"I think mountaineering is ... dangerous activity."
Only one activity is mentioned in your sentence. In this context, the blank could be used for (1) an article (e.g. a, an, the) to provide more specificity to your noun (i.e. activity): "I think mountaineering is a dangerous activity." OR (2) a superlative adjective (e.g. the most xxx) since we are comparing a quality or characteristic (i.e. the degree of danger) among more than two things.
Since "a" is not found among the four options, we have to assume that a superlative adjective is an appropriate answer.
Just as a side discussion, in your sentence, although no other outdoor activities are listed, it is understood that mountaineering is compared with all other outdoor activities in the world. Hence, from this perspective, a superlative adjective is still needed.
Answer: I think mountaineering is the most dangerous activity.
Another example: Russia is the biggest country in the world. (Here, it is understood that the land area of Russia is compared with every other country in the world. This is a comparison of more than two countries; hence, a superlative adjective is needed.)
I hope this helps you.