On the common app the choices are:
American Indian or Alaska Native
Asian
Black or African American
Native Hawaiian or Other Pacific Islander
White
I am from India, born in India, but for some reason I am reluctant to pick “Asian”. Perhaps it’s the fact that selective colleges tend to discriminate against Asians 
How would it look to colleges (such as Penn) if I don’t include what I identify myself as?
Im indian too but I’m a us citizen but i’m still didn’t declare my race on the common app.
Honestly I don’t think it has any impact on admission (unless you’re a URM which asian is definitely not) but I left it blank just to avoid any bias addmissions might have.
Though my name sounds Indian though so I think that gives it away anyway.
The race/origin questions on all applications are required to be there under federal (US Government) regulations and are there to provide the government with data on numbers of applicants and those admitted in those groups, particularly those who are either US citizens or permanent residents. Under the same regulations, no applicant can be required to answer the questions and no applicant can be penalized for failure to answer them.
Correct. Answering the questions are optional. Having said that, if race is a factor for a particular college, you should not be so naive as to think that by simply not answering the race question that the college won’t find out that you are Indian.
^well, maybe if OP’s name is John Smith, son of David and Susan Smith.