: Indian working in US on H1B - Do I have to pay taxes on interest earned from Savings Bank Account in India I am an Indian citizen, currently living in US. I am on H1-B visa and employed in a company. I stay there pretty much

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Here is a helpful article that may answer your question about your tax liability for income earned in India.
www.hmalegal.com/2/post/2013/03/making-the-big-move-considering-the-tax-liability-of-moving-to-the-united-states-on-an-h-1b-visa.html.
How you are taxed all depends whether you are considered a resident or non-resident alien in the United States. The article explains how you know if you are one or the other. If you are considered a resident alien you will be subject to taxes like any US citizen would be...good luck!

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Scenario 1:

I have a savings bank account in India. It has Rupees One Lac (Rs.
100000). The interest it earns per year is Rupees Four Thousand (Rs.
4000).

Now, in India up to Rupees Two Lacs, it attracts no tax. So, the
aforementioned interest attracts a tax of Rupees Zero.

Question: Do I have to declare this interest in US as part of my tax
filing?

YES.

Scenario 2:

I earn (through various interests out of Savings Bank account or Fixed
Deposits) a total of Rupees Three Lac (Rs. 300000) per annum.

Now, in India I have to pay a tax of Rupees Ten Thousand (Rs. 10000).
This is calculated @ 10% of the amount above the base amount of Rupees
Two Lac. Now, do I have to declare the earning of Three Lac in US and
pay tax for the same as well? Also, is it OK (per Double Taxation
Avoidance Agreement) that I can deduct the amount of tax paid Rupees
Ten Thousand (Rs. 10,000) converted into US dollars while showing the
total income of Rupees Three Lac (Rs. 300000) earned in India?

You declare the whole income (including the part exempt from local taxes). You use form 1116 to calculate the portion of Indian taxes paid that you can credit (i.e.: deduct dollar to dollar from your tax liability) on your US tax return. US taxes interest at ordinary income rates, which is definitely higher than the 10% you paid in India, so you'll pay additional taxes (this is not double taxation, as your Indian taxes are credited to the liability calculated).

Scenario 3

If I have a land, which is worth Rupees Ten Lacs (Approx ,000 @
Rs.50/USD), do I have to file an FBAR? (Note: This land does not earn
any income).

No. FBAR is only for accounts. For 8938 might be relevant if you hold the land not in your personal name (through a trust/company/partnership etc). Additional forms might be required, talk to your tax adviser.

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As you are a Resident Alien, you will have to declare all your income and pay tax in US. Hence in both Scenario 1 and 2 you have to pay tax in US.

Edit: There is double tax avoidance treaty. Read the text at law.incometaxindia.gov.in/DIT/File_opener.aspx?fn=http://law.incometaxindia.gov.in/Directtaxlaws/cbdt/dta/A1_USA.htm
FBAR to my knowledge is for active accounts and not for Land / assets.