1
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $A=\left[\begin{array}{ll}x & 1 \\ 1 & 0\end{array}\right], x \in \mathbb{R}^{+}$and $A^4=\left[a_{i j}\right]_2$. If $a_{11}=109$, then $\left(A^4\right)^{-1}=$

A
$\left[\begin{array}{rr}109 & 33 \\ 33 & 10\end{array}\right]$
B
$\left[\begin{array}{ll}10 & 33 \\ 33 & 10\end{array}\right]$
C
$\left[\begin{array}{cc}10 & 33 \\ 33 & 109\end{array}\right]$
D
$\left[\begin{array}{cc}10 & -33 \\ -33 & 109\end{array}\right]$
2
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $A=\left[\begin{array}{cc}5 a & -b \\ 3 & 2\end{array}\right]$ and $A \cdot \operatorname{adj} A=A A^T$, then $5 a+b$ is equal to

A
$-$1
B
5
C
3
D
13
3
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
4
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
$\left(\frac{1}{-4}\right)\left[\begin{array}{ll}3 & -1 \\ 7 & -1\end{array}\right]$
MHT CET Subjects
EXAM MAP