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

Let $\alpha, \beta$ and $\gamma$ be real numbers.

If $\left[\begin{array}{ccc}7 & 5 & \alpha \\ \beta & 2 & 11 \\ 3 & \gamma & 1\end{array}\right]\left[\begin{array}{l}1 \\ 3 \\ 2\end{array}\right]=\left[\begin{array}{c}\alpha+\beta \\ -2 \alpha+\beta-2 \gamma \\ \alpha+2 \beta+3 \gamma\end{array}\right]$, then $100+\frac{2 \alpha+11 \beta}{\gamma}=$

A

27

B

-25

C

225

D

-227

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

If $\left[\begin{array}{ccc}0 & 2 & a \\ b & 0 & 4 \\ -3 & c & 0\end{array}\right]$ is a skew-symmetric matrix, then $\left[\begin{array}{ll}a & b \\ b & a\end{array}\right]\left[\begin{array}{ll}b & c \\ c & b\end{array}\right]=$

A

$\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]$

B

$\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$

C

$\left[\begin{array}{cc}2 & -8 \\ -8 & 2\end{array}\right]$

D

$\left[\begin{array}{ll}2 & 8 \\ 8 & 2\end{array}\right]$

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

If $\left[\begin{array}{ccc}-1 & 2 & b \\ a & 5 & 6 \\ 3 & c & 7\end{array}\right]$ is a symmetric matrix, then $\left|\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right|=$

A

0

B

-121

C

143

D

-143

4
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

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

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