The Indian Rupee (INR) seems fairly stable against the USD (1 USD = 62-64 INR) in the recent times even though most other currencies have weakened against USD, some by 20-30%. Apparently, INR is responsive to most other currencies these days except the USA. Is it related to the strength of the Indian economy, or that INR has already fallen to its lowest point well before other currencies?
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 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 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.
That is because India maintains strong economic relations with the United States. In addition, India might be looking at maintaining a fixed currency with the US. In exchange, India would have to give up Monetary Autonomy, or Free Flow of Capital.
As far as I know, India does not restrict the flow of capital to and from the country, so I assume that most policies are more government related when it comes to the US (although the new bilateral agreement is to work to reduce that). Overall, India's strong economic relations with the United States and a tied trade allows them to maintain growth.
In fact, recently with numerous trade agreements, I wouldn't say India has reached it's lowest point (that would be a few years ago), but is rather trying to secure a very high peak for the next 5-10 years.
In economic theory, the primary determinants of exchange rates are the supply and demand of tradable goods and services (of course, these include capital as well). According to textbook economics, the exchange rate is determined by the intersection of these supply and demand curves.
The fact that the US-India exchange rate has remained relatively stable implies that not much has changed in the fundamentals that determine this supply and demand, i.e. these curves have not shifted.
To answer your question, you would have to look at what goods and services constitute trade between US and India and if there have been any recent changes in policy/production concerning those goods.