Two quantities A and B have different dimensions. Which mathematical operation given below is physically meaningful

The correct option is A/B.

Step-by-Step Explanation:
According to the principle of homogeneity of dimensions in physics, only physical quantities having the same dimensions can be added or subtracted.
Therefore, if quantities $A$ and $B$ have different dimensions:

1. The operation $A+B$ is not physically meaningful because we cannot add quantities with different physical natures (for example, we cannot add force to velocity).
2. The operation $A-B$ is not physically meaningful for the same reason.

However, there is no restriction on multiplication or division of physical quantities with different dimensions. When we divide or multiply quantities with different dimensions, we get a new physical quantity with new dimensions.
For example, dividing distance (length) by time gives velocity, which is a highly meaningful physical quantity. Thus, the operation $A/B$ is physically meaningful.