7. .
Now using Integration by Parts with and and the integral becomes
.
Now make the substitution and the integral becomes
.
Don't know, I'm wondering that too. It might depend on the boundaries of that particular year. I think with sufficient training and wise choice of questions, most people can get more than ten right within the time limit. But you have to keep in mind that they are not doing them in the regular way -- with the explicit substitutions and all. For example, it's much more efficient to do # 10 as follows: