1
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
$0 \leq a \leq 4$
2
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
3
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
4
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The set of all real values of $x$ satisfying the inequality $\frac{7 x^2-5 x-18}{2 x^2+x-6}<2$ is
A
$\left(-\infty,-\frac{2}{3}\right] \cup[3, \infty)$
B
$\left(-2,-\frac{2}{3}\right) \cup\left(\frac{3}{2}, 3\right)$
C
$(-\infty,-2) \cup\left(\frac{3}{2}, \infty\right)$
D
$\left[-\frac{2}{3}, \frac{3}{2}\right)$
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