1
TG EAPCET 2024 (Online) 9th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
The product of all the values of $(\sqrt{3}-i)^{\frac{2}{5}}$ is
A
$2(\sqrt{3}-i)$
B
$2(\sqrt{3}+i)$
C
$2(1-\sqrt{3} i)$
D
$2(1+\sqrt{3} i)$
2
TG EAPCET 2024 (Online) 9th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
The number of common roots among the 12 th and 30th roots of unity is
A
12
B
9
C
8
D
6
3
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\sqrt{5}-i \sqrt{15} \doteqdot r(\cos \theta+i \sin \theta),-\pi<\theta<\pi$, then $r^2\left(\sec \theta+3 \operatorname{cosec}^2 \theta\right)=$

A
40
B
60
C
120
D
180
4
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The point $P$ denotes the complex number $z=x+i y$ in the argand plane. If $\frac{2 z-i}{z-2}$ is a purely real number, then the equation of the locus of $P$ is

A
$2 x^2+2 y^2-4 x-y=0$
B
$x+4 y-2=0$ and $(x, y) \neq(2,0)$
C
$x-4 y-2=0$ and $(x, y) \neq(2,0)$
D
$x^2+y^2-4 x-2 y=0$
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