Hello,
There are a lot ofcompetitive exams you can choose from, both regionally and nationally, to get into best colleges of engineering, designing, medical, agriculture, pharmacy and many more.
Let us look at the national level competitive exams after 12th for various streams:
Engineering

a. Joint Entrance Examination (JEE) Main
b. JEE Advanced
c. Birla Institute of Technology and Science Admission Test (BITSAT) entrance exam
    d. COMED-K
    e. IPU-CET (B. Tech)
    f. Manipal (B. Tech)
    g. VITEEE
    h. AMU (B. Tech)
    i. NDA Entrance with PCM (MPC)

Medical

a. National Eligibility Cum Entrance Test (NEET)
b. AIIMS
c. JIPMER
Defence Services a. Indian Maritime University Common Entrance Test
b. Indian Navy B.Tech Entry Scheme
c. Indian Army Technical Entry Scheme (TES)
d. National Defence Academy and Naval Academy Examination (I)
Fashion and Design
a. National Institute of Fashion Technology (NIFT) Entrance Test
b. National Institute of Design Admissions
c. All India Entrance Examination for Design (AIEED)
d. Symbiosis Institute of Design Exam
e. Footwear Design and Development Institute
f. Maeers MIT Institute of Design
    g. National Institute of Fashion Design
    h. National Aptitude Test in Architecture
    i. Center for Environmental Planning and Technology (CEPT)

Social Sciences

a. Banaras Hindu University
b. IIT Madras Humanities and Social Sciences Entrance Examination (HSEE)
c. TISS Bachelors Admission Test (TISS-BAT)

Law

a. Common Law Admission Test
b. All India Law Entrance Test (AILET)
Science
a. Kishore Vaigyanik Protsahan Yojana (KVPY)
    b. National Entrance Screening Test (NEST)

Mathematics

a. Indian Statistical Institute Admission
b. Admissions to Universities
c. Banasthali Vidyapith Admission


Hope it helps.