The basic structure of the sentence:

Because of its effectiveness in bringing about good results

                                 Phrase                                                                +  this teaching method has been

Because it has some other advantages,                                         adopted by most……….. .

                                 Clause

The underline portion of question is modifier of the main sentence.

The modifier has two portion both starts from ‘Because of ….’. First portion of the modifier is phrase and second portion is clause.

Since, both portion of modifier is connected with coordinate, both will be either phrase or clause.

In that sense, choice-(D) maintains the parallelism of both modifiers.

                            its effectiveness in bringing about good results

Because of  +                         Phrase                                                           +  this teaching method          

                             some other advantages,                                                          has been….. 

                                                 Phrase

because exercise + builds stamina + decreases tension + absenteeism is reduced

                                                     Clause (Active)                 Clause (Active)                       Clause (Passive)

In the above underline, after the conjunction ‘because’ there exists three clauses two in active form and the last one in passive form.

The clauses are connected with coordinate. So, the clauses should be in same structure.

From that sense, option-(C) is appropriate in structure.

because exercise + builds stamina + decreases tension +  reduces absenteeism

                                                     Clause (Active)                 Clause (Active)                       Clause (Active)

The sentence in the question is compound and connected with coordinating conjunction ‘and’. So, both the clauses should be in similar structure. The first clause is in active form, but the last clause is in passive form. This is quite absurd, rather should be parallel.

The older girls had a birthday party to get us acquainted and it was deeply appreciated by me

                                 Clause (Active)                                                                                                 Clause (Passive)

In the above structure, both clause should be in either passive or active form, but passive form is quite verbose and unnecessary.

In that sense, option-(A) is appropriate to express the meaning with parallelism. 

I appreciated the birthday party which the older girls gave to get us acquainted.

                     Clause (Active)                                                                  Clause (Active)

Many economists in our country maintain  +  that  + 

                           Main clause

the current low inflation rate not only promotes investments in subsidiaries but also made it more profitable                                            Subordinate clause

The subordinate clause structurally used coordinating conjunction not only …………. but also. The clause next to not only is in present form but in next portion of but also past form has been used unnecessarily.

Choice-(A) makes the right form of tense in both portion (present form). In choice –(D) the word ‘enough’ has been replaced. So, Choice-(A) is the right answer.

not only + promotes investments in subsidiaries  + but also  +  made it more profitable

                             Present form                                                                                                        Past form

not only + promotes investments in subsidiaries  + but also  +  makes it more profitable

                             Present form                                                                                                        Present form

Seemingly, it seems the existence of conjunction ‘that’ makes the sentence complex, that means there are two clauses in the sentence. But in the sentence, there is no finite verb indeed! Actually ‘that’ confused us. As there is no main clause, the presence of subordinating clause is meaningless. Hence, we need to make the sentence correct with finite verb.

So, Choice-(D) is appropriate option to make sentence both meaningful and grammatically correct.

Because of his illness  + the singer has not  +  and  +   apparently will not sing +    within a week

Adverbial phrase                                     Clause-1                                                       Clause-2                       Adverb of clause-2

Apparently two clauses are connected with a coordinate ‘and’. The first clause has subject (the singer) and auxiliary verb (has) but no main verb. Without main verb, auxiliary verb can’t express the meaning. So, Choice-(D) is the right answer as it maintains the same sentence structure in the both of the clauses and other choices unnecessarily changes tense or basic meaning.

               the singer     +     has not    +    sung

                       Subject                       Aux. Verb            Main Verb

In the first part of the sentence there is no verb, it’s a phrase prepositional phrase as it starts with preposition. In the second portion, the verb is ‘was written’, but in the passive form and the verb has no subject.

Actually, this is not a complete sentence. The main part of the sentence has been unnecessarily turned into passive form.

So, Choice-(D) makes the sentence complete as there exists ‘Sub + Verb + Object’ basic structure.

Without expecting a reply   +   a letter    +   was written     +      to the police

            Prepositional phrase                        Subject                    verb                               Object         

                                                                                                    Passive form

Reading the sentence at a glance, it seems that the sentence is very much complicating, but its quite easy sentence in structure.

At first, we observe the main part of the underline sentence (many personal things were purchased by the secretary of the club). This clause has been changed into passive form unnecessarily.

In the clause ‘that had no legal authorization’, that is a relative pronoun of ‘personal things’. Now, the question is why it is so away from the antecedent. It should be immediate next to antecedent.

So, Choice-(C) stated the sentence properly in active form keeping the meaning unchanged. 

The original sentence has a parallelism error. In a list, all the verbs should be in the same form.

• The first three verbs (make, wash, do) are in the base form, but relaxing is in the -ing form, which is inconsistent.
• Option D correctly changes relaxing to relax, ensuring all verbs are in the base form for parallel structure.

The sentence compares hiring the best possible candidate with following rigid rules. To maintain correct grammatical structure, "than that such rigid rules be followed" (Option C) is the best choice because here “Error of Parallelism” occurs.

The clause after that is in Subject + be + V format. So, second clause should also follow the first clause.