.:function of central bank :.

The central bank has been described as "the lender of last resort", which means that it is responsible for providing its economy with funds when commercial banks cannot cover a supply shortage. In other words, the central bank prevents the country's banking system from failing.

However, the primary goal of central banks is to provide their countries' currencies with price stability by controlling inflation. A central bank also acts as the regulatory authority of a country's monetary policy and is the sole provider and printer of notes and coins in circulation. Time has proved that the central bank can best function in these capacities by remaining independent from government fiscal policy and therefore uninfluenced by the political concerns of any regime. The central bank should also be completely divested of any commercial banking interests. 

Central banks are responsible for overseeing the monetary system for a nation (or group of nations), along with a wide range of other responsibilities, from overseeing monetary policy to implementing specific goals such as currency stability, low inflation and full employment. The role of the central bank has grown in importance over time

The important functions of Central Banks are as follows:-

1-Sole right of note issue
The Central Bank in every country, now, has the monopoly note issue. The issue of notes is governed by certain regulation which is enforced by the state.

2-Banker to the state
A Central Bank acts as a banker to the government. It holds cash balances of the government free of interest.

3-Banker's bank.
The central bank acts as a banker to the commercial banks.

4-Banker's clearing house
The Central Bank acts as a clearing house for the settlement of mutual obligations of different commercial banks. If a difference exists, it is paid by a cheque drawn on the banks accounts carried at the Central Bank.

5-Lendor to the last resort
The Central Bank helps the member banks in times of crisis.

6-Financial agent
The Central Banks act as financial agents for the government. It is an agent for the government in purchasing and selling of gold and foreign exchange.

7-Effective monetary policy
The aim of the government is to create employment in the country, resist undue inflation and achieve a favorable balance of payment.

8-External functions
The Central Bank also performs a number of external functions.

ref: investopedia & blurtit