As per the eligibility criteria of NIOS for taking admission in class 12th you need to have a class 10th degree now there are two ways,
First, you take admission in the same year in which you passed your 12th then you need to study both 11 and 12th.
Second, if you don't want to study 11th class separately then you can take admission in class 12th but now the duration of the course is 2 years.
Now as you have already taken a three year gap you cab directly sit for the class 12th examination.
Hope it helps.
Thank you.

Hello Siddhartha, 

Yes, you can definitely do so. NIOS board only conducts a class 12 exam. They do not have any examination for class 11. For being eligible to take the class 12 NIOS board exam you need to have a class 10 pass certificate and need to be at least 15 years of age.  Since you meet the required criteria, you can sit for the examination. 

Hope this helps  :)