No you cannot give an  NIMCET examination after graduating in bachelor of arts. For being eligible for this entrance examination the candidate has to be graduate either from:

• Bachelor of Science
• Bachelor of Science Honours
• Bachelor of Technology or
• Bachelor of engineering

The candidate must have scored at least 60% marks in the aggregate.

For more: https://www.google.com/url?sa=t&source=web&rct=j&url=https://it.careers360.com/articles/nimcet-eligibility-criteria/amp&ved=2ahUKEwin9KvAscX0AhWVZd4KHSL2CdkQFnoECAQQAQ&usg=AOvVaw23_TVPbUEQi-YTF8_AyRTx&ampcf=1