The correct answer is: Only conclusion II follows.
The statement only tells us that Nation X faced growing international opposition for its decision to explode eight nuclear weapons at its test site. It does not tell us anything about the citizens of Nation X or about the motivations of the other nations that opposed the decision. Therefore, we cannot conclude that the citizens of Nation X favoured the decision or that some powerful countries do not want other nations to become as powerful as they are.
Conclusion I is not supported by the statement because the statement does not tell us anything about the citizens of Nation X. It is possible that the citizens of Nation X did not favour the decision, but the statement does not provide any evidence to support this conclusion.
Conclusion II is supported by the statement because the statement tells us that Nation X faced growing international opposition for its decision. This suggests that some powerful countries did not want Nation X to become more powerful. However, the statement does not tell us why these countries opposed the decision, so we cannot conclude that they were motivated by a desire to prevent Nation X from becoming as powerful as they are.
Therefore, the only conclusion that can be drawn from the statement is conclusion II.