On our strict definition of narrow money, M₁, money does not earn interest. Therefore by holding money as opposed to a close substitute such as a savings account, you are giving up the interest you could have earned. That interest is measured by the nominal interest rate, i.e. the interest rate in money terms. The real interest rate is the interest rate on a loan of fixed purchasing power. If inflation is x% a year, something that cost $100 will cost $(100 + x) after a year; so if the real interest rate is r%, after a year you will have to pay back $(100 + x)(100 + r)/100, which is very close to $(100 + x + r) [to be precise, it is (100 + x + r + xr/100); if x and r are both reasonably small, we can ignore xr/100]. So in money terms, the interest rate is (x + r) -- the nominal interest rate is the real interest rate plus the inflation rate.

If the inflation rate increases, the velocity of money will also increase -- inflation and velocity tend to move together, so a is the right answer. If the inflation rate increases, the money in your pocket is becoming worth less in terms of real goods at a faster rate; therefore you will want to hold money for less time, hold less money, than before. That means money is going to circulate faster, the velocity of money will increase.