Verbal Analogies

 A lack of imperiousness shows a fawnish attitude, a lack of directness leads to equivocate.

 Die is a tool used for shaping. Similarly drill is used for boring. 

 Punditsare persons who are learned, or who are or act authoritative.Partisans are people who support a particular person or cause and are therefore characterized by allegiance.

 A mercenery is used as an adjective, someone who kills for money, i.e someone who desires money. Similarly a person who is vindicitive seeks revenge.

 Troubled and distraught are synonyms, like tranquil and placid.

 A stationary structural element that is designed to support an airplane'swingis called astrut.A buttressis a stationary structure whose primary purpose is to support awall.  

 The relationship is that of a unit and the tools and techniques needed to manage this unit. Business: Strategy has the same relationship.

 An artist uses paint to produce paintings. Therefore, the relationship is that of a visual artist and his/her basic tool. The same relationship can be seen in option 2.

 A carpenter makes or produces  furniture. This relationship is seen in option 2, where a sculptor makes idols.

 A terrorist causes violence, hence, the relationship is of a cause and effect. Among the given options, option 3 has the same relationship( riots cause destruction).

 The relationship is of a negative emotion and positive emotion. Only option 1 agrees with this relationship.

Lace is a type of cloth used to decorate the garments like gown, which are worn. Similarly, as given in option (1), frosting is commonly termed as icing used to cover cake or pastries for decoration. Therefore, these two are related together on this account and we can mark the given pair as suitable analogy for the question.

Captain is a head of a team and similarly, a skipper, also known commonly as commander is head of a crew in a ship. So, these two pairs are of same kind. Thus, option (4) is correct.

'Sotto Voce' refers to a term referring to undertone so that not to be overheard and 'Echo' is repetition of sound by reflection or by repetition, therefore, these two words can appropriately be considered as antonyms. So, an antonym pair would help us find answer to this question. 'Blase' refers to having indulged in pleasure so much as to be unexcited by it and 'Ennui' refers to weariness and dissatisfaction resulting from lack of activity or interest. This is only pair one can find among those provided which has some contrasting traits, rest do not exhibit any particular relation. Therefore, option (4) is correct answer.

The meaning of term 'vampy' is to act, to seduce or beguile by using feminine charms. So, most suitable of among the given words is in option (1).