Was Mohammad gauri killed by prithviraj chauhan?

Absolutely not, according many historians, Mohammad ghauri died much later than prithviraj chauhan. Prithviraj after being defeated by Mohammad of ghor in the second battle of Tarain was taken to ghazni and was executed over there. Mohammad of Ghor died 14 years later at Dhamiak which is located near Jhelum.

In 1191AD Mohammad Ghori met Prithvi Raj Chauhan in the first battle of Tarain where Prithvi raj chouhan was victorious. Later on in the second battle of Tarain (1192 AD).Prithvi Raj was defeated by Mohammad Ghori.