The given question requires us to identify the odd word from a list of options. Let's analyze each option's geographic or administrative characteristics to determine the odd one out:
- Ghaziabad - This is a city in the state of Uttar Pradesh, India. It is known as a rapidly growing industrial city and is part of the National Capital Region.
- Varanasi - This is a city in Uttar Pradesh noted for its cultural heritage and religious significance, particularly in Hinduism.
- Gorakhpur - Another city in Uttar Pradesh, known for its religious sites and as a major industrial and trading hub in Eastern Uttar Pradesh.
- Bhagalpur - This city is located in the state of Bihar. It is not part of Uttar Pradesh and is historically significant as an important trade and cultural city in Bihar.
Upon examining the options, it is clear that three cities (Ghaziabad, Varanasi, and Gorakhpur) are all located in Uttar Pradesh, whereas Bhagalpur is located in Bihar.
Therefore, the odd word is Bhagalpur, as it differs from the others by being in a different state.