1
AP EAPCET 2021 - 20th August Morning Shift
MCQ (Single Correct Answer)
+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
2
AP EAPCET 2021 - 20th August Morning Shift
MCQ (Single Correct Answer)
+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.
3
AP EAPCET 2021 - 20th August Morning Shift
MCQ (Single Correct Answer)
+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 $$b=0$$
4
AP EAPCET 2021 - 20th August Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$z_1=2+3 i$$ and $$z_2=3+2 i$$, where $$i=\sqrt{-1}$$, then $$\left[\begin{array}{cc}z_1 & z_2 \\ -\bar{z}_2 & \bar{z}_1\end{array}\right]\left[\begin{array}{cc}\bar{z}_1 & -z_2 \\ \bar{z}_2 & z_1\end{array}\right]$$ is equal to

A
$$13 I$$
B
$$I$$
C
$$26 I$$
D
Zero matrix
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