I would want to know if it is permissible to recite two different Surahs on a Rakah in Obligatory Prayers.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

It is permissible for a praying person to recite more than one chapter in one Rak'ah after having recited Al-Faatihah (i.e. the opening chapter of the Quran), and it is confirmed that the Prophet did so. This applies whether the prayer is an obligatory prayer or a supererogatory prayer.

Allaah Knows best.