HELLO VARSHA!

To get NITs and IITs to pursue master degree courses with core branches you need at least 40 score in gate. This figure may changed as cuttoff deprend upon level of paper and number of applicants.You can let it around 50 out of 100 under general category.You may get non core branch in NITs but also probability of getting nits with this score will be less.

You can ask if you have any other queries.

GOOD LUCK!