Kolkata

I hope, this will help you.
https://www.google.co.in/url?sa=t&source=web&rct=j&url=https://career.webindia123.com/career/dates_and_events/entrance/medi/national-institute-of-homoeopathy-bhms-admissions.htm&ved=0ahUKEwie0t7o-8TVAhUGYo8KHXvWBzsQFgiyAjAb&usg=AFQjCNHi0LEVRCvmbViwAvcvDuXezwqk4w

Dear Suman,
Not just in India, but in the entire world, you can never do engineering and medical through distance mode. So don't ask for B.Tech college in distance mode in Kolkata as you will not find and even if any college offers B.Tech in correspondence, means they are violating the rules of AICTE. Go and complaint them. So, go for regular B.Tech program.
Ask any query at anytime.
Good day.

You have a lot of options left with you as you have done you Masters. If you are very much interested in academics, then Ph.D is the obvious choice for you after completion of your M.Tech.
If not, then there are number of corporate giants that seek M.Tech pass outs as they want to hire subject matter experts. M.Tech makes you eligible for jobs in such big companies like google, Microsoft and more.

You can get in many private engineering colleges which have their own set of criteria for admission. I would suggest you for UEM Kolkata and to know more about the college visit here:
https://www.shiksha.com/university/university-of-engineering-and-management-kolkata-47398

Hi Shekh,
Without appearing for the entrance examination, you will not be eligible for admission into the Institute.

Hello Ayan,
Previous year's marks for entrance exam are valid for only one session so you can't use this rank this year.
You can take admission in a private college for B.Tech as there are many good private colleges for B.Tech in Kolkata.

HI Hrithwik,
The cutoff varies every year according to the number of students applying for examination and number of seats available. It would be advisable that you get in touch with college authorities/official page directly for accurate cutoff which can help you in figuring out the appropriate college.