1
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

If $$A=\frac{1}{7}\left[\begin{array}{ccc}3 & -2 & 6 \\ -6 & -3 & 2 \\ -2 & 6 & 3\end{array}\right]$$, then

A
$$A^{-1}=A$$
B
$$A^{-1}=A^T$$
C
$$A^{-1}$$ does not exist
D
$$A^{-1}=-A$$
2
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

If $$A=\left[\begin{array}{cc}\alpha^2 & 5 \\ 5 & -\alpha\end{array}\right]$$ and $$\operatorname{det}\left(A^{10}\right)=1024$$, then $$\alpha=$$

A
$$-$$2
B
$$-$$1
C
$$-$$3
D
0
3
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

Let $$A=\left[\begin{array}{ccc}5 & \sin ^2 \theta & \cos ^2 \theta \\ -\sin ^2 \theta & -5 & 1 \\ \cos ^2 \theta & 1 & 5\end{array}\right]$$. Then, maximum value of $$\operatorname{det}(A)$$ is

A
$$-125$$
B
200
C
$$-\frac{255}{2}$$
D
$$145$$
4
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

If $$\frac{x^4+24 x^2+28}{\left(x^2+1\right)^3}=\frac{A x+B}{x^2+1}$$ $$+\frac{C x+D}{\left(x^2+1\right)^2}+\frac{E x+F}{\left(x^2+1\right)^3},$$ then the value of $$A+B+C+D+E+F=$$

A
21
B
22
C
28
D
29
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