English Language

The word 'coerce' means to compel or force someone to do something. Among the options, 'Compel' is the synonym that best matches 'coerce'. 'Entice' and 'Coax' imply persuasion by attraction or gentle urging, which is different from coercion.

Option B is grammatically correct and fits the sentence structure properly: 'Our father advised us not to be sad as he thought that his decision would bring betterment in the long run.' The phrase 'not to be sad' correctly follows the verb 'advised' in reported speech.

The sentence is a third conditional, which refers to a hypothetical past situation and its possible past result. The correct form is 'If they had bought new batteries, their torch would have worked better.' Option C uses the past perfect tense 'had bought,' which is appropriate here.

The correct preposition to use with 'impression' in this context is 'under.' The phrase 'under the impression' means to believe something that is not true, which fits the sentence perfectly.

The word 'adamant' means refusing to be persuaded or to change one's mind, which is synonymous with 'obstinate'. The other options do not convey the same meaning.

In this sentence, 'The woman I spoke to' is correct because the relative pronoun 'who' or 'whom' can be omitted when it functions as the object of the verb in the relative clause. Option C is the most natural and grammatically correct choice.

The verb 'admire' is typically followed by a noun or a gerund phrase to indicate what is being admired. In the sentence, 'He admired having seen the musical show...' the gerund phrase 'having seen' correctly functions as the object of 'admired.' Using the infinitive 'to see' or the passive form 'being seen' is not grammatically appropriate here. Therefore, option A is correct.

The word 'deferential' means showing respect or courteous regard. None of the options 'Volatile' (unstable), 'Fraught' (full of), or 'Quick' (fast) are synonyms of 'deferential'. Therefore, 'None of these' is the correct answer.