I believe you got what you were looking for but just my two cents:
Salary negotiation is an art. If you search on the Net you will find enough articles. In short however, I would recommend NOT doing the following:
" If I have offer letter in my hand for 3, 00000 lakhs. Is it advisable? To show the offer letter to HR and demand for hike in salary according to that offer letter."
I would never do that. Firstly, talk to your immediate supervisor/manager. HR generally has no say in salary issues. When you ask for a raise, ask for the amount instead of the percentage hike. It may be the same thing but it has to be put in a polite manner.
If you want to convey to your manager that you might look elsewhere or have another offers in hand put it diplomatically by saying that the market is hot, I know my value, ... etc. That is enough of a hint. If you go around demanding and even if they give in, they will always remember that you hijacked them into giving you a pay raise. A colleague of mine did the same thing in my company by demanding a pay raise from his manager. Now the next time he does this he will never get a proper raise. Also, since the senior management knows this, if it is time to downsize he is going to be the first in the firing line.
Also, it is a misconception that raises can be given only during appraisals. This is not true. Actually what you are asking is not a raise - which is generally only 15-20% average in India. You are asking for a salary ADJUSTMENT to the current market level. This comes from a different pot of money. There is no need to wait for your appraisal. You may ask anytime. A good time would be to ask for an adjustment when your supervisor is
a: in a good mood,
b: a project you were involved in has gone particularly well,
c: after lunch.
Research has shown:
1: Avoid asking for a raise on Monday's and Friday's.
So good luck and don't give up if they say 'No' the first time. Persist. Persist. Persist. It may take months. I speak from personal experience. And in the end if they really do NOT give you the raise you are looking for then obviously they do not value you as an employee and it is time to look elsewhere.