Please help with these kanji
 

Ok, little background. I bought for DS a program that is basically a mixed between a good dictionary and basic English lesson, made in Japan for Japanese (漢字そのまま楽引辞典). Inside there are quiz about kanji (always made for Japanese, thus people who already know Japanese).
One of the quiz is called 同じ読みの漢字. I assumed it was kanji with same meaning...but I am no longer sure :O Can you help me to understand? This are some of the question that puzzle me.

１　診る
　　夢を？る (answer 見る)
２　産む
　　新記録を？む (answer 生む)
３　建つ・断つ・絶つ・裁つ
　　茶柱を？つ　(answer 立つ)
These are just some of them. By what I know (maybe wrong) 診る is used more for seeing people (like doctors). 生む is give birth for human or animal or producing something (like profits), not making a new record. Then those 4 たつ, some mean cut and some mean build up (if not wrong 立つ in that case can mean floating).
Is it just an exercise of same sound and synonimous or I just don't know how to use those (and other) kanji?
Thank you in advance.

That isn't like you, is it?

読み　≠　meaning
読み　= reading　

Did it say を? If so, it's incorrect.
________

This is all about homophones.

No sorry I mistyped...of course intransitive can't have direct object :)

Thank you for the answer. I thought that they would give similar meaning kanji as a clue for the quiz and that incidentally they used the ones with the same reading. Now I guess I can take those quiz with a different knowledge.

「新記録を生む」 is a correct expression because 生む can also mean "to bring about" or "to produce something that didn't exist before".