there are many engineering entrance exam which you can apply for moreover there are many courses other than engineering which you can appear for.

following are the list of exams you can apply for 

BITSAT
VITEEE
EAMCET
KCET
MHTCET
COMEDK

if you are interested in defense you can also apply for the exams likes of:

indian maritime university entrance exam 
national defense academy examinations {conducted twice in a year}
Indian navy BTech entry scheme through class 12 results 
Indian Army Technical Entry Scheme.

all the best if you have any query regarding the exams feel free to ask us!