Step 1: Sort the cities into two groups.
One group has coastal or river trading hubs. The other group has places that were not set up as colonial trade centres.
Step 2: Place each city.
Bombay, Kolkata and Madras are famous colonial port cities that fed the empire's trade. Bhopal is an inland city that was the capital of a princely state.
Step 3: Pick the odd one out.
The question asks for the city outside the system. The odd one out in the list is Bhopal.
Step 4: Confirm with the option numbers.
Bhopal is the fourth listed city, so the answer is option 4. The first three cities are all colonial port towns, so they cannot be the answer.
Step 5: Cross-check the result.
Double check with a simple reason. A colonial economic system needed ports to ship goods and big towns to run trade. Bombay, Calcutta and Madras did exactly this job. Bhopal does not appear in that list of colonial port and presidency cities, so it is the one left outside, which confirms option 4.
Final Answer:
Bhopal is the outsider, option 4.
\[ \boxed{\text{Option 4}} \]