You need to set Clipboard Handling in the preferences. You can do that in the interface (Edit > Preferences > Clipboard Handling), and you can probably set it in your script, too.
I tried to do it manually. I set the clipboard handling paste to All information, but it wont work .I dont have idea how to set Clipboard Handling in the preferences through scripting.. Can you please tell me how to do it through scripting.
I don't know. You can find that in Jongware's object-model reference. It's in many posts in this forum, and Google will certainly find it.
@Ranjan – instead of "cut" and "paste" you could use the move() method of the texts object of your source text frame or your selection, if text ist selected.
See my snippet with annotations:
//In InDesign CS5.5 you can use the click order in the UI to determine //what selected object is  and  etc. //if you select two objects,  is the first one,  the second one. //So to move formatted text from the left to the right text frame //first click on the left text frame, hold shift and click on the right one //before executing this code: var sel = app.selection; sel.texts.move(LocationOptions.AFTER,sel.insertionPoints);
More generally spoken:
You could also move selected text to another insertionPoint: