My duke generates an odd noise and when I looked under my seat what I saw was an open air filter box because of the broken screws. When I took my bike to the service center what they told was to replace the air box completely which costs 3k. Is it okay that I fix this by applying some glue temporarily ? or how should i solve it?
Provided it is not a stressed or load bearing member...
You should be ok glueing or plastic welding it however you like. As long as it is securely attached to the bike. You can probably drill holes in it and use cable ties to hold it in place. Beyond that its really about what it looks like and how much it bothers you.
However the important part is to ensure that the filter element seals properly with the engine intake so that all air drawn into the engine is filtered. If it isnt then dust and other fine material will be sucked into your engine which will increase wear and reduce the life of your engine.