1
MHT CET 2025 21st April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The third element in the second row of adjoint of a matrix $A=\left[a_{i j}\right]_{3 \times 3}$ (where $a_{i j}=2 i+j$ ) is

A
2
B
-2
C
4
D
-4
2
MHT CET 2025 20th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\left[\begin{array}{lll}1 & 3 & 3 \\ 1 & 4 & 4 \\ 1 & 3 & 4\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}12 \\ 15 \\ 13\end{array}\right]$, then the value of $x^2+y^2+z^2=$

A
6
B
12
C
3
D
14
3
MHT CET 2025 20th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

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

A
$\left[\begin{array}{cc}\cos 2 x & -\sin 2 x \\ -\sin 2 x & \cos 2 x\end{array}\right]$
B
$\left[\begin{array}{ll}\cos 2 x & -\sin 2 x \\ \sin 2 x & \cos 2 x\end{array}\right]$
C
$\left[\begin{array}{cc}-\cos 2 x & \sin 2 x \\ \sin 2 x & \cos 2 x\end{array}\right]$
D
$\left[\begin{array}{ll}-\cos 2 x & \sin 2 x \\ -\sin 2 x & \cos 2 x\end{array}\right]$
4
MHT CET 2025 19th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $A=\left[\begin{array}{rr}1 & 2 \\ -1 & 4\end{array}\right]$ and $A^{-1}=\alpha I+\beta A \alpha, \beta \in R$ where I is the identity matrix of order 2 , then $4(\alpha+\beta)=$

A
$\frac{8}{3}$
B
$\frac{2}{3}$
C
$\frac{10}{3}$
D
$\frac{1}{3}$
MHT CET Subjects
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