HI,,

GETTING INTO IITS FOR STRUCTURE ENGINERRING YOU MAY APPOX REQUIRED ABOVE 680- 750 SCORE

BUT YOU CAN TRY IN IIT Kanpur,IIT Roorkee AS cutoff in this comparatively low around 570-650

AND Yes you can apply to NITS But not top ones as for top nit like nit warangal its required around 700 score for general cat in structure branch

for more details check the link

https://engineering.careers360.com/articles/gate-cutoff-for-nits

https://collegedunia.com/exams/gate/cutoff