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I hope it doesn't count as misrepresentation as I honestly thought my job was not qualifying as it wasn't based on LMIA, but it is on a closed work permit which was based on PNP nomination.

No, it is not misrepresentation...
 
Date MD Sabab Alam first became qualified to practice in this occupation

If the "primary occupation" is:
  • a qualified trade (four-digit code begins with 632, 633, 72, 73, 82, 92), this is the date they became qualified to practice on their own in Canada. (For example, when they moved from apprentice to being a licensed tradesperson.)
  • any other job, this is the date they first obtained the minimum education or training stated in the NOC description. (Note: if the NOC only states high school, this is the date they graduated.
What about this? Should I mention the date I started? It doesn't ask which day though, only Month and year.

The date you completed your education.