Study questions platform-wide or filter by specific tests with correct answers revealed.
Sharks belong to which class of vertebrates?
Class Chondrichthyes includes cartilaginous fish (sharks, rays). Osteichthyes are bony fish. Echinodermata are starfish etc.; Urochordata are tunicates.
Two complex numbers $z_1$ and $z_2$ satisfy $|z_2|=1$ and $\dfrac{z_1-2z_2}{2-z_1\bar{z}_2}$ is unimodular, but $z_2$ is not unimodular. Where does $z_1$ lie?
Let $w = \frac{z_1-2z_2}{2-z_1\bar{z}_2}$, with $|w|=1$.
$|z_1-2z_2|^2 = |2-z_1\bar{z}_2|^2$
$(z_1-2z_2)\overline{(z_1-2z_2)} = (2-z_1\bar{z}_2)\overline{(2-z_1\bar{z}_2)}$
$|z_1|^2 - 2z_1\bar{z}_2 - 2\bar{z}_1z_2 + 4|z_2|^2 = 4 - 2z_1\bar{z}_2 - 2\bar{z}_1z_2 + |z_1|^2|z_2|^2$
$|z_1|^2 + 4|z_2|^2 = 4 + |z_1|^2|z_2|^2$
$|z_1|^2(1-|z_2|^2) = 4(1-|z_2|^2)$
Since $|z_2|\neq1$: $|z_1|^2=4\Rightarrow|z_1|=2$. So $z_1$ lies on a circle of radius 2.
The corpus luteum is primarily formed from which structure after ovulation?
After ovulation, the ruptured Graafian follicle collapses and transforms into the corpus luteum under LH influence. The ovum is released; oogonium and oocytes are germ cells.
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