Yes, registration on the Udyam Registration Portal is completely free.
Micro: Investment - Up to ₹1 crore, Turnover - Up to ₹5 crore
Small: Investment - Up to ₹10 crore, Turnover - Up to ₹50 crore
Medium: Investment - Up to ₹50 crore, Turnover - Up to ₹250 crore