1
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

The locus of a point $$z$$ satisfying $$|z|^2=\operatorname{Re}(z)$$ is a circle with centre

A
$$\left(0, \frac{1}{2}\right)$$
B
$$\left(-\frac{1}{2}, 0\right)$$
C
$$\left(\frac{1}{2}, 0\right)$$
D
$$\left(0,-\frac{1}{2}\right)$$
2
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

Multiplicative inverse of the complex number $$(\sin \theta, \cos \theta)$$ is

A
$$(\sin \theta, \cos \theta)$$
B
$$(\sin \theta,-\cos \theta)$$
C
$$(\cos \theta,-\sin \theta)$$
D
$$(-\cos \theta, \sin \theta)$$
3
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$\sum_\limits{k=0}^{440} i^k=x+i y \Rightarrow x^{100}+x^{99} y+x^{242} y^2+x^{97} y^3=$$

A
0
B
$$-$$4
C
4
D
1
4
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$e^{i \theta}=\operatorname{cis} \theta$$, then $$\sum_\limits{n=0}^{\infty} \frac{\cos (n \theta)}{2^n}=$$

A
$$(4+2 \cos \theta) /(5-4 \cos \theta)$$
B
$$(4-2 \cos \theta) /(5+4 \cos \theta)$$
C
$$(4-2 \cos \theta) /(5-4 \cos \theta)$$
D
$$(4+2 \cos \theta) /(5+4 \cos \theta)$$
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