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With 83.75 percentile you won't be able to get a call from any IIM not even any of the ultra new IIM. One more problem will be your sectional cut-off. With 39 percentile in one of the section, you won't qualify to be further evaluated in many colleges. So make sure that in any college you apply there is no sectional cut-off.
You can definitely apply for IITs accept IIT Mumbai and IIT Delhi. With rest of the IITs, you will have a good chance to get a call for second round of WSAT and interview. But make sure to check out the eligibility criteria and the sectional cut -off before applying. If there will be any sectional cut-off then your application will be straight rejected.
All the best!!
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