What connection can you make between Darwin and nationalism, imperialism, and war?
The connection you can make here is that Darwin's ideas of natural selection were taken by people studying society and applied to human societies. According to "Social Darwinism," the fittest survive in human society as well.
This helped intensify feelings of nationalism. People in various countries felt they were the fittest. They wanted to prove this through imperialism and through war. They felt that their "fitness" entitled them to rule the human world and they wanted to prove that through war.
Many such people also thought war was good for a country. They felt that engaging in war would make their country stronger. It would do so in a way similar to the way exercise helps an individual. By going to war, the country would be become more "fit."