Auxiliaries and Modals (Simple Usage)

"Am" indicates use of present tense. But "last week" means past tense will be used. As "was" is used with "I" so "was" is correct answer.

"Could" is used to make polite requests especially which usually refer to the near future. Hence, "could" is the correct answer.

"Next summer" indicates future. Hence, "will" is correct answer.

"Are" is the correct answer.

"Might not" suggests that it is possible that he is not there. Hence, "might" is the correct answer.

"Jewels" refers to a plural so "are" is the correct answer.

As "moon" is singular so "is" is the correct answer.

It indicates continuous tense (1^st form of verb + ing) and one of them (child or mother) will go. So, clearly it's singular. Hence, the correct answer is "is".

As "today" indicates present tense and "parents" plural. Hence, "are" is the correct answer.

As it is continuous tense is/am/are/was/were will be used. But flock means one group. If we go through the options "was" is the correct option. 

"Is" is used with a singular. As "parents" is plural the correct answer is "are".

"Physics" is one subject and is singular. Hence, the correct option is "is".

Where two subjects are joined by the conjunction 'or', the verb will connect with the second subject. Here the second subject is the plural 'twins'.

"Can" means be able to. Hence, it is the correct answer.

"Must" is used to express necessity or strong recommendation. "Must not" can be used to prohibit actions. Hence, it is the correct answer.