hi Aratrik,
You can definitely get admission to Elphinstone College, Mumbai. But there are some minimum eligibility criteria which say that you must have Biology in your 10+2 and should have passed from any recognizable board. Other than these criteria, you should pass with a minimum of 40% in your 10+2. If you are in the final year of 10+2 you can also apply in this college for BSc in biotechnology.
There are some other rules and criteria which you have to follow after joining the college and I am writing those points below
1. You have to choose certain subjects every year as a choice.  
    For ex-: you have to choose Botany, Zoology, Statistics, chemistry as the chosen subject along with the main or honors paper i.e. Biotechnology.
2. Second year and third year optional subjects will be based on the subjects that you have chosen in the 1st year.





Other than this college, there are also some good colleges that provides you to do BSc in Biotechnology. I am providing some college names below and you can consider them...
1. Christ University, Bangalore
  ( Eligibility criteria-:10+2 or HSC exam from any recognized board of education
     Selection procedure-:Marks in 10+2 and score in Christ University Entrance Test )
2. The Oxford College Of Science, Bangalore
  ( Eligibility criteria-: Admissions are done on the basis of merit in 10+2 level examination or Pre-university course)
3. Fergusson College, Pune
   ( Eligibility criteria-: you should have passed class 12th in Science stream and the selection is on the basis of merit list which has been released by the university itself )
4. Jaipur National University(JNU)
    ( Eligibility criteria-: Your 12th pass out should be in science stream with any of the subjects from Biology/ Mathematics or Agriculture or Biotech will be admitted. The selection procedure is by releasing a merit list and a long with this the interview taken by the university)
If you need more help...i am always here
Ask me if any other doubts are there
Thank you and best of luck.