Step 1: Understanding the Question:
We need to pick from four art forms the one that Mughal rulers actively supported.
Step 2: Recall the Mughal art output:
Mughal rulers from Akbar to Shah Jahan kept large studios. These studios produced manuscripts with miniature paintings, calligraphy and decorated borders. The whole process of putting such a book together is called bookmaking.
Step 3: Test each option against the time period:
Installation is a twentieth century concept, so it cannot be Mughal. Graphic art as a printed design field is also modern. Sculpture of people was not a Mughal preference.
Step 4: Use the process of elimination:
Removing installation, graphic art and sculpture leaves only bookmaking.
Step 5: Conclusion:
Bookmaking matches the known Mughal practice, so option (3) is the answer.
Step 6: Cross-check the other options.
Option (1) is wrong because installation is a modern gallery practice. Option (2) is wrong because graphic art as printed design grew with presses and design schools. Option (4) is wrong because the Mughals preferred carved ornament and inlay in architecture over free standing figures. This leaves bookmaking, which the royal workshops practised daily, so (3) stands.
Final Answer:
Option (3), bookmaking, is the art form the Mughals patronized.