The condition for diffraction is

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 $mm$?

Two full turns of the circular scale of a screw gauge cover a distance of $1\,mm$ on the main scale. The total number of divisions on the circular scale is $50$. Further,it is found that the screw gauge has a zero error of $+0.03\,mm$. While measuring the diameter of a thin wire,a student notes the main scale reading of $3\,mm$ and the number of the circular scale division in line with the main scale is $35$. The diameter of the wire is .......... $mm$.

The approximate value of $(1.0002)^{3000}$ is

$A$ ball rolls without slipping. The radius of gyration of the ball about an axis passing through its center of mass is $K$. If the radius of the ball is $R$,what fraction of its total energy is associated with its rotational kinetic energy?

The differential equation of the family of parabolas with vertex at $(0, -1)$ and having axis along the $Y$-axis is