Well with all of the factors considered, I do not think that the cut-off for Electronics and communication engineering will reach a rank of about 57000 even in the second special round. Last year it was about 40000 for female home state candidates. 

We also have to consider the fact that the cut-off for NIT Patna is increasing slowly because of the upgradations made in the infrastructre and curriculum. However, Mechanical Engineering may come close to your rank so you can opt for it.