What is the ruling on swearing on the Qur'an unintentionally, while the swearer knows that what he is swearing to is untrue?

Mixing between non-mahram men and women is not permissible except under specific Sharia guidelines. Swearing an oath about something that is not true is a "Ghamus oath," which is considered one of the major sins. The sin is compounded if the oath is sworn upon the Qur’an. The obligation regarding a Ghamus oath is sincere repentance. Some scholars have also stated that expiation is obligatory for it.