Step 1: Find the cause.
Hand-made paper falls only when a cheaper rival appears. The rival here was machine made mill paper, which could be made faster and sold cheaper.
Step 2: Date the rival.
Machine paper mills spread across India during the nineteenth century, along with large imports of paper from Europe.
Step 3: Check earlier centuries.
In the sixteenth and seventeenth centuries and most of the eighteenth century, hand paper was still the main kind used for books, records and letters.
Step 4: Select the option.
The decline matches the nineteenth century, which is option 4.
Step 5: Second check.
It also helps to think about cost and speed. A hand sheet needed many days of work by a skilled craftsman, while a mill could make thousands of sheets a day. That gap in cost only became decisive when mills grew in number, which happened in the nineteenth century. Earlier centuries therefore cannot be the period of decline, and option 4 is confirmed.
Final Answer:
The 19th century is correct, so option 4.
\[\boxed{\text{Option 4}}\]