The police also attacked the demonstrators with batons after they tried to break through barricades.
According to several media outlets, the protests broke out after police forcibly took a hunger striker to hospital.
The protesters are demanding, among other things, that India's education minister resign after suspected irregularities in medical school examinations.
The Cockroach Party was formed after controversial statements by Indian judge Surya Kant. He is said to have once compared young unemployed people who turned to activism to cockroaches.
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