Ayurvedic Medicine

Yes, you can surely pursue Ayurveda in India without any entrance exams; you can refer below for some of them:

Hope this proves beneficial to you!

Government Ayurveda college, Thiruvananthapuram cutoff will be released after the declaration of AIAPGET results for admissions to MD, MS and PG diploma courses. Meanwhile candidates can check the previous year's cutoff. 

MD in Ayurveda(kavachikitsa) :165

MD in Ayurveda (agadathantra) :355

MD in Ayurveda (swasthavritha) :299

There are approximately 4 colleges across Tamil Nadu offering Ayurved courses in different modes - full time, distance/correspondence, part-time classroom, online and virtual classroom. Among these, private: 2 and public / government: 1 colleges.
Name:
Thiruvalluvar University
Vellore
Govt
Top 15 in Tamil Nadu and 
Sri Jayendra Saraswathi Ayurveda College and Hospital

Ayurvedic online courses often run between INR 25,000 to INR 55,000. Ayurvedic cooking classes, sports nutrition courses, nutritional counseling courses, and an online course on herbal medicines are just a few of the many Ayurvedic courses that are accessible. 

Numerous short-term Ayurvedic courses are offered both online nad offline by the National Institute of Ayurveda, SDM College of Ayurveda, DY Patil Vidyapeeth in Pune, and Ayurvedic Healing Village in Kerala. The course lasts anywhere from 1 week to 3 months. 

You can study an online programme in Ayurvedic diet and nutrition after finishing the BNYS course, which will aid in your understanding of diet planning, nutrition, and Ayurvedic principles. Following this course, you can start a food supplementary company or work as a clinical nutritionist, nutrition coach, or public health nutritionist. 

If you are interested in learning more, there are more courses available, including courses on Ayurvedic cooking, sports nutrition, nutritional counseling, and herbal medicines through an Ayurvedic herbology course.