Yes, two-year droppers can apply for NSIT/DTU. NSIT and DTU take admission through JEE Mains. JEE doesn’t have any age restrictions or rules regarding drop years.
Students can attempt JEE six times, over the period of 3 years after their 12th. So, you will find students in NSIT and DTU, who took 2 drop years for their JEE preparation.
Admission applications to NSIT/DTU are submitted by the students under the Joint Admission Counselling process. This procedure is conducted by IIIT Delhi, IGDTUW, NSIT (now NSUT), and DTU for admission to these prestigious tier-1 colleges. The examination that is conducted for considering admission applications is the Joint Entrance Examination (Main). More than 12 lakh students register for this examination. And the eligibility criteria of this exam deny any kind of limitation on the age of the candidate. So, a two year age lag is certainly not a limitation on any candidate’s eligibility. There are almost two thousand students studying in one batch at these colleges and almost all kinds of students take admission. So, adjusting in the college environment will not be a difficulty for any 2-year dropper.