Electrical Engineering

You can get a number of government job opportunities in both the branches. Like for ECE-BSNL (TTA & JTO), DMRC, IOCL, Indian Space Research Organisation. Jobs in Railways: Bharat Heavy Electronics Limited, Steel Authority of India Limited, Gas Limited, National Thermal Power Corporation, Electronics Corporation of India Limited, BARC (Bhabha Atomic Research Center), UPSC (Union Public Service Commission), Indian Navy, and DRDO (Defence Research and Development Organisation).
Bank Probationary Officer
Indian Engineering Services.
There are a lot of jobs for EE:
National Thermal Power Corporation (SSC-JE)
DRDO Defence Research and Development Organisation
Bank Probationary Officer
Indian Engineering Services
DMRC
Bharat Heavy Electronics Limited.
Best of luck.

Well even with 27K rank, it is certainly possible that you'll just make it into some of the NITs. If you apply for home state quote, I guess you'll certainly qualify for some branches that are less in demand such as textile, food processing, integrated M.Sc material science and metallurgy, etc. However, if you really want to bag that NIT tag with a good branch, you'll have to rely on the northeastern and new NITs like Silchar, Meghalaya, Agartala, Sikkim, etc. As their general cut-offs are also way too low. So, it's your decision to go for some better NIT with your home state quota or you can opt for North Eastern NITs or even other government institutions with your desired seat.