Q. Supply of money remaining the same when there is an increase in demand for money, there will be

Answer: (b) an increase in the rate of interest

Inflation occurs when the aggregate quantity of goods demanded at any particular price level is rising more quickly than the aggregate quantity of goods supplied at that price level.
If the money supply grows faster than overall economic growth, inflation will occur. If the difference between the money supply growth and the growth of the economy becomes too wide, hyperinflation occurs.
Central banks use interest rates to control demand and inflation. If inflation is high, they raise their target for short-term interest rates. Higher interest rates make borrowing costs less attractive for firms and consumers, which leads to less demand for goods and investment.
Since inflation is caused by demand outstripping supply, lowering demand to bring it in line with supply relieves the pressures that were raising prices.

There are several situations that occur where increases in the money supply do not cause inflation.

Economic growth may match money supply growth. If the level of economic growth is equal to the level of money supply growth, prices traditionally remain stable.
There are variations in the velocity of money circulating. In a recession, the Fed may choose to increase the money supply; however, the spending patterns of consumers will vary during this period—including periods of decreased spending due to higher unemployment and less disposable income.
The economy has spare room to grow. During a recession, an economy is not operating at full capacity. Though an increase in the money supply provides additional resources, there may be minimal to no demand for additional capital as the economy grapples with stunted economic growth.