India maintains a de facto floating peg to the US dollar. They run fairly high trade deficits driven by their fast growth. Because of this, the Reserve Bank of India has needed to devalue the currency several times over the last five years. The first event occuring in mid 2011, the second in mid 2013. So
So yes, it's true that the Rupee is fairly stable against the dollar, but this is because of foreign exchange manipulation by the Indian central bank. Alongside this, it is important to keep in mind that they cannot maintain their control over the exchange rate and have free flow of capital and monetary authority, so this peg will inevitably break down. If
If you take a look at the IRB balance sheet you'll probably see a falling foreign exchange reserves balance, and judging by the time between the last two events the Rupee probably won't stay stable for long.