Hi mounikhetan,
If you're looking for topics, it's probably a good idea to start by really solidifying the difference between the two types of essays. I hadn't thought of the difference in quite some time so I looked it up myself to be sure. There is a nice ehow post that breaks it down pretty succinctly:
The Difference Between Discursive & Argumentative Essays | eHow.com
The main difference is that in an argumentative essay you make a strong, persuasive case for one side of a debate. In a discursive essay, you provide a more balanced approach (usually you would still slightly favor one side or make a conclusion but it is a more objective, balanced discussion).
Here is one idea for a topic: Dogs are better than cats.
In the argumentative essay you might start your intro with a few reasons why dogs are better than cats, then provide a paragraph each to expand on those few points, and then conclude. You still don't want to be biased, but you would be making a strong argument here.
In a discursive essay, you might highlight a few benefits and downsides to both dogs and cats. You might also highlight that it depends on personal preference (for some people, a dog who likes affection is a good thing, but maybe for others they want a cat, who might or might not be a bit more independent). I'm just throwing a few ideas off the top of my head here for an example of course.
If you want something a bit more serious, pick a current political or economic issue from your country. Maybe a bill that is about to be passed. Or maybe a famous person made a comment on TV recently that received a lot of reaction, both for and against. You can really pick just about anything that people might argue about.
Hope that helps and good luck.