1
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $\mathrm{A}=\left[\begin{array}{cc}1 & 2 \\ -5 & 1\end{array}\right]$ and $\mathrm{A}^{-1}=x \mathrm{~A}+y \mathrm{I}_2$, (where $\mathrm{I}_2$ is unit matrix of order 2), then

A
$x=\frac{-1}{11}, y=\frac{2}{11}$
B
$x=\frac{1}{11}, y=\frac{-2}{11}$
C
$x=\frac{-1}{11}, y=\frac{-2}{11}$
D
$x=\frac{1}{11}, y=\frac{2}{11}$
2
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Suppose A is any $3 \times 3$ non-singular matrix and $(\mathrm{A}-3 \mathrm{I})(\mathrm{A}-5 \mathrm{I})=0$ where $\mathrm{I}=\mathrm{I}_3$ and $\mathrm{O}=\mathrm{O}_3$. Here $\mathrm{O}_3$ represent zero matrix of order 3 and $\mathrm{I}_3$ is an identity matrix of order 3 . If $\alpha A+\beta A^{-1}=4 I$, then $\alpha+\beta$ is equal to

A
13
B
7
C
12
D
8
3
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

For the system $x-y+z=4,2 x+y-3 z=0$, $x+y+z=2$, the values of $x, y, z$ respectively are given by

A
$2,1,1$
B
$2,1,-1$
C
$2,-1,1$
D
$-2,1,1$
4
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $A=\left[\begin{array}{cc}2 & -2 \\ 4 & 3\end{array}\right]$, then $A^{-1}=$

A
$-\frac{1}{2}\left[\begin{array}{cc}3 & 2 \\ -4 & 2\end{array}\right]$
B
$\frac{1}{14}\left[\begin{array}{cc}3 & 2 \\ -4 & 2\end{array}\right]$
C
$\frac{1}{14}\left[\begin{array}{cc}-3 & -2 \\ 4 & -2\end{array}\right]$
D
$-\frac{1}{14}\left[\begin{array}{ll}3 & -2 \\ 4 & -2\end{array}\right]$
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