1
MHT CET 2023 10th May Morning Shift
+2
-0

If $$B=\left[\begin{array}{lll}1 & \alpha & 2 \\ 1 & 2 & 2 \\ 2 & 3 & 3\end{array}\right]$$ is the adjoint of a $$3 \times 3$$ matrix A and $$|A|=5$$, then $$\alpha$$ is equal to

A
25
B
27
C
3$$\sqrt3$$
D
5
2
MHT CET 2023 9th May Evening Shift
+2
-0

If $$\left|\begin{array}{ccc}\cos (A+B) & -\sin (A+B) & \cos (2 B) \\ \sin A & \cos A & \sin B \\ -\cos A & \sin A & \cos B\end{array}\right|=0$$, then the value of $$B$$ is

A
$$\mathrm{n} \pi, \mathrm{n} \in \mathbb{Z}$$
B
$$(2 \mathrm{n}+1) \frac{\pi}{2}, \mathrm{n} \in \mathbb{Z}$$
C
$$(2 \mathrm{n}+1) \frac{\pi}{4}, \mathrm{n} \in \mathbb{Z}$$
D
$$2 \mathrm{n} \frac{\pi}{3}, \mathrm{n} \in \mathbb{Z}$$
3
MHT CET 2023 9th May Evening Shift
+2
-0

Let $$A=\left[\begin{array}{ccc}1 & 1 & 1 \\ 0 & 1 & 3 \\ 1 & -2 & 1\end{array}\right], B=\left[\begin{array}{c}6 \\ 11 \\ 0\end{array}\right]$$ and $$X=\left[\begin{array}{l}a \\ b \\ c\end{array}\right]$$, if $$\mathrm{AX}=\mathrm{B}$$, then the value of $$2 \mathrm{a}+\mathrm{b}+2 \mathrm{c}$$ is

A
10
B
8
C
6
D
12
4
MHT CET 2023 9th May Morning Shift
+2
-0

If $$A=\left[\begin{array}{cc}2 & -1 \\ -1 & 3\end{array}\right]$$, then the inverse of $$\left(2 A^2+5 A\right)$$ is

A
$$\frac{1}{95}\left[\begin{array}{ll}7 & 3 \\ 3 & 4\end{array}\right]$$
B
$$\frac{1}{95}\left[\begin{array}{cc}-7 & 3 \\ 3 & -4\end{array}\right]$$
C
$$\frac{1}{95}\left[\begin{array}{cc}-7 & -3 \\ 3 & 4\end{array}\right]$$
D
$$\frac{1}{95}\left[\begin{array}{ll}4 & 3 \\ 3 & 7\end{array}\right]$$
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