1
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $A+B=\left[\begin{array}{cc}1 & \tan \frac{\theta}{2} \\ -\tan \frac{\theta}{2} & 1\end{array}\right]$ where $A$ is symmetric and $B$ is skew-symmetric matrix, then the matrix $\left(A^{-1} B+A B^{-1}\right)$ at $\theta=\frac{\pi}{6}$ is given by

A
$\left[\begin{array}{cc}1 & 2 \sqrt{3} \\ 2 \sqrt{3} & 1\end{array}\right]$
B
$\left[\begin{array}{cc}-1 & -2 \sqrt{3} \\ 2 \sqrt{3} & 1\end{array}\right]$
C
$\left[\begin{array}{cc}0 & 2 \sqrt{3} \\ 2 \sqrt{3} & 0\end{array}\right]$
D
$\left[\begin{array}{cc}0 & -2 \sqrt{3} \\ 2 \sqrt{3} & 0\end{array}\right]$
2
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

For the matrix $A=\left[\begin{array}{ccc}2 & 0 & -1 \\ 3 & 1 & 2 \\ -1 & 1 & 2\end{array}\right]$, the matrix of cofactors is

A
$\left[\begin{array}{ccc}0 & 8 & -4 \\ -1 & 3 & 2 \\ 1 & -7 & 2\end{array}\right]$
B
$\left[\begin{array}{ccc}0 & -8 & 4 \\ -1 & 3 & -2 \\ 1 & -7 & 2\end{array}\right]$
C
$\left[\begin{array}{ccc}0 & 8 & -4 \\ 1 & -3 & 2 \\ -1 & 7 & -2\end{array}\right]$
D
$\left[\begin{array}{ccc}0 & -8 & 4 \\ -1 & 3 & 2 \\ -1 & -7 & 2\end{array}\right]$
3
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $A=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & a & 3 \\ 3 & 2 & 2\end{array}\right]$ and $B=\left[\begin{array}{ccc}-2 & 0 & b \\ 7 & -1 & -2 \\ c & 1 & 1\end{array}\right]$ and if matrix $B$ is the inverse of matrix $A$, then value of $4 a+2 b-c$ is

A
6
B
$-$14
C
14
D
$-$6
4
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
$x=\frac{1}{11}, y=\frac{2}{11}$
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