Final answer:
The religion that originated in India and rejects the caste system, advocates that life's suffering is caused by desire, and liberation is possible through renouncing desire is Buddhism.
Step-by-step explanation:
The religion formed in India that does not have the caste system and whose main teaching is that life is full of suffering due to desire, but can be transcendent without it, is Buddhism (option a). Siddhartha Gautama, also known as Buddha, founded Buddhism around the 6th century BCE. The core of Buddhist teaching is encapsulated in the Four Noble Truths, which explain the origin of suffering and the path to liberation. These truths are 1) life involves suffering, 2) suffering is due to attachment and desires, 3) elimination of desires can end suffering, and 4) following the Eightfold Path leads to the cessation of suffering and achieves Nirvana, which is a state of freedom from the cycle of rebirth. Buddhism spread across the Indian Subcontinent and emphasizes personal spiritual development and the attainment of a deep insight into the true nature of life. Unlike Hinduism, Buddhism does not subscribe to the caste system, making it revolutionary during the time of its origin.