What is the expiation (کفارۃ) for placing ones hand on the Holy Quran and taking a false oath if one was compelled to?
الجواب حامدا و مصلیا
Taking false oaths is a major sin, so much so that it cannot be expiated by anything except sincere repentance. This is why one should refrain from taking false oaths in all circumstances.
And Allah knows best.