For a deep out-of-the-money option:

A deep out of the money option will not react much to the change in the price of the underlying. In fact, the more out of the money it is, the more unresponsive it will be to changes in the prices of the underlying. Therefore, its delta will approach zero. Since delta is zero, gamma, which measures the rate of change in the delta, will also be zero as delta is unchanging. Therefore Choice 'a' is the correct answer.