denote the sum of all the diagonal elements of $M$. Let $A$ be a $3 \times 3$ matrix such that $|A|=\frac{1}{2}$ and trace $(A)=3$. If $B=\operatorname{adj}(\operatorname{adj}(2 A))$, then the value of $|B|+$ trace $(B)$ equals :

A
56
B
132
C
174
D
280
4
JEE Main 2024 (Online) 9th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$B=\left[\begin{array}{ll}1 & 3 \\ 1 & 5\end{array}\right]$$ and $$A$$ be a $$2 \times 2$$ matrix such that $$A B^{-1}=A^{-1}$$. If $$B C B^{-1}=A$$ and $$C^4+\alpha C^2+\beta I=O$$, then $$2 \beta-\alpha$$ is equal to

A
16
B
10
C
8
D
2
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