What all languages are supported for iOS application. Is it only objective-C?
Thanks
All UIs must use UIKit, which is an Objective-C API. Back-end code can be written in C or C++ (Objective-C++ as well).
There are frameworks which provide a wrapper on top of UIKit, such as MonoTouch, which allows you to use C# to develop iOS applications. There are other solutions such as Titanium, or embedding a Lua runtime in your application.
You can also implement all of your drawing as OpenGL and use plain C or C++, with a thin Objective-C wrapper to receive touches, load system resources (files, etc) and generate the GL context.
extern "C" support for ObjC - just make a normal C API (not an Objective-C API) and everything will work (provided your header uses plain C). Note that you can even have an Objective-C object cast back and forth from void* and id to make an opaque handle.There are other solutions, e.g. Monotouch, but Objective-C is what Apple does, what most people use, and what I would recommend.
It is possible to write an iOS app solely in C++ using a third-party framework like nui.
But I've found Objective-C and Objective-C++ to be the most productive and straightforward languages to use for iOS.
You may find various libraries that allow you to code in languages other than Obj-C. I have myself used phonegap and spiked out titanium (both allow coding in javascript). But ultimately, there is nothing better than the language supported by Apple themselves, since it gives you much flexibility and independence (from third party libraries) for coding. We (me and my team) had to abandon the phonegap and titanium code in favor of Obj-C (though that may be because of some particular needs or our project).