No , there is no negative marking in NATA examination. 

ABOUT NATA

NATA, National aptitude test for architecture, is an entrance exam which is conducted by National Institute of advanced studies in architecture (NIASA) the body of council of Architecture in India. This entrance exam is a national level examination. Students who are willing to study Bachelor of architecture or some other relevant architecture courses at all recognized institutions across India, can give NATA after their 12th examination.
NATA measures drawing and observation skills, sense of proportion, aesthetic sensitivity and critical thinking ability.

NATA is 3 hour test within which candidates have to answer 125 questions. There will be 1 mark, 2 marks and 3 marks questions. Candidates will have to answer 75 one mark questions, 25 two marks questions and 25 three marks questions. Total 200 questions and 200 marks examination. Duration of exam is for 3 hours. The entire question paper will be in English and  there is no negative marking. 

If a candidate willing to crack NATA, he/she have to know well about NATA entrance exam very well. It will help them to prepare for the examination. 

TIPS TO PREPARE FOR NATA

• All the questions that come in NATA entrance will come from 10-12th standard syllabus. NATA requires a basic knowledge of general aptitude, The drawing part will test your creative imagination along with your sense of perspective.  So you need to study well from class 10 if you have plan to sit fir NATA. 
• As PCM will come from 10-12th standard, you will very much aware about the chapters and subject very well. So you just need to revise those in last months. 
• Last month preparation in very crucial as you have to revise physics, chemistry, maths, general aptitude as well as drawing all together. So to avoid pressure you can start your preparation keeping another month in your hand. 
• to be honest, you don’t need any coaching classes for NATA preparation because it will test your aptitude, knowledge and creativity. 
• practice according to the previous your questions, it will help you to get idea about the question pattern. 

So, it wont take a long term to get prepare for NATA if you follow a good strategy for the entire syllabus and revise how many times you want, because practice will make it perfect!

Hope this helps! 
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See the application fees structure for NATA, 

http://https://designfresher.com/forum/question/what-is-the-fees-for-nata-application