KIT College of Engineering, Kolhapur

I don't have much idea about the college you have named but I'd suggest you to go for UEM, Kolkata as it is the best college for B.Tech in mechanical engineering with good consistent record. For your information about the college and its courses with fee structure see the link:
https://www.shiksha.com/university/university-of-engineering-and-management-kolkata-47398

It is probably 6-10 Lacs per annum as of 2016.

Hi,
Anywhere around 90-100 marks is the expected cut-off for College of Engineering, Trivandrum this year.

I don't think so as they have got the worst management.

Elitte Institute of Engineering and Management (EIEM) is a co-educational, private diploma Engineering college located in sub-urban of Kolkata, West Bengal,West Bengal (India),India. It offers Diploma courses in Engineering and Technology. The college was set up by the Pinnaccle Educational Trust in 2009, and it will average college for mechanical engineering.

You can check for engineering college on this link-
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor
You have high chances in NIT Patna, Hamirpur, Silchar, Agartala.

It is a good institute with good faculty and top notch placements.