1
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
The system of equations $$ x+2 y+3 z=6, x+3 y+5 z=9 \text {, } $$ $2 x+5 y+a z=12$ has no solution when $a=$
A
5
B
6
C
7
D
8
2
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $ \alpha, \beta, \gamma $ are the roots of $ \begin{bmatrix} 1 & -x & -2 \\ -2 & 4 & -x \\ -2 & 1 & -x \end{bmatrix} = 0 $, then $ \alpha \beta + \beta \gamma + \gamma \alpha = $
A
6
B
8
C
0
D
-4
3
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the determinant of a 3rd order matrix $ A $ is $ K $, then the sum of the determinants of the matrices $ A^4 $ and $ (A - A^4) $ is
A
2K
B
0
C
$ K^2 $
D
$ K $
4
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

While solving a system of linear equations $A X=B$ using Cramer's rule with the usual notation if

$$ \Delta=\left|\begin{array}{ccc} 1 & 1 & 1 \\ 2 & -1 & 2 \\ -1 & 1 & 5 \end{array}\right|, \Delta_1=\left|\begin{array}{ccc} 5 & 1 & 1 \\ 4 & -1 & 2 \\ 11 & 1 & 5 \end{array}\right| \text { and } X=\left[\begin{array}{l} \alpha \\ 2 \\ \beta \end{array}\right] \text {, then } \alpha^2+\beta^2= $$

A
9
B
13
C
5
D
25
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