In Jainism, "Bija Uday" refers to the fruition of karmic seeds, and "Yugpradhan" relates to the chief or prominent souls (often referring to spiritual leaders or Tirthankaras) of an era (Yuga).

Jain cosmology divides time into cycles called Utsarpini (ascending half-cycle) and Avasarpini (descending half-cycle), each of which has six unequal periods called aras. Each ara has its own characteristics, and certain spiritual events and personalities are associated with specific aras.

The term "last Yugpradhan" would refer to the last prominent soul or Tirthankara of a specific era. According to Jain tradition, in the current Avasarpini (descending cycle), there are 24 Tirthankaras, with Mahavira being the last (24th) Tirthankara.

If you are asking about the "Bija Uday" of the last Yugpradhan, it can be understood as the manifestation or fruition of the karmic potential that leads to the birth and spiritual rise of the last Tirthankara (Mahavira) in this era. Jain texts explain that the Tirthankaras attain their status due to the fruition (uday) of their accumulated punya (meritorious karma), often referred to as Tirthankara-nam-karma. When the right combination of karmas comes into fruition (Bija Uday), the soul is born in the world as a Tirthankara and becomes a spiritual guide for that era.

In summary:

• The last Yugpradhan in the present Avasarpini is Lord Mahavira.
• His becoming a Tirthankara is due to the Bija Uday (fruition) of specific karmas, especially Tirthankara-nam-karma.
• This is a significant event in Jain cosmology, marking the conclusion of the line of Tirthankaras for the current time cycle.

If you have a more specific context or are referring to a different Yuga or concept, please clarify further!