1
TS EAMCET 2023 (Online) 12th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\alpha$ and $\beta$ are non-zero integers and $z=(\alpha+i \beta)(2+7 i)$ is a purely imaginary number, then minimum value of $|z|^2$ is
A
0
B
2809
C
2808
D
1
2
TS EAMCET 2022 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $\alpha$ and $\beta$ are the roots of the equation $x^2-2 x+2=0$, then $\alpha^{2020}+\beta^{2020}=$

A

$2^{1011}$

B

$-2^{1011}$

C

$2^{2021}$

D

$2^{-2021}$

3
TS EAMCET 2022 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $z=\frac{-1-i \sqrt{3}}{2}$, then $\sum_{k=1}^{2022}\left(z^k+\frac{1}{z^k}\right)^2=$

A

0

B

2022

C

4044

D

1011

4
TS EAMCET 2022 (Online) 20th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

$\{x \in[0,2 \pi] / \sin x+i \cos 2 x$ and $\cos x-i \sin 2 x$ are conjugate to each other} $=$

A

$\left\{\frac{\pi}{4}, \frac{\pi}{2}, \frac{3 \pi}{4}, \pi, \frac{5 \pi}{4}, \frac{3 \pi}{2}, \frac{7 \pi}{4}, 2 \pi\right\}$

B

$\left\{\frac{\pi}{4}, \frac{3 \pi}{4}, \frac{5 \pi}{4}, \frac{7 \pi}{4}\right\}$

C

$\left\{\frac{\pi}{2}, \pi, \frac{3 \pi}{2}, 2 \pi\right\}$

D

$\phi$

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