In 1975, my father (Indian) bought a house in India for USD.15k. In 2006, I inherited the same house. It was through family settlement and so I paid about USD.250K to my siblings. At that time my share in the property was about USD.250 so the property was worth USD.500k. Today, if I sell the property, I may get about USD.1M. How will IRS assess capital gains and what will be their estimated figure? Will the base Fair Market Value be USD.500k (the value when I inherited the property) or USD.15K (the value when the property was originally bought by my father)?

You get a step up in basis to the time you inherited the property.

However. You should have filed Form 3520 when you inherited the property. If you did not, matters become more complicated.

Also, all transactions have to be denominated in $ using the exchange rate at the time of the transaction, not today's exchange rate. This is irrespective of whether you actually converted the sum into $.