Tamls have their own language, which is spoken in Singapore and Sri Lanka - the word Kari is a Tamil word, not an Indian one.
Yes Tamils have their own language, and it is spoken outside of India, but mostly inside of India, in Tamilnadu, which is in the South of India. Tamil is an Indian laguage. It seems that you, and this forum's unfortunate Harry, are mistakenly assuming that the Northern Indian lingua franca called Hindi is "Indian" while Tamil is not. Both Hindi and Tamil are Indian languages. The latter is not an Indo-European language, but it is Indian nonetheless.