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The correct answer is option 3, Bhimbetka. Bhimbetka is a UNESCO World Heritage Site located in Madhya Pradesh, India. It is famous for its ancient rock shelters, where cave paintings dating back to prehistoric times are found.
Option 1, Amarkantak, is incorrect. Amarkantak, also known as Amarakuta, is a pilgrimage town in Madhya Pradesh, but it does not have any known prehistoric cave paintings.
Option 2, Badami, is also incorrect. Badami, located in Karnataka, is known for its rock-cut cave temples dating back to the 6th century. These temples are not associated with prehistoric cave paintings.
Option 4, Nasik, is incorrect as well. Nasik, located in Maharashtra, is known for its historical and religious significance, but it does not have any prehistoric cave paintings.
Therefore, the correct answer is option 3, Bhimbetka, as it is the place where cave paintings of prehistoric times are found.