1
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
2
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
$$\frac{1}{95}\left[\begin{array}{ll}4 & 3 \\ 3 & 7\end{array}\right]$$
3
MHT CET 2022 11th August Evening Shift
+2
-0

If $$A=\left[\begin{array}{lll}1 & 2 & 1 \\ 3 & 1 & 3\end{array}\right]$$ and $$B=\left[\begin{array}{ll}2 & 3 \\ 1 & 2 \\ 1 & 2\end{array}\right]$$, then $$(A B)^{-1}=$$

A
$$\left[\begin{array}{ll}\frac{17}{5} & \frac{9}{5} \\ 2 & 1\end{array}\right]$$
B
$$\left[\begin{array}{cc}\frac{-17}{5} & \frac{9}{5} \\ 2 & -1\end{array}\right]$$
C
$$\left[\begin{array}{ll}\frac{17}{5} & 2 \\ \frac{9}{5} & 1\end{array}\right]$$
D
$$\left[\begin{array}{cc}\frac{-17}{5} & 2 \\ \frac{-9}{5} & -1\end{array}\right]$$
4
MHT CET 2022 11th August Evening Shift
+2
-0

Given $$A=\left[\begin{array}{ccc}x & 3 & 2 \\ 1 & y & 4 \\ 2 & 2 & z\end{array}\right]$$, if $$x y z=60$$ and $$8 x+4 y+3 z=20$$, then $$A$$.(adjA)

A
$$\left[\begin{array}{ccc}60 & 0 & 0 \\ 0 & 60 & 0 \\ 0 & 0 & 60\end{array}\right]$$
B
$$\left[\begin{array}{ccc}108 & 0 & 0 \\ 0 & 108 & 0 \\ 0 & 0 & 108\end{array}\right]$$
C
$$\left[\begin{array}{ccc}20 & 0 & 0 \\ 0 & 20 & 0 \\ 0 & 0 & 20\end{array}\right]$$
D
$$\left[\begin{array}{ccc}68 & 0 & 0 \\ 0 & 68 & 0 \\ 0 & 0 & 68\end{array}\right]$$
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