A main verb in base form is required after the infinitive marker 'to' so 'perform' is the correct word. Hence, option (c) is correct. All the other options cannot fit in the blank.
NOTE:
Infinitive: The infinitive is the base form of a verb, often preceded by to.
Consider the sentences given below:
· To err is human. [like a noun, the infinitive 'to err' is the subject of the verb 'is']
· My father likes to cook. [like a noun, the infinitive 'to cook' is the object of the verb 'likes']
· To vote in elections is our right. [the infinitive 'to vote', like a noun, is the subject of the verb 'is', but, like a verb, it also takes an object (elections)]
· Radha went to the lake to fetch water. [the infinitive 'to fetch', like a noun, is the object of the verb 'went', but, like a verb, it also takes an object (water)]
· The above sentences illustrate various ways in which infinitives are used. It can both act as a noun and a verb.