1
TG EAPCET 2024 (Online) 9th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $A X=D$ represents the system of linear equations $3 x-4 y+7 z+6=0,5 x+2 y-4 z+9=0$ and $8 x-6 y-z+5=0$, then
A
$\operatorname{Rank}(A)=\operatorname{Rank}([A D])=1$
B
$\operatorname{Rank}(A)=\operatorname{Rank}([A D])=2$
C
$\operatorname{Rank}(A)=\operatorname{Rank}([A D])=3$
D
Rank $(A) \neq \operatorname{Rank}([A D])$
2
TG EAPCET 2024 (Online) 9th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $(x, y, z)=(\alpha, \beta, \gamma)$ is the unique solution of the system of simultaneous linear equations $3 x-4 y+z+7=0$, $2 x+3 y-z=10$ and $x-2 y-3 z=3$, then $\alpha=$
A
3
B
-3
C
-1
D
1
3
TG EAPCET 2024 (Online) 9th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $\alpha, \beta, \gamma$ are the roots of the equation $2 x^3-5 x^2+4 x-3=0$, then $\Sigma \alpha \beta(\alpha+\beta)=$
A
8
B
4
C
2
D
$\frac{1}{2}$
4
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$A, B, C$ and $D$ are square matrices such that $A+B$ is symmetric, $A-B$ is skew-symmetric and $D$ is the transpose of $C$. If $A=\left[\begin{array}{ccc}-1 & 2 & 3 \\\\ 4 & 3 & -2 \\\\ 3 & -4 & 5\end{array}\right]$ and $C=\left[\begin{array}{ccc}0 & 1 & -2 \\\\ 2 & -1 & 0 \\\\ 0 & 2 & 1\end{array}\right]$, then the matrix $B+D=$
A
$\left[\begin{array}{ccc}-1 & 6 & 3 \\\\ 6 & 2 & -2 \\\\ 3 & -2 & 6\end{array}\right]$
B
$\left[\begin{array}{ccc}-1 & 6 & 3 \\\\ 3 & 2 & -2 \\\\ 1 & -2 & 6\end{array}\right]$
C
$\left[\begin{array}{ccc}3 & 2 & -2 \\\\ 2 & 6 & 3 \\\\ -2 & 3 & 2\end{array}\right]$
D
$\left[\begin{array}{ccc}1 & -2 & 6 \\\\ -2 & 3 & 2 \\\\ 6 & 2 & 1\end{array}\right]$
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