grammatical number - Problem with choosing between singular and plural nouns

I would like to find out how to use singular and plural nouns correctly. I have tried grammar books, but I can't find anything on agreements of nouns in the object position. Please kindly explain to me whether the sentences below are correct and whether there are any differences between their use. Also this type of grammar problems if filed under what names in grammar books. Thanks!!!

A)

I can't offer any simple solution
I can't offer any simple solutions

B)

I want to get better school results
I want to get a better school result

C)

They can't obtain a sense of accomplishment
They can't obtain senses of accomplishment

D)

Students should do more sports to help them build a healthy body
Students should do more sports to help them build healthy bodies

Answer

The context of the sentence in relation to the other sentences in a paragraph should guide the decision to use a singular or plural noun.

A)
   I can't offer any simple solution
   I can't offer any simple solutions

Either one is correct. The better choice depends upon the greater context. The second may sound more correct because "any" as an adjective can be defined as "one, some, or all indiscriminately of whatever quantity" (Merriam-Webster) which implies that the object being modified is plural. Another definition of "any" is "one or some indiscriminately of whatever kind" which does not imply plurality.

B)
   I want to get better school results
   I want to get a better school result

Again either is correct.

 My homework and test grades stink.  I want to getter better school results.
 I did poorly in that class at summer camp.  I want to get a better school result

In the first, "results" is referring to school grades. In the second, result refers to a specific class.

C)
    They can't obtain a sense of accomplishment
    They can't obtain senses of accomplishment

Technically, both are correct.

 They can't obtain a sense of accomplishment.  The ladies have to create a goal for the committee first.  
 They can't obtain senses of accomplishment.  The ladies have to create their individual goals first.  

In the first example, the ladies share a single "sense" as indicated by their participation in a committee. In the second each lady has her own "sense" as indicated by "individual". That said, just because a sentence isn't technically incorrect doesn't mean it might not sound off. In my ear that is a result of the combination of "senses" (plural) and "accomplishment" (singular).

 D)
    Students should do more sports to help them build a healthy body
   Students should do more sports to help them build healthy bodies

The context of sports and their effect on health indicate that each student has his or her own body and so the second is correct. As you mention, the students aren't building Frakenstein during gym class.

June Casa Grande's Grammar Snobs Are Great Big Meanies has a great chapter on singular and plural word choices.

 The Rolling Stones are awesome. 
 The Who is awesome too.