Hello all guys! I am preparing for the test in Nov. And after I have finished the 4 practice test, I have some problems about these 4 tests.

1.GR0568 #40(C)

40. For which of the following rings is it possible for the product of two nonzero elements to be zero?

(A) The ring of complex numbers

(B) The ring of integers modulo 11

(C) The ring of continuous real-valued functions on [0, 1]

(D) The ring a+b^1/2 :a and b are rational numbers

(E) The ring of polynomials in x with real coefficient

2.GR0568 #44

44. A fair coin is to be tossed 100 times, with each toss resulting in a head or a tail. If H is the total number of heads

and T is the total number of tails, which of the following events has the greatest probability?

(A) H=50

(B) T >= 60

(C) 51 < H < 55

(D) H >=48 and T >= 48

(E) H <5 or H > 95

Should I deduce from the graph of normal distribution? I just cannot figure out how to calculate it.

3.GR0568 #61

61. Which of the following sets has the greatest cardinality?

(A) R

(B) The set of all functions from Z to Z

(C) The set of all functions from R to {0, 1}

(D) The set of all finite subsets of R

(E) The set of all polynomials with coefficients in R

4.GR0568 #65

65. Which of the following statements are true about the open interval (0, 1) and the closed interval [0, 1]?

I. There is a continuous function from (0, 1)onto [0, 1].

II. There is a continuous function from [0, 1]onto (0, 1).

III. There is a continuous one-to-one function from (0, 1) onto [0, 1].

(A) None (B) I only (C) II only (D) I and III only (E) I, II, and III

And I also have troubles on another 2 tests: GR9367 #43, GR9367 #57,GR9367 #60

Thank you all guys! Any help will be greatly appreciated!