Exam

Yes, of course, you can get admission. You can join any private college.

Some common and important topics in logical reasoning are Coding and Decoding, Seating arrangements, Analogy, Letter Series, Number Series, Clocks and Calendars. These topics need good attention.

You need these book:
Loney's Coordinate Geometry and Trigonometry
Hall and Steven's Geometry
Hall and Knight's Elementary Algebra and Higher Algebra
Calculus by GP Thomas
University Physics by Resnick and Halliday
University Physics by Sear Zemansky
Problem in Physics, Irodov
Organic Chemistry by Morrison B

Karnataka PGCET is the exam you will have to give in order to take admission in this institute.
https://www.shiksha.com/college/m-v-j-college-of-engineering-whitefield-bangalore-20690
Browse to your desired course and you can check the information there.

University Physics by Resnick and Halliday
University Physics by Sears Zemansky
Irodov's Problem in Physics and Solution
Calculus by GP Thomas
Loney's Trigonometry and Coordinate Geometry
Hall and Knight's Elementary Algebra and Higher Algebra
Organic Chemistry by Morrison Boyd.

Not at all. Most people pursuing CAT have a gap in their education. It doesn't affect your CAT score.

Hall and Knight's Elementary and Higher Algebra
Loney's Trigonometry Coordinate Geometry
Calculus by GP Thomas.

The UGC NET Exam is over and the results have been declared. The exam was conducted in more than 80 subjects and the UGC NET Exam cut-off score was different for each subject. You have not mentioned the subject you want to know the UGC NET cut-off- https://scoop.eduncle.com/cbse-ugc-net-result, but

The entrance exam for JNU will completely go online for the next session and exam date is exactly not confirmed but it is in last week of December 2018.