WHY NOT!
Give your best shot to it.
Don't look at them as just 7 months!
7 months mean almost 210-214 days. Okay?
And is this WB council exam is the same as CBSE Boards? If yes then obviously you can finish that thing in just a preparation of a month.
See, do not waste your time in making a time table and all that stuff. Please don't!
It's of no use. If you're using SOCIAL MEDIA(fb,WhatsApp,insta, Snapchat and even careers 360) stop it right now.
Nobody in the future will ask you how many hours you spent in using mobile phones or meeting your loved one!
LEAVE EVERYTHING AS A SECONDARY OPTION.
Just to say as we all know. IIT HI SAB KUCH NAHI H. PR AGAR TUMHE VAHI PAR JANA H TOH FIR IIT HI TUMBARE LIYE SAB KUCH H!
If you get bored then you can watch some successful people's advice on YouTube. But not more than  2-3 videos per day as it is a time waste!

See do not go on the no.of hours you have to study.
Go for the no. Of hours of concentration!!!

IIT is everything for you if you're determined enough and YES YOU CAN CRACK IT.