The highlighted part of the sentence is incorrect. 'Let' only takes the objective pronoun after it. So, we cannot use the subjective pronouns 'she' and 'I'. Option (a) is also incorrect according to this rule. Also, 'let' is followed by a bare infinitive (infinitive without 'to'). As per this, options (b) and (c) are also incorrect.
Among the given options, the phrase in option (e) is the correct choice.
Hence, option (e) is the correct answer.
Note:
Objective Pronouns: The pronouns me, you, us, him, her, it, and them are called objective pronouns because they act as the objects of verbs and prepositions: Anjali drove us home.
Subjective Pronouns: The pronouns I, you, we, he, she, it, and they are known as subjective pronouns because they act as the subjects of verbs: We went to the party.
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.