Which are the important entrance exams to be taken for pursuing maths, architecture and design courses in India, particularly in Chennai?

Hello Srimathy, Please refer to the following link: https://en.wikipedia.org/wiki/List_of_admission_tests_to_colleges_and_universities#India

NATA exam conducted by Council of Architecture is accepted throughout India in most of the Architecture colleges.

Well, you have to enroll in NATA exam for B.Arch. Whereas for designing course like BFA in Painting, Photographer, Animation, etc. aptitude exam will be required and you have to check college's request as well.