Engineering

You must be asking about one particular college and seems to have typed incomplete question here. There is a process on Shiksha which will assist you to find a college as per your rank. This rank predictor compiles things for you:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

B Tech or any other technical engineering degree is not offers via distance mode. To do such a degree via distance or even non-attendance mode is a waste of time and money as well. One does not learn anything.

Closing rank changes from year to year. You can check the closing ranks. With your rank, you have quite a good chance of getting admission into IEM. Give your preferences accordingly and hope for the best.

Hello Kunal,
Almost every student desires of CSE hence, only this in top 10 percentile can hope for admission. But then hope is everything. Right? Wait till last round of counseling, some miracle may happen.

Hello,
I am afraid your rank is really low. But then miracles do happen and I would advise you to have hope till last round of counselling.

Hello Harsh,
Please look at the reality. You say you have dropped one year for preparing for JEE Mains. Can you get better results if study along with B.Sc? But you can always try. Yes, admissions in IIM are given to graduates of different disciplines.

Hello Anushka, I feel your rank is a bit on the lower side. However, to help you out I am attaching a link that will predict college for you:
https://www.shiksha.com/b-tech/resources/wbjee-college-predictor

Honestly speaking there are few chances as compared to last year's cut off. You can still check this year's cut off for any change.

On the basis of JEE Mains scores, you can take admission to NITs and other colleges, or you can opt for JEE Advanced for admission to IITs, IISc. and ISM Dhanbad.