Can I apply to Harvard?

I am thinking of applying to Harvard and other US schools. But I am not sure since the competition is insanely tough. So the following is my profile and please tell me do I stand any chance for getting selected?
Profile:-
1)Jee mains and advanced rank 1331 and 1003 respectively
2)Kvpy SX scholar
3) Sat score 1530/1600
4)Sat subject physics, chemistry,maths(lvl.2) scores 760,750,770
5) AP physics ( all 4) a total of 18/20 credits, Chemistry 4/5 and Calculus BC 4/5 credits.
6) Class 12th boards 95% and 10th 96%

Extra curricular activities:
1)GK quizzer: Represented school twice at zonal level and once at the national level
2)Athletics: participated in inter DPS athletics meet and CBSE clusters
3)Served as GK club secretary, president and Student secretary during 3 years.

Supplementary materials:

  1. Wrote a Research paper on gravitational lensing.
  2. Conducted and designed several experiments (9 in total) on topics like aerodynamic tunnel and cathode rays etc
  3. made 2 research Projects on organic fuel and traffic management
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You should apply! Having even a single research paper at a school level is an incredible feat, and sets you apart from the crowd. Just blindly go ahead and apply. Make sure your application is good.

Devote some days in making a good application...Google and YouTube is gonna help you a lot in this...i have also found a plenty of resources in Quora too.. where are you studying now? Do find someone great who can help you with recommendation letters!

Yes you should apply.

  1. Do you want aid? I've seen my seniors not get in even in need blind colleges due to aid thing(unofficially ofcourse).
  2. You should retake sat if you can and get a score of around 75 percentile of Harvard which is 1570. You can get in even at this score (I too have 1530 :P) but a 1570 will only increase your chances.
  3. Apply to many schools (partially bcoz of point 1). You can get into Caltech, Princeton, Yale, Johns Hopkins, NUS, NTU, HKUST etc which are also great schools.

I too have questions for you

  1. How much did taking these APs cost? Did your school had AP classes too?
  2. That SAT subject test score is low by your standards. Are you doing to report them as well? If you don't mind sharing why's it low?
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Agreed..!!! Cover letter plays very important role. So give ur tym to write a good cover letter nd try to connect ur Alumini Via Seniors. They will guide you in a better way.

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Just a tip don't just apply for HARVARD go for other foreign universities also they offer much better opportunities than any average indian university.
Look for the universities that have good opportunities in your area of interest and do apply for them.