MATH 210
Exam 2
March 22, 1996
1.
Let A and B be sets and suppose
then
(a)
20
(b)
30
(c)
15
(d)
50
(e)
None of the above.
2.
Let A and B be sets. Using Venn diagrams, or otherwise, simplify:
(a)
(b)
(c)
(d)
(e)
None of the above.
The next three problems refer to the following survey results: 120 students are surveyed about their courses:
28 study only Geography,
45 study History,
42 study Mathematics,
12 study Geography and History but not Mathematics,
25 study Geography and Mathematics,
15 study History and Mathematics,
20 study Geography and History
3.
How many study Geography or History?(a)
65
(b)
72
(c)
34
(d)
40
(e)
None of the above
4.
How many study Geography or History?(a)
80
(b)
73
(c)
90
(d)
110
(e)
None of the above.
5.
How many do not study Geography, History or Mathematics?(a)
5
(b)
10
(c)
15
(d)
20
(e)
None of the above.
For the next two problems consider the following linear programming problem:
Maximize C = 2x + y subject to the constraints:
6.
The maximum is:(a)
120
(b)
36
(c)
60
(d)
30
(e)
None of the above.
7.
The maximum occurs at a point with x-coordinate:(a)
2
(b)
16
(c)
30
(d)
44
(e)
None of the above.
8.
For sets A and B, which of the following are ALWAYS true?
(a)
(i) only.
(b)
(ii) only.
(c)
(ii) and (iii) only.
(d)
(ii), (iii) and (iv) only.
(e)
Some other selection.
9.
If A = {1,2,3,5,6} and B = {2,4,6}, then
(a)
{1,2,3,4,5,6}
(b)
{2,6}
(c)
{1,3,5}
(d)
{4}
(e)
None of the above.
10.
Compute C(1000,2):(a)
(b)
1000! / 2!
(c)
(d)
999
(e)
None of the above.
11.
Compute P(1000,2):(a)
(b)
1000! / 2!
(c)
(d)
999
(e)
None of the above.
12.
Three married couples attend a concert. They sit in a row of six seats. In how many ways can they be seated if every husband will sit next to his wife?(a)
8!
(b)
6
(c)
12
(d)
48
(e)
None of the above.
13.
Judges at an ice-skating competition must award a first and a second prize. If there are sixteen contestants, in how many ways can the prizes be awarded?(a)
240
(b)
120
(c)
256
(d)
31
(e)
None of the above.
14.
In a class of sixteen students, two are to receive an A. In how many ways can this be done?(a)
240
(b)
120
(c)
256
(d)
31
(e)
None of the above.
15.
A manufacturer makes two kinds of sweaters: wool and cotton. It costs $5 to make a wool sweater and $4 to make a cotton sweater. The company can make at most 120 sweaters per week and budgets no more than $500. Suppose there is a profit of $6 on each wool sweater and $5 on each cotton sweater. What is the maximum profit?(a)
$950
(b)
$500
(c)
$405
(d)
$620
(e)
None of the above.
© Department of Mathematical Sciences, Northern Illinois University, DeKalb IL 60115
Prepared 10/15/97 by Dr. Anders Linnér (
alinner@math.niu.edu)