Grouping the Cities:
- To find the group among the given cities, we need to identify a common characteristic or attribute that the cities share.
- Let's analyze each city and see if we can find any similarities or differences.

Mumbai:
- Mumbai is a major city in India and the capital of the state of Maharashtra.
- It is known for its bustling city life, financial center, and the Bollywood film industry.
- Mumbai is located on the western coast of India.

Bengaluru:
- Bengaluru, also known as Bangalore, is the capital city of the state of Karnataka.
- It is a major tech hub in India and has numerous IT companies and startups.
- Bengaluru is located in the southern part of India.

Chennai:
- Chennai is the capital city of the state of Tamil Nadu.
- It is a major cultural, economic, and educational center in South India.
- Chennai is known for its beautiful beaches and historical landmarks.

Puducherry:
- Puducherry, also known as Pondicherry, is a union territory in India.
- It was a former French colony and still exhibits French influence in its architecture and cuisine.
- Puducherry is located on the southeastern coast of India.

Hyderabad:
- Hyderabad is the capital city of the state of Telangana and also a major city in Andhra Pradesh.
- It is known for its rich history, architecture, and delicious cuisine, especially the famous Hyderabadi biryani.
- Hyderabad is located in the southern part of India.

Identifying the Odd One Out:
- Upon analyzing the given cities, we can observe that Mumbai, Bengaluru, Chennai, and Puducherry all have a common characteristic - they are all capital cities.
- However, Hyderabad stands out as it is not a capital city.
- Therefore, the city that does not belong to the group is Hyderabad (option E).

Conclusion:
- The cities Mumbai, Bengaluru, Chennai, and Puducherry form a group as they are all capital cities.
- Hyderabad is the odd one out as it is not a capital city.