B.Sc Entrance Exam

You can check last year's cut-off at the official site (cetug.puchd.ac.in).

Hi,
Aspirants meet the eligibility criteria to secure admission in undergraduate programmes offered at Allahabad University (AU), if they have cleared their 10+2 or equivalent qualifying examination from a recognized board. Allahabad University conducts UGAT to provide admission in B.A. B.Sc. B.Com courses at undergraduate level. Please refer the link below for more information:
https://www.shiksha.com/university/university-of-Allahabad-3574?q=University+of+Allahabad&rf=searchwidget&landing=ilp
All the best.

Simple, attempt just those questions which and are known to you.
Read the guidelines carefully.
Focus on previous year question papers and prepare from that.

Yes, there are a lot of universities that provide entrance test for your need. You can check universities nearby you.

Please check the following link for detailed information about syllabus for NCHMCT Entrance Exam:
https://www.shiksha.com/hospitality-travel/hotel-hospitality-management/exams/amp/nchmct-jee/syllabus.

The application form is already out.

No, candidate of other state are not eligible for this exam.