Step 1: Understanding Uttara Mimamsa.
Uttara Mimamsa, or the later part of the Mimamsa system, refers to the Vedanta system. It is called "Uttara" or "the later part" because it focuses on the interpretation of the Upanishads, which come after the Vedic rituals (Karma-Kanda). Vedanta emphasizes knowledge (Jnana) over ritual action and explores the nature of the self and the ultimate reality, Brahman.
Step 2: Analyzing the Options.
- 1. Vedanta System: This is correct. Vedanta is the Uttara Mimamsa, dealing with the philosophical teachings of the Upanishads.
- 2. Carvaka System: Carvaka is a materialistic school of thought that does not accept the authority of the Vedas or Vedanta.
- 3. Nyaya System: Nyaya focuses on logic and reasoning, not directly related to the Vedanta philosophy.
- 4. Jaina System: Jainism is an independent philosophical system and does not fall under Mimamsa or Vedanta.
Step 3: Conclusion.
The correct answer is 1. Vedanta System.
Final Answer:
\[
\boxed{\text{The correct answer is 1. Vedanta System.}}
\]