When something is "mutual" it is held by multiple people. For example, three people could have a "mutual hatred" for corn on the cob. This hatred is common to each of the members of the group. We also speak of a "mutual enemy". This very clearly means "common enemy." Thus, "common" is the most obvious choice for this question.

The adjective "extensive" describes something that covers a large area—whether literally or metaphorically. An extensive plot of land is a very large plot of land. An extensive collection of books "covers" many topics and authors. Extensive knowledge "covers" many topics. (You can think of it meaning that each of these "extends" over a large area.) Now, this does not mean that something that is "extensive" completely covers its given "area;" however, it can seem close to being complete. The word "exhaustive" means comprehensive. At least among the options provided here, this is by far the best.

The word "fragile" means weak or easily broken. Now, most of your options are likely tempting, for they remind you of glass, which is easily broken, but the only option that directly indicates a kind of fragility or weakness is "delicate." When something is "delicate," it is not very strong. Sometimes, we speak of "delicate health" in someone who is sickly. We can also speak of a "delicate situation," meaning that the situation could fall apart easily.

When something is tainted, it loses its purity. For instance, a water supply can be tainted by having small amounts of paint poured into as well as small amounts of soda. In both cases, the water supply loses its purity. Tainting does not have to do with poison necessarily, so be careful not to choose an answer based on this. Instead, the best option is "polluted," which can apply to any kind of the actions mentioned above as examples of tainting.

The word "superfluous" comes from Latin roots that literally mean overflowing. (The "super-" prefix means "over or above" and "-fluous" clearly means "flowing.") When something is "superfluous," it is excessive or beyond one's current needs. While such things could be "overwhelming" or even outragous / exorbitant, they are always unnecessary. Thus, this simple word is the best option for this question!

"Extemporaneous" means done without preparation, improvised. To provide further help, "partitioned" means divided, split into multiple regions; "forestalled" means delayed; "supplanted" means replaced; "remedied" means fixed. 

"Potable" means drinkable, able to be safely drunk. The suffix -able often means able to be. To provide further help, "fecund" means abundant, full of life, fertile; "edible" means able to be eaten. 

"Titanic" means very large. Think of the famous ship the Titanic, it was known for two qualities -being supposedly unsinkable and being very, very large. The word "titanic" means extremely big. 

"Esoteric" means known by only a few, arcane. It is generally used to describe knowledge, so "esoteric knowledge" means arcane knowledge, known only by a select few. To provide further help, "monotone" means boring; "celestial" means divine, heavenly; "truculent" means aggressive; "protracted" means drawn out, taking a long time. 

"Exiguous" means a very small amount, meager, scant. To provide further help, "ample" means more than enough; "sufficient" means enough, good enough; "garrulous" means talkative; "cogent" means a well-made, clear argument.