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Yes, M.Sc Zoology in Annamalai University is approved by UGC. Grade 'A' accredited by NAAC and is a State University also a Member of AIU.

No, it is confined only to Andhra Pradesh state and the rank is not considered by the Telangana state, they consider only TSLAWCET rank for admission.

You can consider following colleges:
Bundelkhand University
IFS India Education Department
Dr. Bhim Rao Ambedkar University, Agra
Amity Institute of Forensic Sciences
Osmania University, HyderabadDr. Hari Singh Gour University of Madras
Lok Nayak Jayaprakash Narayan National Institute of Criminology and Forensic Science (LNJN NICFS), Delhi
Gujarat Forensic Sciences University
These are the top 9 best forensic science colleges in India.

NATA/ IIT JEE paper 2 are the 2 exams, which will get admission in B.Arch in Government/ Private colleges.

For that, first focus on your B.Tech syllabus, in that almost all the topics that will come in your IES exam will be there. Study those materials carefully and then if you want, you can join a coaching institute for the same, but if you study your syllabus carefully you need to do anything more.