Madhu, 

The course of genetic engineering is offered by

• Indian Institute of Technology, Kharagpur.
• Indian Institute of Science, (IISc), Bangalore.
• Indian Institute of Technology, Madras.
• Indian Institute of Technology, Delhi.
• All India Institute of Medical Sciences, New Delhi.
• Indian Institute of Science, Bangalore.

Sorry to say madhu you won't get any branch in NIT TRICH UNDER HOME STATE QUOTA. 

Even Production engineering closes at 28000 rank.  And your rank will be around 40000.

So you won't get anything in NIT TRICHY.