1
TG EAPCET 2025 (Online) 4th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $\omega \neq 1$ is a cube root of unity, then one root among the 7th roots of $(1+\omega)$ is

A

$1+\omega$

B

$1-\omega$

C

$\omega-\omega^2$

D

$\frac{\omega}{\omega-\omega^2}$

2
TG EAPCET 2025 (Online) 4th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $1+2 i$ is a root of the equation $x^4-3 x^3+8 x^2-7 x+5=0$, then sum of the squares of the other roots is

A

0

B

$2+i$

C

$-4-4 i$

D

$8 / 3$

3
TG EAPCET 2025 (Online) 4th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \left(\frac{1+i}{1-i}\right)^{228}= $$

A

$-4\left(\frac{1-i}{1+i}\right)^{226}$

B

$4\left(\frac{1-i}{1+i}\right)^{226}$

C

$\left(\frac{1-i}{1+i}\right)^{228}$

D

$-\left(\frac{1-i}{1+i}\right)^{228}$

4
TG EAPCET 2025 (Online) 4th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

Let $z=x+i y$ represent a point of $P(x, y)$ in the argand plane. If $z$ satisfies the condition that amplitude of $\frac{z-3}{z-2 i}=-\frac{\pi}{2}$ then the locus of $P$ is

A

the circle $x^2+y^2-3 x-2 y=0$.

B

the arc of the circle $x^2+y^2-3 x-2 y=0$ intercepted by the diameter $2 x+3 y-6=0$ containing the origin and excluding the points $(3,0)$ and $(0,2)$.

C

the arc of the circle $x^2+y^2-3 x-2 y=0$ intercepted by the diameter $2 x+3 y-6=0$ not containing the origin and excluding the points $(3,0)$ and $(0,2)$.

D

the circle $x^2+y^2-3 x-2 y=0$ not containing the point $(0,2)$.

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