Engineering

Yes, you need to write DCET exam conducted in Karnataka and depending on your rank you can select a college.
To my personal opinion, try to get MVIT as it is ranked higher in the lateral entry with a cut-off around 1500.
All the best.
The fee will be around 50K for general but you can get scholarship i

TFW rank means rank under Tuition fees waiver scheme. It shows your rank among those students whose family income is less than 2 lacs (around ). At the time of counselling your GMR matters only. If your general merit rank is good and you are a TFW student, you can get admission under TFW quota, and

As admission is based on the score obtained in Uttar Pradesh State Entrance Examination (UPSEE). Check out the UPSEE college predictor below for details:
https://www.shiksha.com/upsee-college-predictor

Check out the COMEDK college predictor below:
https://www.shiksha.com/b-tech/resources/comedk-college-predictor

Follow the KCET college predictor below:
https://www.shiksha.com/b-tech/resources/kcet-college-predictor

I would not recommend you to join Gurukula Kangri Vishwavidyalaya, Haridwar for ECE, for more details check, the reviews below:
https://www.shiksha.com/university/gurukula-kangri-vishwavidyalaya-haridwar-25246/reviews?course=204929&sort_by=year of graduation&type=question

Since both the colleges are similarly great, I truly lean towards you ought to go for mechanical or any center branch in IIT (ISM) as after it got moved up to an IIT the school arrangements has expanded even from previously and countless are going to the grounds for grounds enlistment. So, its bette

No, its not possible to apply for MBA without entrance exams.

If you think you can get into IIT next year, then think twice and drop but CSE from NIT Patna is also a good option.