Step 1: Understanding the Concept:
Air routes connect major urban centers across continents.
The Mediterranean-South Asian route is a major global corridor connecting Europe, Africa, and Asia.
To arrange these cities from West to East, we must look at their longitudinal positions on the world map.
Step 2: Detailed Explanation:
Let's check the geographical location of each airport:
1. Rome (Italy): Located in Europe at approximately \(12.5^{\circ}E\). It is the westernmost city among the options.
2. Cairo (Egypt): Located in Northeast Africa at approximately \(31.2^{\circ}E\). It is east of Rome.
3. Mumbai (India): Located on the western coast of India at approximately \(72.8^{\circ}E\). It is much further east than Cairo.
4. Bangkok (Thailand): Located in Southeast Asia at approximately \(100.5^{\circ}E\). It is the easternmost city in this list.
A flight traveling from the West (Europe) to the East (Southeast Asia) would encounter these cities in the order: Rome $\rightarrow$ Cairo $\rightarrow$ Mumbai $\rightarrow$ Bangkok.
This corresponds to the sequence 1-2-3-4.
Step 3: Final Answer:
The correct West-to-East sequence is 1-2-3-4.
The correct option is (A).