If you don't want mathematics stream, you can select Biology and Physical Sciences in intermediate and after intermediate, you can pursue MBBS, MDS, Ag B.Sc. BV Sc and so many other courses with this biology stream qualification of +2 or Intermediate. I am giving below some good school of State syllabus in Keala.
1. Mannam Memorial Residential Higher Secondary School. It is a co-educational boarding school in Neeramankara, Thiruvananthapuram, Kerala state, India. It has classes from Kindergarten to Class XII.
Address: NSS College Rd, Neeramankara, Pappanamcode, Thiruvananthapuram, Kerala 695018
2.Loyola School, Thiruvananthapuram. It is a private Jesuit school for boys It is in the suburb of Sreekariyam in Thiruvananthapuram city, in the Indian state of Kerala.
Address: Sreekariyam - Aakkulam Rd, Opposite CTCRI, Bapuji Nagar, Sreekariyam, Thiruvananthapuram, Kerala 695017, Phone: 0471 259 8585
3.Christ Nagar Higher Secondary school. It was started in 1976. It is in Thiruvananthapuram, India, recognised by the state government of Kerala as a minority educational institution. In 2002, Christ Nagar English High School was upgraded to higher secondary level.
Address: 11, 273, Keston Rd, Kanaka Nagar, Kowdiar, Thiruvananthapuram, Kerala 695003
Phone: 0471 231 8485
4. Nirmala Bhavan Higher Secondary School. It is founded in 1964.
Address: Shree Mahadeva Temple, PMG TTC Road Opp Kowdiar, Nanthancodu, Thiruvananthapuram, Kerala 695003
5. St. Thomas Higher Secondary School Address: Poonthura, Thiruvananthapuram, Kerala 695026
Phone: 0471 251 1122