1
MHT CET 2024 2nd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $A=\left[\begin{array}{cc}3 & -1 \\ -4 & 2\end{array}\right]$, then $A^{-1}$ is

A
$\left[\begin{array}{cc}1 & -\frac{1}{2} \\ 2 & \frac{3}{2}\end{array}\right]$
B
$\left[\begin{array}{cc}1 & \frac{1}{2} \\ -2 & \frac{3}{2}\end{array}\right]$
C
$\left[\begin{array}{cc}1 & -\frac{1}{2} \\ -2 & \frac{3}{2}\end{array}\right]$
D
$\left[\begin{array}{ll}1 & \frac{1}{2} \\ 2 & \frac{3}{2}\end{array}\right]$
2
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$A=\left[\begin{array}{ll}1 & -1 \\ 2 & -1\end{array}\right], B=\left[\begin{array}{cc}1 & 1 \\ 4 & -1\end{array}\right]$$, then $$(A+B)^{-1}$$ is

A
$$\left[\begin{array}{cc}\frac{-1}{2} & 0 \\ \frac{-3}{2} & \frac{1}{2}\end{array}\right]$$
B
$$\left[\begin{array}{cc}\frac{1}{2} & 0 \\ \frac{3}{2} & \frac{-1}{2}\end{array}\right]$$
C
$$\left[\begin{array}{cc}\frac{1}{2} & 0 \\ \frac{-3}{2} & \frac{1}{2}\end{array}\right]$$
D
$$\left[\begin{array}{ll}\frac{1}{2} & 0 \\ \frac{3}{2} & \frac{1}{2}\end{array}\right]$$
3
MHT CET 2023 14th May Morning Shift
MCQ (Single Correct Answer)
+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
4
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+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
$$\left[\begin{array}{cc}\cos 2 x & -\sin 2 x \\ -\sin 2 x & \cos 2 x\end{array}\right]$$
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