There are alternative ways to get admission in B.Tech Computer Science Engineering (CSE) without taking an entrance exam, and yes, it can be done. Several private universities and deemed universities provide direct admission for students who score over 50-60% in Physics, Chemistry, and Mathematics in their class 12 board exams. A few other universities may set their own entrance examination which may not be as competitive like JEE. There are also state level counseling processes which may offer some seats on the merit basis which do not require appearing for competitive examinations.
Another widely used alternative is through the management quota available in the private colleges. This alternative route is most likely to require payment of a higher fee, and the percentage of the management quota available will vary from institution to institution. Some other universities also allow lateral entry for students with a diploma in the relevant discipline to directly enter into the second year of B.Tech CSE. Specific research should be done to find appropriate colleges along with their requirements and the scholarships that might be available to increase the chances of admission and reduce costs.