Can an application for TAN be made on a plain paper?

No. TAN Application can be made only on Form 49B. The application form can be downloaded from the website of the Income Tax Department (www.incometaxindia.gov.in)or NSDL (http://tin.nsdl.com ) or printed by local printers or obtained from any other source. The application is also available at TIN Facilitation Centres.