1
MHT CET 2023 14th May Morning Shift
+2
-0

Let $$A=\left[\begin{array}{cc}2 & -1 \\ 0 & 2\end{array}\right].$$ If $$B=I-{ }^3 C_1(\operatorname{adj} A)+{ }^3 C_2(\operatorname{adj} A)^2-{ }^3 C_3(\operatorname{adj} A)^3$$, then the sum of all elements of the matrix B is

A
$$-$$1
B
$$-$$3
C
$$-$$4
D
$$-$$5
2
MHT CET 2023 13th May Evening Shift
+2
-0

If $$A=\left[\begin{array}{cc}1 & \tan x \\ -\tan x & 1\end{array}\right]$$, then $$A^T \cdot A^{-1}=$$

A
$$\left[\begin{array}{ll}-\cos 2 x & \sin 2 x \\ -\sin 2 x & \cos 2 x\end{array}\right]$$
B
$$\left[\begin{array}{cc}\cos 2 x & -\sin 2 x \\ \sin 2 x & \cos 2 x\end{array}\right]$$
C
$$\left[\begin{array}{cc}\cos 2 x & \sin 2 x \\ -\sin 2 x & \cos 2 x\end{array}\right]$$
D
$$\left[\begin{array}{cc}\cos 2 x & -\sin 2 x \\ -\sin 2 x & \cos 2 x\end{array}\right]$$
3
MHT CET 2023 13th May Morning Shift
+2
-0

If $$A=\left[\begin{array}{ccc}1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4\end{array}\right]$$ and $$A_{i j}$$ is a cofactor of $$a_{i j}$$ then the value of $$a_{21} A_{21}+a_{22} A_{22}+a_{23} A_{23}$$ is

A
0
B
$$-$$2
C
4
D
3
4
MHT CET 2023 12th May Evening Shift
+2
-0

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

A
$$-$$1
B
1
C
5
D
$$-$$5
EXAM MAP
Medical
NEET
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12