Maharashtra

If you don't want to take any exams then there are college based exams like DY Patil has its own exam Symbiosis has its own exam SNAP, Narsee Monjee has its own exam and on the basis of their cut-off scores, you will get admission, otherwise, there is as such no provision to get admission for any course without any entrance exam.

Getting admission in Pune University is tough as the total procedure is done through CAP rounds by DTE Maharashtra.
You can apply through any exam MHCET, CMAT, MAT, ATMA, etc.
But MHCET exam consideration is better
If you applied with other entrance exams then cut off is goes more than 99+ Percentile
In MH-CET it also depends of Category
If you are in Reserved category and Maharashtrian student then cut off is low
Best of luck!