Step 1: Understanding the Question:
This question asks for the historical ruling family or dynasty associated with the construction and residency of the famous Mysore Palace (Amba Vilas Palace) in Karnataka.
Step 2: Key Formulas and approach:
Identify the major regional kingdoms of Karnataka.
Recall which dynasty ruled the Kingdom of Mysore from the late medieval period up until Indian independence.
Step 3: Detailed Explanation:
• The Mysore Palace was the official residence and seat of the Kingdom of Mysore's ruling family, the Wadiyar dynasty.
• The Wadiyar dynasty was established in 1399 and ruled Mysore almost continuously until 1950, with a temporary interruption by Hyder Ali and Tipu Sultan.
• The current structure of the palace was commissioned in 1897 and completed in 1912 under Rajarshi Krishnaraja Wadiyar IV, following the destruction of the old wooden palace in a fire.
• Other dynasties like the Cholas (Tamil Nadu), Kadambas (Banavasi), and Chalukyas (Badami) belong to different eras and geographical territories.
Step 4: Final Answer:
The Mysore Palace is associated with the Wadiyar dynasty, making Option (B) the correct choice.