The correct answer is b) Vadodara.
The Gaekwad dynasty was a Maratha dynasty that ruled the princely state of Baroda in Gujarat, India, from 1721 to 1948. The dynasty was founded by Damaji Rao Gaekwad, who was appointed as the Peshwa’s (prime minister) governor of Gujarat in 1721. Damaji Rao’s son, Pilaji Rao Gaekwad, succeeded him in 1732 and expanded the Gaekwad’s power and influence. Pilaji Rao’s grandson, Sayajirao Gaekwad III, was the most famous ruler of the Gaekwad dynasty. He ruled from 1875 to 1939 and is credited with modernizing Baroda and making it one of the most prosperous princely states in India.
The Gaekwad’s capital city was Vadodara, which is now a major city in Gujarat. Vadodara was founded in the 16th century by the Mughal emperor Akbar. It was later captured by the Marathas in the 17th century and became the capital of the Gaekwad dynasty in the 18th century. Vadodara is a major center of education, culture, and industry. It is also home to a number of historical and cultural landmarks, including the Lalbhai Dalpatbhai Museum, the Maharaja Sayajirao University of Baroda, and the Vadodara Palace.
The other options are incorrect because they are not the capital city of the Gaekwad dynasty. Surat is a city in Gujarat that was once an important trading center. Rajkot is the capital of the Indian state of Gujarat. Junagadh is a city in Gujarat that is known for its historical and cultural landmarks.