1
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let A and B be $3 \times 3$ real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations $\left(A^2 B^2-B^2 A^2\right) X=O$. where $X$ is $3 \times 1$ column matrix of unknown variables and $O$ is a $3 \times 1$ null matrix, has

A
a unique solution
B
exactly two solutions
C
no solution
D
infinitely many solutions
2
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $A\left[\begin{array}{ll}2 & 1 \\ 7 & 4\end{array}\right]$ then $\left(A^2-5 A\right)^{-1}$ is

A
$\left(-\frac{1}{4}\right)\left[\begin{array}{cc}-3 & 1 \\ 7 & -1\end{array}\right]$
B
$\left(\frac{1}{4}\right)\left[\begin{array}{cc}-3 & 1 \\ 7 & -1\end{array}\right]$
C
$\left(\frac{1}{4}\right)\left[\begin{array}{ll}3 & 1 \\ 7 & 1\end{array}\right]$
D
$\left(\frac{1}{-4}\right)\left[\begin{array}{ll}3 & -1 \\ 7 & -1\end{array}\right]$
3
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
$\left[\begin{array}{c}-2 \\ 1 \\ -1\end{array}\right]$
4
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
$3$
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