Often we come across cases similar to your's. But the question remains -
Can a private employer terminate an employee "without assigning any reasons" for the termination?
People often have this misconception that a private employer can terminate an employee without assigning any reasons for the termination. However, it is against the employee termination policy in India. The reasons need to be stated and the employees should be given the due chance to explain themselves.
Without going into specifics, it's necessary to study your case with relevant documents. You may go through the cases cited in this link for proper appraisal of your case.
https://indiankanoon.org/search/?formInput=terminate%20without%20any%20reason.