$\sinh^{-1}(2^{3/2})$ is equal to :

If $\operatorname{cosec} \theta = \frac{p+q}{p-q}$,then $\cot \left(\frac{\pi}{4} + \frac{\theta}{2}\right)$ is equal to

Chemical $A$ is used for the removal of temporary hardness of water. Compound $A$ reacts with $Na_2CO_3$ to produce caustic soda. When $CO_2$ gas is passed through $A$,it turns milky. What is the chemical formula of $A$?

Explain the difference between Heartwood and Sapwood.

If $\int \sec ^2 x \operatorname{cosec}^4 x \, dx = -\frac{1}{3} \cot ^3 x + k \tan x - 2 \cot x + C$, then $k$ is equal to

Which of the following statements are correct?
$(i)$ In prokaryotic cells,a special membranous structure formed by the extension of the plasma membrane into the cell is known as polysome.
$(ii)$ The smooth endoplasmic reticulum is the major site for synthesis of glycoproteins.
$(iii)$ $RuBisCO$ is the most abundant protein in the whole biosphere.
$(iv)$ Mitochondria,chloroplasts and peroxisomes are not considered as part of endomembrane system.
Of the above statements: