Since you are interested to have advanced knowledge in any one of the domains Robotics, Quantum Mechanics, Nanotechnology and Cosmology at the later stage, I would advise you to show your inner passion for both Physics and Mathematics.
To understand the complexities of Physics, you should have conceptual clarities in Mathematics especially in the areas of Calculas, Matrix, Linear Algebra, Complex Number, Vector Algebra, Infinite vector, Trigonometry etc and you would be required to apply these while dealing with the advanced studies of Physics.
The streams discussed above are the extensive studies of Physics in the different domains. In order to clarify these domains, you should be familiar with their definitions. Let us discuss the term one by one -
Cosmology is the detailed study of the branch of Astronomy involving the origin and evolution of the universe. It can be better understood with the application of higher Mathematics.
Nanotechnology relates to the products using tiny materials being used in Electronic devices, Catalysis , Sensors etc
Quantum Physics would deal with extensive studies of Physics in the field of Black Body Radiation, Bohr Model for explaining spectral lines, Stern Gerlach Experiment etc with the application of different branches of Mathematics as discussed above.
However, Robotics is entirely a different branch in the sense that this branch employs the basics of Computer Engineering, Mechanical and Electronic Enginnering.
If you are interested to go in the specialised course relating to Cosmolology or Quantum Mechanics, take up the course of B.Sc with the combination of Physics, Chemistry and Mathematics or still better take up the course of Physics ( Honours) from a reputed university and for post graduation you can seek admission in the following institutions-
1) Tata Institute of Fundamental Research, Mumbai
2) Raman Research Institute, Bengaluru.
3) Indian Institute of Astrophysics,Bengaluru.
4) Physical Research Institute, Ahmedabad.
5) IIT Mumbai
6) IIT Chennai
7) IIT Kanpur etc.
IIT provides five year integrated course for the persuasion of both undergraduate and post graduate level. You will have to qualify the entrance test of IIT to avail this integrated course. During your post graduation stage, you need to take up the specialisation course either in cosmology or in the quantum mechanics.
Other institutes too have their own entrance tests to screen the deserving aspirants.