Govind Ballabh Pant Institute of Engineering and Technology

Hi Malay,Admission in this college is done through both Patanagar University entrance exam and through JEE Mains. If you have not appeared for university entrance exam, then you can get seat by JEE Mains counselling also. You will get top branches with 83 percentile in JEE Mains exam. Best of luck.

Yes, you can give the GATE exam after B.Tech and after that, you have the various opportunities to join the PSU or any other government sector jobs which demand the GATE qualification.

Yes, you can get lateral entry in mechanical engineering.
For more information, click the links:
https://www.gbpuat.ac.in/academics/admissions/index.html
https://www.shiksha.com/college/govind-ballabh-pant-engineering-college-gbpec-uttarakhand-other-24262

Admissions are being done on the basis of Common Entrance Testa (CET) conducted by Guru Gobind Singh IP University as per government rules. Around INR. 2 Lakh students apply for the CET and 70000 students qualify for the admissions in GGSIPU. Out of this, a few sharp minded students having up to 4500 rank in CET get a chance for admission in GBPEC. Hence, there is no lateral entry scheme in GBPEC for B.Tech courses.

Now, you have to do all India counselling.
Or, wait for state counselling in Uttrakhand. It will probably start from 15th of July.