Explanation:

- The National Youth Festival celebrates the talent and spirit of the youth in India with cultural events and activities.

- It is organized every year to coincide with the birth anniversary of a significant personality.

- Option 1: Jawaharlal Nehru was the first Prime Minister of India but is not directly associated with the National Youth Festival.

- Option 2: Sardar Vallabhbhai Patel was a key figure in India's independence movement and is celebrated for his contributions to national unity, but not the inspiration for the NYF.

- Option 3: Swami Vivekananda is the correct answer. His birth anniversary on January 12 is celebrated as National Youth Day, inspiring the National Youth Festival.

- Option 4: Mahatma Gandhi, known for his nonviolent philosophy, is a central figure in Indian history but not directly connected to the NYF.