Indian Institute of Science Education and Research admits students after class 12 for BS-MS, after Bachelors for I.PhD and after Masters for PhD. It is a premier institute standing behind IISc in facilities and support for education and research in basic and advanced science.

For entry to BS-MS, its through JEE, KVPY or IISER test. For I.PhD, its JAM as well as IISER test. So you can refer to all those previous year questions in respective sites. For test conducted by IISER for entry the question paper is uploaded by coaching centres, so you have to search it on the internet for such questions. For more information you may also refer to https://engineering.careers360.com/articles/iiser-2016-sample-papers and https://admission.aglasem.com/iiser-aptitude-test-model-paper-1/

And for syllabus you can refer to IISER websites for their tests.