The correct answer is: a) Designing the Indian National Flag.
Pingali Venkayya was an Indian freedom fighter, social reformer, and a textile designer from Andhra Pradesh. He is best known for designing the Indian National Flag. He was born in Machilipatnam, Andhra Pradesh, in 1876. He started his career as a teacher, but later became a textile designer. He designed the Indian National Flag in 1921. The flag was adopted by the Indian National Congress in 1931. Pingali Venkayya died in 1963.
Option b) is incorrect because Pingali Venkayya did not lead the Salt Satyagraha in Coastal Andhra. The Salt Satyagraha was a major nonviolent protest campaign led by Mahatma Gandhi in 1930. The campaign was against the British salt monopoly.
Option c) is incorrect because Pingali Venkayya did not compose patriotic songs. He was a textile designer and a freedom fighter.
Option d) is incorrect because Pingali Venkayya did not establish schools for the underprivileged. He was a textile designer and a freedom fighter.