1. He would always ignore the fact of such a contradiction in his inner thought.

A. there to be B. there being C. it being D. there having been

2. A convenient way is to set the food on a piece of aluminum oil, to the air for half an hour, and then cover it with a dish.

A. let it stay open B. let it stayed open

C. letting it stay open D. letting it stay opened

3. They us willingly but that they happened to be short of hands, too.

A. would help B. would have helped

C. were going to help D. must have helped

4. Research findings show that we spend about two hours dreaming every night,no matter what we during the day.

A. should have done B. would have done

C. may have done D. must have done

5. If you are to catch a train, it is always better to be comfortably early than even a fraction of a minute late.

A. too B. very C. much D. rather

1. Bthere being 做介词of 的宾语，如果是介词for，则用there to be。

2. C分词短语做伴随状语，形容词open在分词短语中做补语，表示状态，不用过去分词，所以D不正确。

3. B此句是含蓄虚拟语气句，暗含的假设条件为：if they hadn’t happened to be short of hands。故应选B。

4. Cmay have done“(不管我们白天)可能做了些什么”，符合句意。should have done“本该做(但实际未做)”;would have done表示与过去相反的假设;must have done是对已发生的情况作肯定推测。

5. A句中too late相当于too late to catch the train，所以选其他词不合适。