Can ultrasound tests show the doctor if a woman is virgin? i have heard that the answer is yes, since it depends on having a intact hymen or not...

No: An ultrasound can not show such a thing. If the hymen is intact this can be seen during a physical exam. The problem is many virgins do not have an intact hymen. Physical activity can open it. If a doctor wanted to know if a patient was a virgin he or she would simply ask them.

No: The only way to know if a woman is a virgin is to have a trusting relationship with her, such that she will tell you the truth about past sexual partners and then ask her if she has had sex in the past.