1
TS EAMCET 2022 (Online) 19th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If the matrix $A=\left[\begin{array}{lll}1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1\end{array}\right]$ satisfies the matrix equation $A^2-4 A-5 I=0$, then $A^{-1}=$

A

$\frac{1}{5}\left[\begin{array}{ccc}-3 & 2 & 2 \\ -2 & 3 & -2 \\ 2 & 2 & -3\end{array}\right]$

B

$\frac{1}{5}\left[\begin{array}{ccc}-3 & 2 & 2 \\ 2 & -3 & 2 \\ 2 & 2 & -3\end{array}\right]$

C

$\frac{1}{5}\left[\begin{array}{ccc}-3 & 2 & 2 \\ 2 & -3 & 2 \\ -2 & -2 & 3\end{array}\right]$

D

$\frac{1}{5}\left[\begin{array}{ccc}-3 & 2 & 2 \\ 2 & -3 & 2 \\ 2 & 2 & 3\end{array}\right]$

2
TS EAMCET 2022 (Online) 19th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

Consider the simultaneous linear equations $A X=B$ and $A Y=Q$. If $A$ is an invertible matrix and $B$ is the unique solution of $A Y=Q$, then the solution of $A X=B$ is

A

$A^{-1}(B+Q)$

B

$\left(A^{-1}\right)^2 B$

C

$A^{-1} B Q$

D

$\left(A^{-1}\right)^2 Q$

3
TS EAMCET 2022 (Online) 19th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $f(x)=\left|\begin{array}{ccc}-\sin x & 2 \sin 2 x & 4 \cos ^2 x \\ \cos x & 4 \sin ^2 x & 2 \sin 2 x \\ 0 & -\cos x & \sin x\end{array}\right|$, then $f\left(\frac{5 \pi}{4}\right)+f^{\prime}\left(\frac{5 \pi}{4}\right)=$

A

0

B

-1

C

-2

D

-4

4
TS EAMCET 2022 (Online) 18th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $A+B=\left[\begin{array}{lll}2 & 1 & 2 \\ 1 & 2 & 0 \\ 0 & 2 & 2\end{array}\right], A B=\left[\begin{array}{lll}1 & 2 & 2 \\ 1 & 1 & 0 \\ 1 & 2 & 1\end{array}\right]$, then $A^2+B(A+B)=$

A

$\left[\begin{array}{lll}4 & 6 & 6 \\ 3 & 4 & 2 \\ 1 & 6 & 3\end{array}\right]$

B

$\left[\begin{array}{lll}4 & 9 & 6 \\ 3 & 3 & 2 \\ 4 & 7 & 4\end{array}\right]$

C

$\left[\begin{array}{ccc}6 & 10 & 8 \\ 4 & 5 & 2 \\ 4 & 9 & 6\end{array}\right]$

D

$\left[\begin{array}{lll}3 & 4 & 4 \\ 2 & 3 & 2 \\ 0 & 4 & 2\end{array}\right]$

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