Go for either one, or both. They are both good languages and there are plenty of tutorials available with a simple Google search. The Java forum here has a "Getting Started" thread stickied at the top. I didn't see one in the C# forum, but searching and asking questions should provide more than enough information to immerse yourself in.
>What next should I go for c# or java?
Conceptually they're both largely the same. I'd recommend learning a completely different language from what you're used to, like Haskell or one of the Lisps. You'll get more out of it than learning yet another C derivative.
I am new to this coding world. Recently I have started with Turbo C/C++. What next should I go for c# or java? Are their any online tutorials available through which I can start by myself?
As you are doing C/C++, you should go for C# because your basics will be revised while learning. Moreover C# is faster to develop in (especially GUI design), has a better IDE then any of the various Java IDEs out there, can perform lower level operations (fixed statements and unsafe code). For online tutorials you can try these sites http://edufire.com http://www.programmingtutorials.com/
Both these links suck horribly. On the former, you can't find anything, and it holds no promise of having anything any good for C#, and the latter is just a site that links to other sites' tutorials, without any discrimination as to the other sites' quality.
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