English

The sentence requires the past perfect tense to indicate an action completed before another past action. 'Had worked' correctly expresses this sequence, making option B the right choice.

The correct preposition to use with 'ability' when referring to a subject like Mathematics is 'in'. The phrase 'ability in Mathematics' is the standard and idiomatic usage in English to indicate proficiency or skill in a subject. While 'good at Mathematics' is common for describing skill, the noun 'ability' is conventionally paired with 'in' rather than 'at'. Options 'for' and 'about' are incorrect in this context.

The correct possessive form to complete the sentence is 'my mother's' because it indicates that Fatima is a friend belonging to or associated with 'my mother'. Option B ('my mother') is incorrect because it lacks the possessive form needed here.

The phrase 'showed no signs of improvement' is the correct and idiomatic expression to describe the situation. 'Displayed' and 'exposed' are less commonly used in this context, and 'view' is a noun, not a verb, so it is incorrect here.

The term 'speed limit' refers to the maximum legal speed allowed on a road. Among the options, 'maximum' correctly fits the blank as it means the greatest amount or highest limit.

The preposition 'since' is used to indicate the starting point of an action or event that continues up to the present, which fits the context of supporting her family from the time of her husband's death.

The word 'elastic' means able to stretch and return to original shape. Its antonym is 'rigid,' which means stiff and not flexible. The other options describe qualities similar to elasticity or flexibility, so 'rigid' is the correct opposite.

The correct preposition to complete the phrase is 'for' as in 'Macbeth's desire for power,' which correctly expresses the object of his desire. The other options do not fit grammatically or semantically in this context.

The word 'brisk' means quick and energetic, which appropriately describes a walk taken just before dinner. The other options do not fit as well: 'vibrant' and 'vivacious' describe lively qualities but are not typically used to describe a walk, and 'slow' is the opposite of what is implied.

The correct preposition to use with 'burst' in this context is 'into,' as the phrase 'burst into tears' is an idiomatic expression meaning to suddenly start crying.