i got 13 marks in gate-2012 ece. can i get an admission through gate score?

The score should help you. Many colleges check to see your problem solving skills and general intelligence levels along with your test scores so you could always get yourself a good institute. As per my knowledge, JRE Institute of Management (in Noida) is a place worth the try if you're looking for

Your gate score card will show whether the score is valid or not

if u have recieved a score card,that mean ur score is valid,hence u can apply for admission in institutes according to ur percentile