1
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
2
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
$-2,1,1$
3
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
$-\frac{1}{14}\left[\begin{array}{ll}3 & -2 \\ 4 & -2\end{array}\right]$
4
MHT CET 2024 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $X=\left[\begin{array}{l}\mathrm{a} \\ \mathrm{b} \\ \mathrm{c}\end{array}\right], \mathrm{A}=\left[\begin{array}{ccc}1 & -1 & 2 \\ 2 & 0 & 1 \\ 3 & 2 & 1\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{l}3 \\ 1 \\ 4\end{array}\right]$. If $A X=B$, then the value of $2 a-3 b+4 c$ will be

A
0
B
$-$4
C
6
D
4
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