1
MHT CET 2021 22th September Morning Shift
+2
-0

If $$A=\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 2 & 3 \\ 1 & 2 & 1\end{array}\right]$$, then the value of determinant of $$A^{-1}$$ is

A
$$-6$$
B
$$\frac{-1}{6}$$
C
$$\frac{1}{36}$$
D
$$36$$
2
MHT CET 2021 22th September Morning Shift
+2
-0

If $$A = \left[ {\matrix{ k & 2 \cr { - 2} & { - k} \cr } } \right]$$, then A$$^{-1}$$ does not exists if k =

A
3
B
$$\pm$$2
C
0
D
$$\pm$$1
3
MHT CET 2021 22th September Morning Shift
+2
-0

The sum of three numbers is 6. Thrice the third number when added to the first number gives 7. On adding three times first number to the sum of second and third number we get 12. The product of these numbers is

A
20
B
3
C
$$\frac{20}{3}$$
D
$$\frac{5}{3}$$
4
MHT CET 2021 21th September Evening Shift
+2
-0

If $$A=\left[\begin{array}{ccc}\cos \theta & -\sin \theta & 0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1\end{array}\right]$$, then $$\operatorname{adj} A=$$

A
$$\left[\begin{array}{ccc}-\cos \theta & -\sin \theta & 0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1\end{array}\right]$$
B
$$\left[\begin{array}{ccc}\cos \theta & \sin \theta & 0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1\end{array}\right]$$
C
$$\left[\begin{array}{ccc}\cos \theta & \sin \theta & 0 \\ -\sin \theta & \cos \theta & 0 \\ 0 & 0 & 1\end{array}\right]$$
D
$$\left[\begin{array}{ccc}\cos \theta & -\sin \theta & 0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1\end{array}\right]$$
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