I want to know whether category has forums or ideas in it

Pradnya - 

 Below query will work for both idea and forums.  If the count is more than 0, it means it has idea or forum inside it. 

SELECT count(*) FROM boards WHERE parent_category.id = 'categoryID'

Just to check only for ideas and forums 

SELECT count(*) FROM boards WHERE parent_category.id = 'categoryID'
SELECT count(*) FROM boards WHERE parent_category.id = 'categoryID' AND conversation_style = 'idea' or conversation_style = 'forum'

https://community.lithium.com/t5/Developer-Documentation/bd-p/dev-doc-portal?section=commv2&collection=boards#constraints-parent_category.id