Tubectomy is a method of sterilization in which

The vapor pressure of water at $80\,^oC$ is $355.5\, mm$ of $Hg$. $A$ $100\, mL$ vessel contains $O_2$ gas at $80\,^oC$ saturated with water vapor,and the total pressure is $760\, mm$ of $Hg$. If the contents of the vessel are transferred to a $50\, mL$ vessel at the same temperature,what will be the partial pressure of $O_2$ in $mm$?

The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is $1000$ at $t = 0$. The number of bacteria is increased by $20 \%$ in $2 \text{ hours}$. If the population of bacteria is $2000$ after $\frac{k}{\log \left(\frac{6}{5}\right)} \text{ hours}$,then $\left(\frac{k}{\log 2}\right)^2$ is

What does "y" represent in the given chart?

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 $A$?

$(\tan ^{-1} x)^2+(\cot ^{-1} x)^2=\frac{5 \pi^2}{8} \Rightarrow x=$