In considering a career in research, particularly in mathematics, it's essential to explore the research opportunities at various institutes such as IIT Kanpur, IISc Bangalore, and IISERs. Each of these institutions offers mathematics programs, and prospective students should examine faculty profiles to identify professors conducting research in their specific areas of interest. If a particular research focus is not a concern, prioritizing entrance exams like JEE is advisable. Additionally, CUET UG provides access to reputable institutions like JNU and DU, while options like IIT JAM after a BSc or NET after an MSc can further facilitate entry into prestigious research programs.