The correct answer is option 'B', Sankhya.

Sankhya is the main off-shoot of Bhagavatism, which is a school of philosophy that emerged in ancient India. Bhagavatism is a religious tradition centered around the worship of Lord Vishnu as the Supreme Being. It is one of the major traditions within Hinduism.

Sankhya, also known as Samkhya, is one of the six major schools of Indian philosophy. It was founded by the sage Kapila and is considered one of the oldest philosophical systems in the world. Sankhya philosophy is primarily concerned with the analysis and understanding of the nature of existence, consciousness, and the universe.

Here is a detailed explanation of Sankhya philosophy and its connection to Bhagavatism:

1. Sankhya Philosophy:
Sankhya philosophy posits the existence of two eternal and independent realities - Purusha (consciousness) and Prakriti (matter or nature). Purusha is the ultimate reality, which is pure consciousness without attributes. Prakriti, on the other hand, is the material cause of the universe and is composed of three gunas (qualities) - Sattva (purity), Rajas (activity), and Tamas (inertia).

2. Connection to Bhagavatism:
Bhagavatism, as a religious tradition, focuses on the worship and devotion towards Lord Vishnu, who is considered the Supreme Being. Within Bhagavatism, the concept of Purusha finds great significance. Lord Vishnu is believed to be the Supreme Purusha, the ultimate consciousness, and the source of all existence.

3. Influence on Bhagavatism:
Sankhya philosophy has had a significant influence on the development of Bhagavatism. The concepts and ideas of Sankhya, such as the duality of Purusha and Prakriti, have been incorporated into the Bhagavata Purana, an important text within Bhagavatism. This text explores various aspects of Lord Vishnu's incarnations, his relationship with the material world, and the liberation of the soul through devotion.

4. Other Schools of Philosophy:
While Sankhya is the main off-shoot of Bhagavatism, it is important to note that there are other schools of philosophy within Hinduism as well. Some of the major schools include Nyaya, Mimamsa, and Vedanta. These schools differ in their approaches to understanding reality, knowledge, and the nature of the self.

In conclusion, Sankhya is the main off-shoot of Bhagavatism. Sankhya philosophy, with its emphasis on the duality of consciousness and matter, has greatly influenced the Bhagavata Purana and the devotional tradition centered around Lord Vishnu. Understanding the connection between these philosophical and religious traditions helps to deepen our knowledge of Indian philosophy and its rich heritage.

B