That's quite a question you've got there!
Okay, here we go, in relation to India:
OLIGOPOLY: A situation where there are only a few sellers in a particular economy who control a particular commodity. They can, therefore, influence prices and affect the competition. In India, an example of this would be mobile telephony - There are only a few operators, examples of which are: Airtel, Idea, BSNL, Reliance
PERFECT COMPETITION: This is an economic situation that really doesn't exist, in which a bunch of conditions are met, not the least of which are free entry and exit from a market, tons of sellers selling the exact same product, and tons of buyers for that product who have perfect knowledge of what it does and how it works. An Indian fish market might be an example of something close to this (though real "perfect competition" doesn't really exist.) At the fist market, lots of sellers gather together to try to sell the same wares, and lots of customers try to buy them with a good knowledge of what they are buying. There is little to prevent someone from joining in on the selling or quitting the market altogether.
DUOPOLY: A market in which two giant brands control most of the product being sold and therefore have a great amount of influence over the factors involved in the selling. This is the one I can't give you a great example of in relation to India...I just can't think of one that is specifically "Indian." Some examples would be Visa & Mastercard and Reuters & Associated Press and International news agencies.
MONOPOLY: A market dominated by one seller. The cable company is an example of this in India (sort of like it is in America.) The cable company in India, facing no competition, is notorious for poor quality and poor service.
MONOPOLISTIC COMPETITION: Here, there are lots of sellers selling similar products that don't differ a whole lot in terms of characteristics or price. Think breakfast cereals. In India, an example of this is the banking system. After financial sector reforms in 1992, the banking system in India has become much more competitive with lots more banks offering similar products at similar prices.
I hope that these examples help you in your research or class!