Hey vishal!

Yes , you can also get admission in SRM university without giving SRMJEE exam , the other way is direct admission .

SRM university  encourages and support students of exemplary talent, SRM Institute of Science and Technology or SRM university offers direct admission and scholarships to first rank students of all the central and state boards in India, top 1000 rankers in IIT JEE, top rankers in each district of Tamil Nadu and exemplary sports persons at National and International level.

So , if you belong to any of the above mentioned groups  , then you can get admission in SRM university. If not , then the only option left is management quota.

Hope it helps!