Firstly lets see chances of getting in a relationship and that too specifically with an IIT girl . .
lets try to understand with mathematical Calculation (Well I love Statistics so I will answer in language of mathematics.) .IIT's have approximately 6:1 ratio of boys over girls[1]. so Girlfriend probability of being in a proximity to a girl is 1/7. But obviously you don't like all the girls in IITs Campus, so suppose you somehow convince yourself to like half of them, then probability of being in vicinity to those girls become 1/14. But" here's the catch, girls you like are popular among your colleagues, so if we take an ideal guess that they will accept you as your boyfriend, then probability of you getting an acceptance is 1/6, also you will be contending among your frats, so probability of you getting succeed equals to 1/6. So your best case probability of being in a relationship equals to 1/504. "
This ratio is nearly equal to the no. of students clearing JEE to total no. of applicants. But, you have put your efforts to make sure that you should be one among 500 odd. Matlab 'Bhai Aap to bond hai '
So here goes my question to all whose ask about gf : "Do you seriously want to put that much effort for being in a relationship with an IIT girl?" I guess its not worth it. Because you can spend that kind of energy in doing any of following:
Studying. Better GPA is always a plus point.
Networking.
Publishing a research paper.
Honing your interests and personal hobbies.
Sports.(Swimming[2], Running can save your life someday)
.
.
Followed by a bottomless quiver of options, which you can discover with your Awesome colleagues. I am not saying that having a girlfriend is bad. In fact its perfectly healthy if you two are mingled purely by mutual interests. But if you are indulge in a dog fight in its pursuit, then its clearly stupid and overrated. 4 years in your college is an awesome experience, please don't waste it over such petty things.
so clearly It is close to impossible, the best bet is to graduate as soon as possible and get a job in a sector/company where sex ratio is better
[1]: Result of JEE Advanced 2016 says that 31996 boys and 4570 girls qualified. Which gives ratio of 1:7 but assuming other branches (Humanity & Sciences, MBA etc.) in IIT and M.Tech have better strength of girls so I am taking gender ratio as 1:6.
[2]: Only 50% people can swim (Time’s survey). An average of 10 people in the U.S. die from drowning each day, according to the Centers for Disease Control and Prevention.