TIFR Centre for Applicable Mathematics

Integrated M.Sc.-Ph.D. Programs in Mathematics are housed at the Tata Institute of Fundamental Research, Mumbai.The process of entrance consists of taking an entrance written test followed by an interview for the successful candidates. The written test cut-off marks will be set separately for Ph.D. and Integrated Ph.D. candidates. Based on those cut-off marks, the candidates are expected to qualify in this written test to become eligible to attend interviews.The final selection is based on the result from the written test and personal interview. 

Yes, summer internships are always good as they provide great practical knowledge and experience.

M.Sc can only be done after completing Bachelors. Therefore, you can apply after that.

Hello,
The M.Sc-Ph.D dual degree in Operations Research is an integrated doctoral programme, for those interested in a research oriented career. The programme is open for students with a Bachelor's degree in Mathematics or Statistics, and interested in research in engineering / interdisciplinary areas. The academic programme leading to the M.Sc-Ph.D dual degree involves foundation courses, advanced courses and research work. The candidate will be awarded both the M.Sc and Ph.D degrees simultaneously on successful completion of the program.
Click on the link:- http://www.ieor.iitb.ac.in/acad/msc_phd.
Thank you.