Question

collect few samples of the modern forms of money and role of banking in india economy

Answer 1

What is money?

Money is not the paper bill one carries in wallet!
Rather it is the measure of value of particular goods and services. 
Remember the measure of value is  the key term here.

Before the so called present form of money, there was a barter system in which people exchanged goods as a means of exchange of value.

Then there was metallic money with gold and silver the major metals. Coins were forged of them.   Previously, coins produced using valuable metals like gold and silver were viewed as standard coins and the monetary system issuing them were alluded to as "gold and silver standards".

With the banking system came the system of MoUs. (Memorandum of Understanding)  These MoUs were equivalent to paper bills, They signified the cash available in a central bank . So these paper bills are the paper moneywhich  is the modern form of money we see every day. It is issued by Central Bank. For India, it is interesting to note that 'one rupee' notes are issued by Ministry of Finance whereas other notes are issued by Central Bank. 

Some other forms of Modern Money are Plastic Money (Credit or Debit Cards)
Credit cards serves as a means of credit money which means the credit holder might not have the actual money but just the credit for the money. It is also a modern form of money

The most recent modern form of money is decentralised electronic money in the form of bitcoins and litecoins. It is the currency by the people itself. Central Bank wants to regulate them

Role of Banking in Indian Economy

Banks help in circulating the flow of money, 
With instruments like CRR(Cash Reserve Ratio), CAR ( Cash Adequacy Ratio) Banks regulate the flow of credit. If credit is cheaply available (CRR and CAR ratio are low ), it means more money is available in economy easily

Banks play a role in Capital Formation
There is a difference between hoarding and saving. If incentives are provided for saving money into bank and not hoarding, it can create more capital that can be utilized for various fruitful purpose.