Step 1: Read what is asked.
We need the host city of the 72nd Miss World 2025 pageant.
Step 2: Recall the country.
The 2025 edition was held in India, which had been preparing to host the event.
Step 3: Narrow to the city.
Within India, the pageant was staged in the Telangana region.
Step 4: Match to the options.
Mumbai, New Delhi, and Jaipur were not the venue, leaving Hyderabad in Telangana.
Step 5: Confirm the choice.
Hyderabad hosted the grand finale of the 72nd Miss World.
Step 6: State the answer.
The host city was Hyderabad. \[ \boxed{\text{Hyderabad}} \]