The passage describes a folk dance form of India that is performed solo or in a group of 3 or 4 females. This dance is associated with the worship of the goddess Manasa. According to mythology, a woman named Behulaa had to perform this dance before the goddess Manasa in order to bring her husband, Lakhindar, back to life.

One striking aspect of this dance is that the dancers leave their hair open while performing. Another unique element of this dance is the use of a sharp weapon called Daa, which is used for sacrifice. The dancers also rotate their heads in a rapid circular motion while performing, all while their hair is left open.

Based on the description provided in the passage, the correct answer is option 2: Deodhani dance. It aligns with all the characteristics mentioned, including the association with the worship of the goddess Manasa and the use of open hair, sharp weapon, and rapid circular head movements.