The correct answers are:
A. They allowed the Agricultural Revolution to take off. - The development of railways facilitated the movement of agricultural produce from rural areas to urban markets, supporting the Agricultural Revolution and enabling agricultural surplus.
C. The British government encouraged competition to maximize growth. - The British government supported the expansion of railways, often through acts of parliament and investments, which encouraged competition among railway companies and led to rapid growth in the railway network.
Thus, options A and C are the reasons for the rapid growth of railways in Britain during the Industrial Revolution.