Question about noc

I am currently working at a State Govt. Primary school. I have applied for a Central Govt. Job and I will be going Document Verification after a month. Though there was no column for me to state that I am a govt. Employer at the time of form fillup, they are asking for a NOC if someone is a govt. employee. I have a few questions to that- 1. What if during the time of DV i don't mention my current job and hide this information? Is there any way that they can find out? 2. The reason I want to hide the same is because previously i wanted a NOC for my higher studies, and they refused to provide me that, so I am thinking they will do the same now too. Is that legal? 3. They ( my employer) told me that we can apply for NOC when I will apply for job, or any higher studies, and because I did not inform them during the application of my higher studies, they did not provide me a NOC. How much truth is in that? 4. If the above is true, then I can say in my present case scenario, that during the time of application for this Central Govt. Job, there was no option for me to state the same, so I did not inform, because I didn't know they would ask a NOC. So, what to do then? I am really looking forward to the answer to these questions. Thankyou.