1
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
2
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$A=\left[\begin{array}{lll}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}\right]$$, then $$A A^T$$ is a

A
symmetric matrix
B
skew-symmetric matrix
C
singular matrix
D
inverse of $$A$$
3
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$A X=D$$ represents the system of simultaneous linear equations $$x+y+z=6, 5 x-y+2 z=3$$ and $$2 x+y-z=-5$$, then (Adj $$A$$) $$D=$$

A
$$\left[\begin{array}{c}8 \\ -16 \\ 40\end{array}\right]$$
B
$$\left[\begin{array}{c}32 \\ 64 \\ -160\end{array}\right]$$
C
$$\left[\begin{array}{c}-16 \\ 32 \\ 80\end{array}\right]$$
D
$$\left[\begin{array}{l}12 \\ 24 \\ 60\end{array}\right]$$
4
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$A=\left[\begin{array}{ll}1 & 0 \\ 2 & 1\end{array}\right], B=\left[\begin{array}{ll}1 & 3 \\ 0 & 1\end{array}\right]$$, then $$\operatorname{det}\left(A^6+B^6\right)=$$

A
$$-68$$
B
$$-106$$
C
$$665$$
D
$$720$$
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