1
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
2
AP EAPCET 2021 - 20th August Morning Shift
+1
-0

The trace of the matrix $$A=\left[\begin{array}{ccc}1 & -5 & 7 \\ 0 & 7 & 9 \\ 11 & 8 & 9\end{array}\right]$$ is

A
17
B
25
C
3
D
12
3
AP EAPCET 2021 - 20th August Morning Shift
+1
-0

If $$A, B$$ and $$C$$ are the angles of a triangle, then the system of equations $$-x+y \cos C+z \cos B=0, x \cos C-y+z \cos A=0$$ and $$x \cos B+y \cos A-z=0$$

A
Only zero solution
B
A non-zero solution for all $$\Delta ABC$$
C
Only zero solution but for certain values of A, B and C
D
A non-zero solution if $$\Delta ABC$$ is an equilateral triangle and not for all triangles.
4
AP EAPCET 2021 - 20th August Morning Shift
+1
-0

If $$\left[\begin{array}{cc}1 & -\tan \theta \\ \tan \theta & 1\end{array}\right]\left[\begin{array}{cc}1 & \tan \theta \\ -\tan \theta & 1\end{array}\right]^{-1} =\left[\begin{array}{cc}a & -b \\ b & a\end{array}\right]$$, then

A
$$a=1, b=1$$
B
$$a=\sin 2 \theta$$ and $$b=\cos 2 \theta$$
C
$$a=\cos 2 \theta$$ and $$b=\sin 2 \theta$$
D
$$a=0$$ and $$b=0$$
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