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If you are a B.Tech 3rd-year student (or even in 2nd year) and you want to apply for an internship at IIT Bombay, the best way to do it is by contacting the professor. You need to follow certain steps to apply for the internship:
Identify the area you want to work on. Make sure you have a good interest in the area, good knowledge of what is currently happening in your area of interest, a good grade in the subject, and a decent CGPA (or percent marks).
Go through the website of IITB and the corresponding department. The website lists details of all the professors, their contact and the area of research. Identify the professor who is doing work in your area of interest.
Prepare a good resume highlighting what you have achieved in the area you want to work on. If you are in the early or middle years of B.Tech you might not have too much to highlight on. In those cases, you can mention the good grades you got in the subject you want to work on. Even a seminar or presentation that you have taken related to the area will be a plus.
Draft and send a mail to the professor. The mail should be catchy, crisp, and to the point. Don’t write too many and don’t write too less. Highlight what you want to do, why you want to do and what have you done so far. Attach your resume also. The professor may not reply to you for the first time. You can send a reminder mail maybe a week later. Even after sending a couple of emails if there is no reply, try calling. (Be careful here. Some professors don’t like directly calling them. You can call some of his students doing research under him and inquire. Normally his student details will also be on the website).
Once you come under the notice of the professor, he might or might not have a phone interview and ask you to come as an intern depending on your performance.
You need to get the consent of your college to do the internship at IITB. You can ask the professor about the formalities for it.
Though it seems simple to read, it will take a considerable amount of time, particularly finding a good professor. So, if you want to do an internship six months from now, you should start as soon as possible. You can always take the help of the faculties in your current B.Tech college. If there is any faculty who has direct contact with any of the professors in IITB, that will be the best way.
You can bypass all the above steps by getting a recommendation from the faculty. If you successfully complete an internship, it will make the professor happy, and he might be willing to give a recommendation letter, which is very valuable for your higher studies.