When you use "
The", it refers to a definite, particular object or person.
Using "
A" refers to no particular object or person.
In your example:
"... is acceptable to Indian" =
Incorrect, because you are using the
Zero Article to refer to a specific person. If you wish to use this form, you could say "acceptable to Indian people", but that changes the meaning of the sentence.
"... is acceptable to the Indian" =
Correct, because you are using the
Definite Article to talk about a definite (specific) person, though it is more common to use "acceptable to the Indian people".
"I'm a Chinese" =
Incorrect, because you are using the
Indefinite Article. We use the indefinite article to talk about "one" person that is not a specific person. We need to add a noun after "Chinese" if we use "a". EG: He is a Chinese person from Shang Hai - not any specific Chinese person.
"I'm Chinese" =
Correct, because you are using the
Zero Article to suggest that your nationality is Chinese, and therefore you are part of the group of people who are Chinese.
See also: http://www.usingenglish.com/glossary/article.html