Synonyms

Undermine means to weaken, damage, or erode something gradually, often from underneath or in a subtle way. Weaken is the correct synonym. Observe means to watch, maintain and sustain mean to support - opposite meanings.

Uncanny means strange or mysterious, often in an unsettling or eerie way. Strange is the correct synonym. Clean, new, and original don't capture the mysterious/eerie quality that uncanny implies.

Unwitting means unintentional, accidental, or done without awareness. Accidental is the correct synonym - both describe something done by chance or without conscious intent. Brave, cheerful, and attractive are positive traits unrelated to unintentionality.

Unfeigned means genuine, sincere, not fake or pretentious. Real is the correct synonym - both words describe authenticity and lack of artificiality. Artificial is the opposite, intelligent is unrelated, covered means concealed.

Unobtrusive means not noticeable or blatant, quiet and understated in manner. Quiet is the correct synonym - both describe something that doesn't draw attention. Confident and daring are bold traits, prominent means noticeable - all opposite meanings.

Dearth means a scarcity or lack of something, particularly referring to an inadequate supply or shortage. The word is often used in contexts like 'dearth of resources' or 'dearth of evidence'. 'Scarcity' is the closest synonym, while distress relates to suffering, agreement to harmony, and honesty to truthfulness.

Decorous means characterized by propriety, good taste, and dignified conduct. It describes behavior that is socially acceptable, proper, and polite. 'Proper' is the closest synonym. Vigorous means strong and energetic, strong is similar to vigorous, and vigilant means watchful or alert.

Dichotomy means division into two parts, kinds, etc.

Deprecate means to express disapproval of something, or to belittle and disparage it. While it can mean 'to regret' in formal contexts, in the sense of 'to depreciate,' 'belittle' is the closest match. Encourage, motivate, and appreciate are all antonyms representing positive actions or attitudes.

'Jargon' means 'special words or expressions used by a profession or group'. 'Slang' means 'a type of language consisting of words and phrases restricted to a particular group of people'.

Thus, synonym of 'jargon' is 'slang'. 

'Inexorable' means 'impossible to change or alter'. 'Unyielding' means 'incapable of being changed'.

'Impugn' means 'to challenge as false'. Thus, its synonym is 'to dispute'.

'Hypothesis' means 'a tentative explanation for an observation'. 'Assumption' means 'a proposition that is accepted as true'. Hence, synonym of 'hypothesis' is 'assumption'.

Correct answer is option 1.

Haggard means appearing exhausted, worn out, or gaunt, typically from fatigue, suffering, or hardship. It describes a tired and drawn appearance. 'Tired' is the correct answer. Agile and energetic are antonyms meaning quick and active, while fresh means rejuvenated or new.