Step 1: Understand the question:
The task is to sort four paintings by the year their execution began. The options only differ in where each painting sits.
Step 2: Find the fixed ends:
Jahangir's Dream belongs to the reign of Jahangir, the last of the emperors linked here, so C must come at the end.
Princes of the House of Timur has roots in Humayun's period, the earliest, so B must come first.
Step 3: Apply this to the options:
Only option 3 has B first and C last. Option 1 has D last, option 2 has D first and A last, and option 4 has C first.
Step 4: Settle the middle pair:
Between Hamzanama (A) and Tutinama (D), Hamzanama began about 1562 and the Tutinama about a decade later. So A comes before D, which fits option 3 exactly.
Step 5: Verify the full chain:
B (about 1550), A (about 1562), D (about 1570 to 1580), C (about 1620) rise steadily, so there is no clash.
Final Answer:
Using the fixed ends and the middle pair, option 3 (B, A, D, C) is the only valid order.
\[ \boxed{\text{Option 3}} \]