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The correct chronological order of the inventions in the field of cotton industry is: 2, 1, 4, 3.
Option 1: 1, 3, 4, 2
This option suggests that James Hargreaves`s Spinning Jenny was the earliest invention. However, this is incorrect.
Option 2: 2, 1, 4, 3 (Correct Answer)
This option correctly arranges the inventions in chronological order. John Kay`s Flying Shuttle was the earliest invention, followed by James Hargreaves`s Spinning Jenny, Richard Arkwright`s Water Frame, and finally Samuel Crompton`s Mule.
Option 3: 4, 1, 3, 2
This option incorrectly places Richard Arkwright`s Water Frame as the earliest invention.
Option 4: 2, 4, 1, 3
This option also incorrectly places Richard Arkwright`s Water Frame before James Hargreaves`s Spinning Jenny.
Therefore, the correct answer is option 2.