1. Let R be a relation defined on the set Z by aRb if a < b. What property/properties are violated?

a)Reflexive & Symmetric

b)Reflexive & Transitive

c)Symmetric & Transitive

d)All three properties (Reflexive, Symmetric, Transitive)

2. The relation "is less than or equal to", denoted "", is NOT an equivalence relation on the set of real numbers. What property/properties are violated?

a)Reflexive

b)Symmetric

c)Transitive

d)All of the above

3. How many elements do we have for AxB if A has 3 elements and B has 5 elements?

a)8

b)9

c)15

d)25

4. If f(x) = 2.x^3 and g(x) = x + 1. What is (f + g) (x)?

a)2x^4 +1

b)3x^3 + 1

c)2x^3 + x + 1

d)none of the above

5. What property is NOT included for an EQUIVALENCE RELATION?

a)Reflexive

b)Symmetric

c)Transitive

d)Anti-Symmetric

6. In how many ways can the letters of the word BEAUTY be arranged?

a)360

b)5!

c)6!

d)7!

7. If f(x) = 2.x^2 - x + 5. What is f(-3)?

a)20

b)29

c)26

d)21

8. Let R be a relation defined on the set Z by aRb if floor value of a = floor value of b. What property/properties are violated?

a)Reflexive

b)Symmetric

c)Transitive

d)None of the above

9. A committee of 5 people is to be chosen from a group of 6 men and 4 women. How many committees are possible if there are to be 3 men and 2 women?

a)130

b)120

c)140

d)180

10. Let R be a relation defined on the set Z by aRb if a-b. What property/properties are violated?

a)Reflexive

b)Symmetric

c)Transitive

d)Transitive

e)None of the above

11. If f(x) = 2.x^3 and g(x) = x + 1. What is (g o f) (x)?

a)2(x+1)^3

b)2x^3 (x+1)

c)3x^3 + 1

d)2x^3 + 1

12. Let R be a relation defined on the set Z by aRb if a=b. What property/properties are violated?

a)Reflexive

b)Symmetric

c)Transitive

d)None of the above

13.If f(x) = x^3 + x - 1. What is f(x^2)?

a)x^5 + x - 1

b)x^5 + x^2 - 1

c)x^6 + x^2 - 1

d)x^9 + x^2 - 1

14.If A = {7, 8} and B = {2, 4, 6}, what is A B.

a){(2, 7), (4, 7), (6, 7), (2, 8), (4, 8), (6, 8)}

b){(7, 2), (7, 4), (7, 6), (2, 8), (4, 8), (6, 8)}

c){(2, 7), (4, 7), (6, 7), (8, 2), (8, 4), (8, 6)}

d){(7, 2), (7, 4), (7, 6), (8, 2), (8, 4), (8, 6)}

15. How many can 3 digits be formed using the digits from 1 to 5 if the digit 2 is never there in the number?

a)24

b)36

c)40

d)52

16. If A = {1, 3, 5}, B = {3, 5, 6} and C = {1, 3, 7}. What is A (B C)?

a){3}

b){1, 3, 5, 6)

c){1, 3 , 5, 7}

d){1, 3, 5}

17. Find out how many distinct three-digit numbers can be formed using all the digits of 1, 2, and 3.

a)4

b)5

c)6

d)7

18. If A = {a, b, d, e}, B = {b, c, e, f} and C = {d, e, f, g}. What is (A B) (A C)?

a){b, d ,e}

b){a, b, c}

c){b, e}

d){a, b, d, f}

19. What is the representation of the shaded region?

a)(A intersection B') intersection C

b)(A' union B) intersection C

c)C union (A intersection B)

d)(A union B) intersection C

20. How many different words can be formed from the alphabets of the word SCISSORS?

a)1440

b)1680

c)1800

d)2100

21. Find out the distinct four-letter words that can be formed using the word SINGAPORE.

a)256

b)1024

c)3024

d)2048

22. In how many different ways can five friends sit for a photograph of five chairs in a row?

a)120

b)24

c)240

d)720

23. If A and B are two sets, and A B consists of 6 elements: If three elements of A B are (2, 5), (3, 7), (4, 7), what are the other elements of A B?

a)(2, 3, 4), (5, 7)

b)(2, 7), (3, 5), (4, 5)

c)(5, 2), (7, 3), (7, 4)

d)(7, 2), (5, 3), (4, 5)

24. Find the number of subsets of the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} having 4 elements.

a)340

b)430

c)330

d)440

25. In how many can the 4 couples sit around a circular table so that no two men are sitting together?

a)7!

b)6!

c)3! x 4!

d)3! x 3!

26. If A = {a, b, d, e}, B = {b, c, e, f} and C = {d, e, f, g}. What is A (B C)?

a){a, b, e}

b){a, b, d, e f}

c){a}

d){d, e f}

27. What is the representation of the shaded region?

a)(A intersection B)' intersection C

b)(A union C) intersection B'

c)(A intersection B') intersection C

d)(A intersection B) union C

28. There are 20 seniors serving the student council of a certain school. Of the 20, 3 have not served before, 10 served on their junior years, 9 served in their sophomore years, and 11 served in their freshman years. There are 5 who served during both their sophomore and junior years, 6 during both their freshman and junior years, and 4 during both their freshman and sophomore years. How many seniors served on the student council during each of their four years in school?

a)2

b)3

c)4

d)5

29. How many can four digits be formed using the digits 0, 1, 2, and 3 (repetition is allowed)?

a)12

b)24

c)256

d)192

30. A survey of 500 television watchers produced the following information: 285 watch football games, 195 watch hockey games, 115 watch basketball games, 45 watch football and basketball games, 70 watch football and hockey games, 50watch hockey and basketball games, and 50 do not watch any of the three kinds of games. How many people in the survey watch all three kinds of games?

a)35

b)25

c)20

d)40