Analogy Questions

Fence protects the Yard & Membrane protects the Cell.

Fence surrounds the Yard and allows the certain objects in & out of it whereas a Membrane surrounds the Cell & only allows specific nutrients inside of it.

Hence, Yard is to Fence as Cell is to Membrane.

Given Transition is to Change, and we know that Transition and change are Synonyms. Similarly, Immobility means not moving and synonym of immobility are motionlessness, stillness,...

Hence, Transition is to change as immobility is to stillness.

Modern is used to refer to something new whereas antiquated is used with respect to something old.

In other words, both terms are the opposite of each other.

From the above analysis, the missing word should be a word that represents the opposite of weak. Strong is used to with great influence. Therefore, the apt word is strong or any synonym of strong like potent, powerful, keen,...

Hence, Modern : Antiquated :: Weak : Strong.

Here Thread and String are Synonyms of each other. Then the answer will be the synonym of Cask. 

• Cask is nothing but a large barrel-like container used for storing liquids, typically alcoholic drinks. 

Ex : Drum, Vessel, Tank, Barrel, Hogshead, Firkin,...

• Here from the options Barrel is the only synonym of Cask.

Thus,  Thread : String :: Cask : Barrel