Diagrammatically show meta centre, centre of gravity and centre of buoyancy when the floating body is at equilibrium and when external angular displacement is applied on it.

A body, partially submerged in a liquid will be in stable equilibrium, if its metacentre:

A uniform narrow tube is bent into a circle of radius R and it lies in a vertical plane. Two liquids of equal volume and having densities $\rho$ and $\sigma \left(\rho >\sigma \right)$ fill the half tube. $\theta$ is the angle as shown in figure. Then

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$