Is it possible to get the sql queries that are used to create the Control Chart, Burndown Chart and Cumulative Flow Diagram
No, because there isn't any.
The reports use the internal API to get some data, and calculate the rest. The API mostly uses the index to get what it needs. So there's very little, if any, SQL being run when you select a report.
What are you trying to do? Why do you want the SQL?
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