Competitive exams is a very broad spectrum, you will be eligible to attempt several exams regardless of the stream from which you completed your graducation.Some are listed below : 

UPSC Civil Service

Bank Exams

GATE Exam

PSUs

SSC CGL

Railways

RBI EXAM

India Army/ NAVY/ AIRFORCE SSB

AFCAT

NDA

CDSE

LIC

IBPS

There are many competitive exams available depending upon in which field you want to go.
Mostly you can give all exams after graduation.
Like :
GATE
CAT
CDS
AFCAT
UPSC( IES IAS )
BANK PO
IBPS clerk
Railway
for CBI
for INVESTIGATION DEPARTMENT
HSSC
Etc.
SO GOOD LUCK.