Explanation: To understand the context of the question, we need to analyze each statement individually and determine their validity based on the knowledge of Karnataka's cultural and mathematical concepts.
1. **Bidriware**: Bidriware is a type of metal handicraft that originates from the city of Bidar in Karnataka. It is known for its intricate designs and the use of zinc and copper alloys, which are then inlaid with silver. The term "Bidriware" is derived from the city of Bidar, and it is a significant part of Karnataka's cultural heritage. Therefore, the statement "Type of metal handicraft from modelling Bidar, Karnataka is not called as Bidriware" is false.
2. **Divisibility by 9**: The divisibility rule for 9 states that a number is divisible by 9 if the sum of its digits is divisible by 9. To check if 3165 is divisible by 9, we sum its digits: \(3 + 1 + 6 + 5 = 15\). Since 15 is not divisible by 9, 3165 is not divisible by 9. Therefore, the statement "The number 3165 is divisible by 9" is false.
3. **Yakshagana**: Yakshagana is a traditional dance-drama form that is popular in the coastal and Malenadu regions of Karnataka. It is a vibrant and colorful performance art that combines dance, music, and dialogue. Yakshagana is an integral part of Karnataka's cultural identity and is recognized as a significant form of traditional dance. Therefore, the statement "Yakshagana is a popular form of dance in Karnataka" is true.
Given the analysis of each statement, we can conclude that only the third statement is true. Therefore, the correct answer is (C) Only 3.
This question tests the understanding of Karnataka's cultural heritage, specifically Bidriware and Yakshagana, as well as the application of the divisibility rule for 9. It is important to carefully evaluate each statement and apply the relevant rules and knowledge to determine the correct answer.