'To-infinitives' are always followed by a verb in base form, the use of 'to untying or cutting' is incorrect. 'Aim' is a verb but a sentence requires a noun as a subject so it will change to gerund as 'aiming'. Prepositions are always followed by a verb in -ing form. So, the use of 'untie' is incorrect.
So, 'several attempts to untie' shows a grammatically correct phrase and gives a meaningful sentence when used in the sentence.
Hence, option (b) is correct.
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. [as 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, as 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.
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