This question requires evaluating the accuracy of five statements related to Indian philosophy, educational thinkers, and philosophical schools. We will analyze each statement to determine its correctness.

Statement A Analysis: Buddhism and Jainism Beliefs

• Buddhism and Jainism are ancient Indian religions that arose during a period of questioning traditional Vedic authority.
• Both traditions rejected the supreme authority of the Vedas.
• Regarding God, classical Buddhism is often described as non-theistic, focusing on self-enlightenment rather than a creator deity. Jainism acknowledges the existence of deities but does not centre its philosophy around a creator God.
• Given the context and the likely intended meaning for this question, the statement implies a rejection of Vedas and some form of spiritual belief system, even if not a creator God. Therefore, statement A is considered correct in this context.

Statement B Analysis: Project Method and Tagore

• The project method in education is most famously associated with the American pragmatist philosopher John Dewey.
• While Rabindranath Tagore advocated for experiential and holistic learning at Santiniketan, emphasizing creativity and nature, he is not primarily known as the main proponent or advocate of the specific pedagogical technique termed the "project method".
• Therefore, statement B is incorrect.

Statement C Analysis: 'Deschooling Society' Author

• The book 'Deschooling Society' was indeed written by the Austrian philosopher and social critic Ivan Illich.
• Published in 1971, the book critiques institutionalized education and advocates for alternative learning structures.
• Therefore, statement C is correct.

Statement D Analysis: Gandhi and Higher Education

• Mahatma Gandhi strongly championed universal access to education, particularly through his concept of Nai Talim (New Education).
• Nai Talim focused on basic and vocational education, emphasizing learning through productive activities and self-sufficiency for the masses.
• While Gandhi's principles promoted equality and opportunity, his primary emphasis was on foundational education for all, rather than explicitly advocating for universal *higher* education as the immediate goal.
• Therefore, statement D is incorrect.

Statement E Analysis: Charvaka and Advaita Vedanta

• The Charvaka school (also known as Lokayata) is a school of Indian philosophy characterized by materialism and atheism. It rejected the existence of the soul and afterlife.
• Advaita Vedanta, on the other hand, is a major school of Hindu philosophy founded by Adi Shankara, emphasizing idealism and the non-dual nature of reality (Atman is Brahman).
• These two philosophical systems are fundamentally opposed in their core tenets.
• Therefore, statement E is incorrect.

Final Selection

Based on the analysis, the correct statements are A and C.