BENGALURU, March 13 (Reuters) - India's Tata Motors has signed a deal to build a 90 billion rupee ($1.09 billion) manufacturing plant in Tamil Nadu, the southern state's industries minister said on Wednesday on social media platform X. ($1 = 82.8141 Indian rupees) (Reporting by Praveen Paramasivam in Bengaluru Editing by David Goodman )