You are asking to fulfill this requirement using crawl rule. But crawl rule is generic for the content source and it will effect all the content source which is not recommended(and also not possible) for excluding some result depending on item values. So I like to solve this using scope which is described below.
For excluding that, first of all you need to add new managed property for the column "Active".
For that go to search service application-> Managed Property-> New managed property. Give property name and map it to the field "Active". Also select the type of the field "Active". Tick the box for allow this property to be used in scopes.
Then go to corresponding scope-> new rule-> choose property query
then choose from "Add property restriction" corresponding managed property name(property name given by you during managed property creation) and "=" "No"(please use exact field value of the document library), then choose Exclude and click "ok".
Add this scope in the search page and run full crawl in the central admin.
I hope this will fulfill your requirement.