The correct answer is: a) British trade and administration.
Colonial infrastructure projects like railways and roads were built primarily to serve the interests of the British Empire. They were used to transport goods and troops, and to facilitate the administration of the colonies. They also helped to open up new markets for British goods and to exploit the resources of the colonies.
Option b) is incorrect because local economic development was not a primary concern of the British. They were more interested in exploiting the resources of the colonies for their own benefit.
Option c) is incorrect because the welfare of Indian peasants was not a priority for the British. They were more interested in extracting wealth from the colonies than in improving the lives of the people who lived there.
Option d) is incorrect because cultural exchange was not a major goal of colonial infrastructure projects. The British were more interested in imposing their own culture on the colonies than in learning about or appreciating the cultures of the people who lived there.