1
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

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

2
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 $(0,2)$.

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

$$ (1-i \sqrt{3})^{2025}= $$

A

$2^{2025}$

B

$2^{2026}$

C

$-2^{2025}$

D

$-2^{2026}$

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

One of the roots of the equation $(x+1)^4+81=0$ is

A

$3\left(\frac{1+i}{\sqrt{2}}\right)$

B

$-\left(\frac{3+\sqrt{2}+3 i}{\sqrt{2}}\right)$

C

$-\left(\frac{3+\sqrt{2}+i}{\sqrt{2}}\right)$

D

$-\left(\frac{3+3 i}{\sqrt{2}}\right)$

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