1
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+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
$$\left[\begin{array}{ccc}68 & 0 & 0 \\ 0 & 68 & 0 \\ 0 & 0 & 68\end{array}\right]$$
2
MHT CET 2021 22th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

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

A
13
B
4
C
$$-$$1
D
5
3
MHT CET 2021 22th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

For an invertible matrix $$A$$, if $$A(\operatorname{adj} A)=\left[\begin{array}{cc}20 & 0 \\ 0 & 20\end{array}\right]$$, then $$|A|=$$

A
$$-$$200
B
200
C
$$-$$2
D
20
4
MHT CET 2021 22th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$A=\left[\begin{array}{ccc}1 & 2 & 1 \\ -1 & 1 & 3\end{array}\right]$$ and $$B=\left[\begin{array}{cc}1 & 2 \\ -3 & 1 \\ 0 & 2\end{array}\right]$$, then $$(A B)^{-1}$$

A
$$\left[\begin{array}{cc}5 & -6 \\ -4 & 5\end{array}\right]$$
B
$$\left[\begin{array}{ll}5 & 6 \\ 4 & 5\end{array}\right]$$
C
$$\left[\begin{array}{ll}-5 & 6 \\ -4 & 5\end{array}\right]$$
D
$$\left[\begin{array}{ll}-5 & -6 \\ -4 & -5\end{array}\right]$$
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