1. What is the least upper bound of the set of all numbers A such that a polygon with area A can be inscribed in a semicircular region of radius 1?

(A)4/5 (B)2/sqrt(5) (C)1 (D)pi/2 (E)2

I though the ans should be pi/4, but there is no such option, why is that?

2.If for all positive x!=1 and if f is continuous at 1, then f(1) is

(A)0 (B)1/e (C)1 (D)e (E)none of the above

3.Of the following equations, which has the greatest number of roots between 100 and 1,000?

(A)sin(x)=0 (B)sin(x^2)=0 (C)sin(|x|^(1/2))=0 (D)sin(x^3)=0 (E)sin(x^(1/3))=0

4.The order of the element of the symmetric group S_5 is

(A) 2 (B) 3 (C) 6 (D) 8 (E) 12

P.S. I'm sorry about the latex, but I have no idea how to make it right..