MHT CET 2025 20th April Evening Shift | Matrices and Determinants Question 2 | Mathematics

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 $x^2+y^2+z^2=$

MHT CET 2025 20th April Morning Shift

MCQ (Single Correct Answer)

-0

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

$\left[\begin{array}{cc}\cos 2 x & -\sin 2 x \\ -\sin 2 x & \cos 2 x\end{array}\right]$

$\left[\begin{array}{ll}\cos 2 x & -\sin 2 x \\ \sin 2 x & \cos 2 x\end{array}\right]$

$\left[\begin{array}{cc}-\cos 2 x & \sin 2 x \\ \sin 2 x & \cos 2 x\end{array}\right]$

$\left[\begin{array}{ll}-\cos 2 x & \sin 2 x \\ -\sin 2 x & \cos 2 x\end{array}\right]$

MHT CET 2025 19th April Evening Shift

MCQ (Single Correct Answer)

-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 $4(\alpha+\beta)=$

$\frac{8}{3}$

$\frac{2}{3}$

$\frac{10}{3}$

$\frac{1}{3}$

MHT CET 2025 19th April Morning Shift

MCQ (Single Correct Answer)

-0

If $A=\left[\begin{array}{ccc}\cos \theta & \sin \theta & 0 \\ -\sin \theta & \cos \theta & 0 \\ 0 & 0 & 1\end{array}\right]$, where $A_{21}, A_{22}, A_{23}$ are cofactors of $a_{21}, a_{22}, a_{23}$ respectively, then the value of $\mathrm{a}_{21} \mathrm{~A}_{21}+\mathrm{a}_{22} \mathrm{~A}_{22}+\mathrm{a}_{23} \mathrm{~A}_{23}=$

$-1$

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