The correct option is
A study
In order to fill in the blank with the most suitable verb, we need to understand the usage of 'make'. 'Make' means to force someone to do something. If 'make' is used in a passive (voice) sentence, we use the word 'to' along with the verb. In an active sentence, we do not use 'to' with the verb. The verbs without the marker 'to', are called bare infinitives.NOTE: Here, 'makes' is used to describe the action in present tense. 'Makes' is the third person form of the verb.
As the given sentence is in active voice, we will use the bare infinitive here.
Option B - As the given sentence already has a verb in third person singular form, we need the secondary verb to be in its original form. 'Studies' is the third person form of the verb and that's why it can't be used here. Hence, option B is incorrect.
Option C - The marker 'to' is used with the verb when the sentence is in passive voice. As the given sentence is in active voice, we need the verb to in its original form without the marker 'to'. 'To study' can't be used here, since the verb is accompanied by the marker 'to'. Hence, option C is incorrect.
Option D - 'Studying' is the participle form of the verb 'study'. As we need the verb in its original form, we can't use 'studying' here. Hence, option D is incorrect.
Option A - 'Study' is a verb, and it is in the original form. Hence, we an use it as the sentence is in active voice. Thus option A is the correct option.
'My teacher makes me study for my exams.'