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1
AP EAPCET 2024 - 20th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $\frac{3-2 i \sin \theta}{1+2 i \sin \theta}$ is purely imaginary number, then $\theta=$
A
$2 n \pi \pm \frac{\pi}{4}$
B
$2 n \pi \pm \frac{\pi}{2}$
C
$n \pi \pm \frac{\pi}{3}$
D
$n \pi \pm \frac{\pi}{6}$
2
AP EAPCET 2024 - 20th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $z=x+i y, x^2+y^2=1$ and $z_1=z e^{i \theta}$, then $\frac{z_1^{2 n}-1}{z_1^{2 n}+1}=$
A
$-i \tan \left(n\left(\theta+\tan ^{-1}\left(\frac{y}{x}\right)\right)\right)$
B
$i \cot \left(n\left(\theta+\tan ^{-1} \frac{y}{x}\right)\right)$
C
$i \tan \left(n\left(\theta+\tan ^{-1} \frac{x}{u}\right)\right)$
D
$i \tan \left(n\left(\theta+\tan ^{-1} \frac{y}{x}\right)\right)$
3
AP EAPCET 2024 - 20th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the point $P$ represents the complex number $z=x+i y$ in the argand plane and if $\frac{z+i}{z-i}$ is a purely imaginary number, then the locus of $P$ is
A
$x^2+y^2+x-y=0$ and $(x, y) \neq(1,0)$
B
$x^2+y^2-x+y=0$ and $(x, y) \neq(1,0)$
C
$x^2+y^2-x+y=0$ and $(x, y)=(1,0)$
D
$x^2+y^2+x+y=0$
4
AP EAPCET 2024 - 20th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$S=\{z \in C /|z+1-i|=1\}$ represents
A
the circle with centre at $(-1,1)$ and radius 1 unit
B
the circle with cente at $(1,-1)$ and radius 1 unit
C
the closed circular disc with centre at $(1,-1)$ and radius 1 unt
D
the closed circular disc with centre at( $-1,1$ ) and radius 1 unt
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