Step 1: Start with the easiest pair.
Ayurveda is widely known as the traditional system of medicine. So B must go with I, Science of Medicine. Now look at which options give B-I.
Step 2: Use the first elimination.
Only option 4 has B-I. Options 1 and 3 give B-II and option 2 gives B-III. Those three are removed straight away.
Step 3: Check A as a test.
Option 4 says A-IV. Shilpashastra deals with sculpture, image making and temple planning, so it is the Science of Architecture. The pairing holds.
Step 4: Check C.
Option 4 says C-II. Dhanurveda is the bow science, taught to warriors, and the Science of Archery is the exact English match. The pairing holds.
Step 5: Check D.
Option 4 says D-III. Jyotisha tracks the sun, moon, planets and stars to fix the calendar and ritual dates, so it is Astronomy. The pairing holds.
Step 6: Conclude.
All four pairs in option 4 are verified, and the other options fail on at least one pair, so option 4 is the answer.
Final Answer:
Option 4 is correct because all four pairs are right.
\[ \boxed{\text{Option 4}} \]