The meaning of term continuous is that there should be no breaking.
In terms of mathematics , a function is said to be continuous function if there are no gaps when you plot the curve on coordinate axis.
In option 1, points scored is an incomplete statement.
Option 2, pages in a book is an example of constant function if you count pages between two pages. But it is a continuous function if page numbers are counted.
Option 3, children in a family is not a continuous function because there are gap in birth of two children.
Option 4, Temperature of an engine varies if engine is moving, otherwise remains constant.
Option (B), pages in a book is a type of data which is BEST described by a continuous model.