Arrange in a hierarchical order by date, the following inventions: I. slide rule; Il. pascaline; IIl, analytical engine; v. difference engine.

The correct hierarchical order by date of the given inventions is: II. Pascaline (1642), I. Slide rule (1620s), V. Difference engine (1822), III. Analytical engine (1837-1871). - Pascaline, invented by Blaise Pascal in 1642, was the first mechanical calculator and is the earliest invention in the list. - Slide rule, invented by William Oughtred in the 1620s, is the next in the hierarchy. - Difference engine, invented by Charles Babbage in 1822, is next in the hierarchy. - Analytical engine, also invented by Charles Babbage, was designed between 1837 and 1871 and is the latest invention in the list. Therefore, the correct answer is: I, II, V, III.