'Sternly' modifies the verb 'rebuked'. We cannot kindly rebuke someone.

'Enquiringly' is the adverb that modifies the look, 'enquiring' and 'inquisitive' are the adjectives and 'enquiry' represents the noun.

'Depression' is a noun, 'depressive' and 'depressing' both act as adjective.

In options, there are only two adverbs; 'seductively' and 'seducingly'. 'Seducingly' is an incorrect formation. Hence, 'seductively' is the required answer.

'Enough' means as much as is necessary or sufficient. 

'Sure' and 'fast' are not adverbs. 'Inevitably' as an adverb agrees with the meaning of the sentence.

'Extremely' is an adverb that answers the question how hard she has worked. 'Extreme' is an adjective.

The adverb should describe how gulped the food. 'Greedy' is an adjective and 'hurry' can act as both a verb and noun. 'Hurriely' is an incorrect formation.

'Adequacy' and 'adequate' are the noun and adjective, respectively. 'Good' is also an adjective. 

'Surprising' and 'surprised' are the adjectives and 'surprisingly' is an adverb.

Only option 4 is an adverb.

'Fluently' answers the question how well does she speak. 'Fluent' and 'fluency' are the adjectives and noun, respectively. 'Good' is an adjective.

 'Victoriously' modifies the election, i.e how was he elected. 'Victorious' is the corresponding adjective and 'victory' is the noun. 

'Basic' and 'essential' are adjectives. 'Rather' is not the suitable adverb for this sentence.

 'Insanely' is an adverb and 'insanity' becomes the noun. 'Insane' is an adjective. Here unreasonable is an adjective. So, an adverb is needed to modify it.