Data Entry - Physics

Opening of flowers in the cymose inflorescence is

If $z=\log (\tan x+\tan y)$, then $(\sin 2x) \frac{\partial z}{\partial x}+(\sin 2y) \frac{\partial z}{\partial y}$ is equal to

Which of the following is not a secondary messenger?

An increase in pressure required to decrease the $200\,L$ volume of a liquid by $0.004\%$ in a container is ........... $kPa$. (Bulk modulus of the liquid $= 2100\,MPa$)

The locus of the centroid of the triangle with vertices at $(a \cos \theta, a \sin \theta)$,$(b \sin \theta, -b \cos \theta)$ and $(1, 0)$ is (where $\theta$ is a parameter).