the number of student(s)

the number of students increases is correct!

2007-12-10 21:19:23 補充：
the number of STUDENT increases 則是錯的.如我們說「人數」增加了, 會說:the number of PEOPLE increases, 卻「不是」 the number of 「person」!以下其他很多例子都是從英英字典找到的, 可見當我們想要表達「the number of 可數名詞」之時, 是必須用眾數來表達:http://dictionary.cambridge.org/define.asp?key=54475&dict=CALD

2007-12-10 21:19:33 補充：
The number of people (不是單數的person) killed in road accidents fell last month.There has been an increasing number of caseS (不是單數的 case) of the disease.A small number of children (不是單數的 child) are educated at home.SLIGHTLY FORMAL A large number of invitations (不是單數的 invitation) has been sent.

2007-12-11 10:53:46 補充：
【補充】以上是字典的例句, 以下再加兩個例子, 希望可幫你明白更多... 假設你想表達 (a) 某地方有10間工廠, 即工廠「數目」是10; (b) 某一間工廠的電話「號碼」是 23456789 及 29876543, 用英文寫便是:the numbeR of factorIES IS 10; (或 the total number 也可以)the numbeRS of THE factorY ARE 23456789 and 29876543希望你明白以上兩個例子的差別!

Q2 is correct. the number of students increases.

我會選擇後者!!!!!!
因為student 係[c}是可數的ｎ
因此the number of students increases 才是正確的

"the number of students increases." is correct.
increase加s是因為要配合"the number"，而學生的數量有增加趨勢的話一定會比一多，所以"the number of students increases."是正確的。