I have been collecting US quarter dollar coins for different states and I have 4 sets of these coins. Can I take them along with me when travelling back to India. Can I take them in my carry on luggage or should I keep them in the check-in baggage. Please suggest.
There is no legal limit to the amount of money you can bring out of the US. However, you do need to fill out forms if you want to bring out more than $10,000. The value of your collection, assuming you have 4 complete sets (including the Denver and Philadelphia mints as @Karlson mentioned) is $100, well below the limit.
There is no limit on the amount of money that can be taken out of or brought into the United States. However, if a person or persons traveling together and filing a joint declaration (CBP Form 6059-B) have $10,000 or more in currency or negotiable monetary instruments, they must fill out a "Report of International Transportation of Currency and Monetary Instruments" FinCEN 105 (former CF 4790).
Considering this collection is probably more valuable to you personally than $100, I would recommend taking it as carry-on. It is a lot of weight, however, I imagine replacing the collection if your checked bag is lost would be very difficult.
There is no legal limit to the amount of money you can bring into India. However, you do need to fill out forms if you want to bring in more than $5,000 USD or more than $10,000 USD, depending on the composition of the money assets. Your $100 value collection falls well below this limit.
From Mumbai Airport Customs:
Any person can bring into India from any place outside India foreign exchange without any value limit. However, a declaration to the Customs authorities shall be made in the prescribed Currency Declaration Form (CDF) in the following cases:- (a) Where the aggregate value of foreign currency notes exceeds US$ 5000/- or equivalent; or
(b) Where the aggregate value of foreign exchange in the form of currency notes, bank notes or traveller’s cheques exceeds US$ 10,000/- or its equivalent.