IISER Entrance Exam

Can you please specify which test are you talking about?

Yes, you will have to since there is no prescribed syllabus for it.

Please refer to the link provided below for details regarding the IISER Entrance Exam pattern, application process, question papers. https://www.shiksha.com/science/exams/iiser-entrance-exam.

Please refer to the link provided below for details on IISER Entrance Exam 2018 Eligibility. You can check for your eligibility to appear for the IISER Entrance Exam from the criteria mentioned at the link provided below:
https://www.shiksha.com/science/exams/iiser-entrance-exam.

IISER 2018 reference books:
Physics for IISER 2018:
1) Concepts of Physics Volume I by H. C. Verma
2) Concepts of Physics Volume II by H. C. Verma
3) NCERT books for class 11-12 (Physics)
4) Fundamentals of Physics, by Halliday, Resnik, and Walker
Chemistry for IISER 2018:
1) NCERT books for class 11-12 (Chemistry)
2) Organic Chemistry by Morrison and Boyd
3) Inorganic Chemistry for IIT-JEE by O. P. Tandon
Mathematics for IISER 2018:
1) Tata McGraw Hill for Mathematics
2) Problems in Calculus of One Variable by I. A. Maron
3) Higher Algebra by Hall and Knight

Yes, you can apply for the same.

Candidates who have cleared their Class XII in Science stream are eligible to apply for IISER Entrance Exam 2018. Please refer to the link provided below for detailed eligibility criteria to appear for the IISER Entrance Exam 2018. Regards. https://www.shiksha.com/science/exams/iiser-entrance-exam.

Yes, OBC cut-off for SB/SX is 45.