MATHEMATICS - APPLIED MECHANICS - Practical Mathematics Exercises

Practical Mathematics Exercises

Exercises Chapter 1 MATHEMATICS

1. suppose A = { 2 , 5 , 7 , 9 , 13 , 25 , 26 }

a) Find n(A)

b) True or False : 7 Î A

c) True or False : 9 Ï A

2. If A = { 1,2,3,4,5} and B = { 4,5,6,7,8 } find the following

a) A Ç B

b) A È B

3. If A = { 1,3,5,7,9 } and B = { 0,2,4,6,8 } find the following

a) A È B

b) A Ç B

4. Suppose n(U) = 150 , n(A) = 37 , n(B) = 84

a) If n(A È B ) = 100 , find n(A Ç B )

b) If n(A È B ) = 121 , find n(A Ç B )

5. How many subsets does A have ? If

a) List all subset of A = { a , b }

b) List all subset of A = { a , b , c }

c) List all subset of A = { a , b , c , d }

6. Find the value of n!/(n - r)! when :

a) n = 5 , r = 5

b) n = 16 , r = 14

7. Every book published has an International Standard Book Number (ISBN) . The number is a code used to identify the specific book and is of the form X-XXX-XXXXX-X , where X is one of digits 0,1,2,…,9 . How many different ISBNs are possible ?

8. Each student at State University has a student I.D number consisting of four digits ( the first digit is nonzero , and digits maybe repeated ) followed by three of the letters A , B , C , D and E ( letters may not be repeated ) . How many different student numbers are possible ?

9. Telephone area codes are three-digit numbers of the form XXX. Originally , the first and third digits were neither 0 nor 1 and the second digit was always a 0 or a 1 . How many three-digit numbers of this type are possible ?

10.The serial number on a dollar bill consists of a letter followed by eight digits and then a letter . How many different serial numbers are possible ?

a) Letters and digits cannot be repeated

b) Letters and digits can be repeated

11. Find the indicated value :

a) ₅P₅ b) ₅C₅

c) _xP_{x – 1} d) _xC_{x – 1}

12. Six local bands have volunteered to perform at a benefit concert , but there is enough time for only four bands to play . There is also some concern over the order in which the chosen bands will perform . How many different lineups are possible ?

13.A V_League has 14 teams . If every team must play every other team once in the first round of league play , how many games must be scheduled ?

14. A compact disc club sends you a brochure that offers any five CDs from a group of 50 of today’s hottest releases . How many different selections can you make ?

15. A group consisting of twelve women and nine men must select a five person committee . How many different committees are possible if it must consist of the following : Three women and two men .