Describe the outcome of the two Battles of Tarain between Pṛithvīraja III and Muhammad Ghurī.

The First Battle of Tarain in 1191 resulted in victory for Pṛithvīraja III, who defeated Muhammad Ghurī. However, in the Second Battle of Tarain in 1192, Muhammad Ghurī returned with a larger army and defeated Pṛithvīraja III. After the defeat, Pṛithvīraja III was executed by Muhammad Ghurī.