1
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

    If the system of equations $a_1 x+b_1 y+c_1 z=0, a_2 x+b_2 y+c_2 z=0$ and $a_3 x+b_3 y+c_3 z=0$ has only trivial solution, then the rank of $\left[\begin{array}{lll}a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{array}\right]$ is

A
2
B
1
C
3
D
0
2
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\omega$ is a complex cube root of unity and if $z$ is a complex number satisfying $|z-1| \leq 2$ and $\left|\omega^2 z-1-\omega\right|=a$, then the set of possible values of $a$ is
A
$0 \leq a \leq 2$
B
$\frac{1}{2} \leq a \leq \frac{\sqrt{3}}{2}$
C
$|\omega| \leq a \leq \frac{\sqrt{3}}{2}+2$
D
$0 \leq a \leq 4$
3
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the roots of the equation $z^3+i z^2+2 i=0$ are the vertices of a $\triangle A B C$, then that $\triangle A B C$ is
A
a right angled triangle
B
an equilateral triangle
C
an isosceles triangle
D
a right angled isosceles triangle
4
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$(r, \theta)$ denotes $r(\cos \theta+i \sin \theta)$. If $x=(1, \alpha), y=(1, \beta), z=(1, \gamma)$ and $x+y+z=0$, then $\Sigma \cos (2 \alpha-\beta-\gamma)$ is equal to

A
3
B
0
C
1
D
-1
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