1
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right]$ and $B=\left[\begin{array}{l}4 \\ 0 \\ 2\end{array}\right]$ such that $\mathrm{AX}=\mathrm{B}$, then $\mathrm{X}=$

A
$\left[\begin{array}{c}-1 \\ 2 \\ 1\end{array}\right]$
B
$\left[\begin{array}{c}2 \\ -1 \\ 1\end{array}\right]$
C
$\left[\begin{array}{c}-1 \\ 1 \\ 2\end{array}\right]$
D
$\left[\begin{array}{c}-2 \\ 1 \\ -1\end{array}\right]$
2
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{w}=\frac{-1-\mathrm{i} \sqrt{3}}{2}$ where $\mathrm{i}=\sqrt{-1}$, then the value of $\left|\begin{array}{ccc}1 & w & w^2 \\ w & w^2 & 1 \\ w^2 & 1 & w\end{array}\right|$ is

A
$-1$
B
$0$
C
$1$
D
$3$
3
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Inverse of the matrix $\left[\begin{array}{cc}0.8 & -0.6 \\ 0.6 & 0.8\end{array}\right]$ is

A
$\left[\begin{array}{cc}0.8 & 0.6 \\ -0.6 & 0.8\end{array}\right]$
B
$\left[\begin{array}{ll}-0.8 & 0.6 \\ -0.6 & 0.8\end{array}\right]$
C
$\left[\begin{array}{cc}-0.8 & -0.6 \\ 0.6 & 0.8\end{array}\right]$
D
$\left[\begin{array}{cc}8 & -6 \\ 6 & 8\end{array}\right]$
4
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
$\left[\begin{array}{cc}0 & -2 \sqrt{3} \\ 2 \sqrt{3} & 0\end{array}\right]$
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