The protest turned violent when demonstrators hurled stones at security forces who fired tear gas and charged with batons, in the capital’s largest protests in five years.
Police said 60 civilians were injured and another 118 police personnel were hurt.
Protests were also held in Mumbai and Bengaluru, drawing hundreds of people.
On Wednesday, hundreds remained camped at Delhi’s Jantar Mantar protest site as the CJP vowed to continue its campaign, which entered the third day.
“Cockroaches are alive,” it said in a social media post, describing Pradhan as “incompetent”.
The CJP has attracted millions of followers on social media since its launch in May, presenting one of the biggest challenges to Modi since the Hindu nationalist leader secured a third term in 2024.
The protests follow a series of controversies that have undermined trust in India’s testing system, including the leak of a medical entrance examination paper that forced more than two million candidates to retake the test.
Another dispute involving the online marking of examinations taken by nearly two million high school students has further fuelled public anger.