Engineering

Go for IITs as it's good for placement. Attempt for JEE.

No, you will not eligible for GATE exam. But, you can do higher studies like PHD and other courses.

IITs are allotted on basis of your JEE Advanced marks. JEE Mains score can land you in NITs.

Frd the syllabus is based on the basis of your 10 +2
Test Pattern for B.A. (Hons). Social Science
Detail
Exam Mode
Offline (Pen/Pencil-Paper based test)
Test Paper Sets
Three
Test level
10+2 standard level
Exam Duration
120 Minutes
Total questions
150 questions
Type of questions
Multiple Choice Questions (MCQs)
T

It costs around 25-30 Lacs in Indian currency for complete degree without any scholarship. But, if you got a scholarship, it will be best option as fees is reduced. And you have to clear SAT exam for this.

Yes, PU-CET is for the B.Sc courses. B.E admission is purely based on the JEE Mains rank.

You can get private colleges but chance of government colleges are quite less. So, if you have registered for any other state level or private college entrance exams, try to do well in them.
All the best.

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Dear Inder!
If you look at Railways Job Vacancies, it has two options, one is technical. In which there requires you the technical degree in B.Tech or Diploma. With B.Sc. You may not ab able to get the core technical job in Railways. In non technical sector, surely you can get the job after B.Sc. If