The student set himself on fire on Friday at the Central University for Tibetan Studies in Varanasi in Uttar Pradesh state.
Self-immolation has regularly been used as a protest against China's actions in Tibet. But Indian police said they are also investigating the 20-year-old's recent exam failures as being a possible cause for his actions.
"We are not entirely clear about the reasons but eyewitnesses told us that he shouted "freedom" before running out, dousing himself with kerosene and setting himself on fire," Sanjay Tripathi, a Varanasi police spokesman, told AFP.
"There were some Tibetan representatives at the institution at the time. But the institute authorities have also told us that they had announced exam results a day earlier and he had failed two exams," Tripathi added.
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The International Campaign for Tibet identified the student as Tenzin Choeying. It quoted Chime Namgyal, head of the Tibetan Youth Congress activist group in Varanasi, as saying Choeying shouted "Victory to Tibet".
Police said they are still investigating and will take statements from Choeying and his family. "The boy is recovering at the hospital. He can speak but has around 50 per cent burns," Tripathi said.
China says its troops "liberated" Tibet in 1951, but many Tibetans accuse the government of religious repression and eroding their culture.
China rejects the accusations and accuses the Dalai Lama, Tibet's spiritual leader who lives in exile in the Indian hill town of Dharamshala, of inciting self-immolations in a bid to split Tibet from the rest of the nation.
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A young farmer self-immolated in southwest China in March, the first Tibetan to set themselves on fire in 2017.
The Tibetan government in exile in India said he was the 146th Tibetan to self-immolate since 2009.
Choeying is the not the first Tibetan to set himself on fire in India. A Tibetan exile set himself alight and died two days later in New Delhi in 2012.
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