'Nagpati' ka vigrah aur samas hoga (The compound word-split and samas type for 'Nagpati' will be)

'Nagpati' means 'lord of mountains' (nag = parvat/mountain, pati = lord). This is a Tatpurush samas because there is a case-relationship (sambandh karak - 'ka') between the two words: 'nagon KA pati' (lord OF mountains). In Tatpurush samas, the latter word (uttarpad) is dominant and a case-marker is implied between the two components. It is not Karmadharaya (which requires adjective-noun or simile relation) nor Bahuvrihi (which would point to a third entity). Thus option 3 is correct.