Yes, these are top private colleges of engineering you should apply for these exams.

You should apply for as many as entrance exam to have good option in your hand.

If you are well prepared for JEE Main exam you can easily crack these exams as JEE Main level is higher. 

You can check the details below

BITSAT-  You can appear in BITSAT to take admission to the Integrated First Degree Programmes of Engineering at its 3 campuses - Pilani, Goa and Hyderabad

BITS Pilani will conduct BITSAT 2018 in online mode, tentatively from the third week of May to the last week of May 2018.

In order to be eligible for this exam you should have 75% aggregate marks in Physics, Chemistry and Mathematics  in your 2th class. Also, in each of the 3 subjects, they must also secure 60% marks separately.

To check the syllabus you can refer below link

https://engineering.careers360.com/articles/bitsat-syllabus

VITEEE- VIT University conducts VIT Engineering Entrance Exam (VITEEE) for admissions to various undergraduate engineering programmes across its Vellore and Chennai campuses. There are nearly 5,000 B.Tech seats for which around two lakh candidates register for VITEEE every year

In order to be eligible for this exam you should have scored an aggregate of 60% in Maths, Physics and Chemistry in 10+2 and for SC, ST, J&K, North Eastern states you should have scored an average 50% marks in Physics, Maths and Chemistry in 10+2 or its equivalent exam.

To apply for the application form you can refer below link

https://engineering.careers360.com/articles/viteee-application-form

To check the syllabus you can refer below link

https://engineering.careers360.com/articles/viteee-syllabus

SRM- SRM University conducts SRM Joint Engineering Entrance Examination (SRMJEEE) for granting admissions at nearly 7,000 undergraduate engineering seats across its four campuses - Kattankulathur, Ramapuram, Ramapuram Part– Vadapalani and NCR Ghaziabad.

You can check the syllabus of the exam below

https://engineering.careers360.com/articles/srmjeee-syllabus

To know in detail about all the exam you can refer below link

https://engineering.careers360.com/exams

Good Luck!!