For a career in Graphic Designing, the best option for you is to take up Master’s in Graphic Design. This program is offered by several IITs and design institutes in India. 

Here are the best institutes for Master’s in Graphic Design or Communication Design-

1. NID (National Institute of Design), Ahmedabad
2. IDC, IIT Bombay
3. Srishti School of Art Design and Technology, (Bengaluru, Pune, Trivandrum)
4. LPU - Lovely Professional University, Jalandhar
5. MIT Institute of Design (MITID), Loni Kalbhor, Pune

IITs hold the Common Entrance Exam for Design (CEED) for admission into their M.Des. Institutes like NID, NIFT, etc. have their own entrance exams for admissions into the Master’s.

Most of the design colleges are open to graduates from all disciplines, given that one clears the entrance test for a Master’s. However, IITs take in students with a graduation in Design, Architecture, Engineering, or an MSc., or students with a background in Arts/Computer Applications.

Basically, you can opt for Graphic Designing courses after a B.Tech in any branch.