The correct option is A Gerund
A gerund is a form of a verb ending in '-ing', it functions as a noun as it becomes the subject of a verb. In the given sentence, "mountain climbing" is the subject as it performs the action of 'to be', "is", against the object in the sentence, "a sport". It functions as a noun as it refers to the name of a sport, hence it's a gerund, and option A is correct. Gerunds and participles have the same form, they're verbs that end with an '-ing', but a participle modifies a noun the same way an adjective does, for example, in 'Hearing the noise, the lady woke up.' 'hearing' is a participle, as it functions as a verb 'to hear' as well as an adjective, modifying the noun 'lady'. Here, the phrase "mountain climbing" does not function as an adjective, but a noun, hence option B is incorrect. Option C isn't correct because 'mountain climbing' is not a present participle, and D isn't correct because it's a gerund.