Cost basis for house received in gift

If I receive a house in Delhi as a gift from a parent,  what is my cost basis for computation of capital gains tax when I eventually sell it? 

My parents bought the house for Rs. X more than 3 years back.  The price using "circle rate" on date of gift to me  is Y. The expected price at future dae of sale in few years is Z

1. I am assuming I will have to register the gift and pay stamp duty. What is the rate of stamp duty in Delhi for gifts from parents? 
2. When I sell the house later in a few years, will I pay tax on Z minus X (indexed for inflation) or Z minus Y (indexed for inflation)
3. If the tax has to be paid on Z minus Y and If the market rate on date of gift is mugh higher than circle rate  Y, is it better or even possible to pay stamp duty now on the higher market rate amount so as to reduce the capital gains amount later.  (This will ofcourse be based on some mathematical modelling on future expected price)

Do any of the answers change if the house is received as an inheritance from a parent rather than as a gift during their life time ?