NDA MATHEMATICS QUIZ - 3

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Question 1:

If $z=(t-4)+i \sqrt{25-t^{2}}$ then locus of $z$ will be:

Question 2:

If $z_{1}=\cos \frac{\pi}{2}+i \sin \frac{\pi}{2}, \quad z_{2}=\cos \frac{\pi}{2^{2}}+i \sin \frac{\pi}{2^{2}}$,

$z_{3}=\cos \frac{\pi}{2^{3}}+i \sin \frac{\pi}{2^{3}} \ldots .$ up to $\infty$ then $z_{1} z_{2} z_{3}$

$\ldots \ldots$ up to $\infty$ . . . . . . . . . 

Question 3:

Which of the following is not correct?

Question 4:

The locus of $z$ satisfying the inequality

$\log _{\frac{1}{5}}|(z-1)|>\log _{\frac{1}{5}}|z+1|$

Question 5:

If $\omega$ be the cube root of unity then

$\left(1+\omega-\omega^{2}\right)^{7}+\left(1-\omega+\omega^{2}\right)^{7}$ is

Question 6:

If $z=\frac{(1+i)^{2}}{2-i}$ then $\operatorname{Im}(z)=$ . . . . . . . .

Question 7:

Value of $\sum_{r=1}^{6}\left(\sin \frac{2 \pi r}{7}-i \cos \frac{2 \pi r}{7}\right)$ is:

Question 8:

If $a+i b=\sqrt{\frac{x+i y}{p+i q}}$ then $\left(a^{2}+b^{2}\right)^{2}$ equals:

Question 9:

If $\left|z_{1}\right|=\left|z_{2}\right|=\left|z_{3}\right|=1$ then $\left|z_{1}+z_{2}+z_{3}\right|=$

Question 10:

Square root of $4-6 \sqrt{-5}$ is: