bc0039-discrete mathematics-model question paper

Model Question Paper

Subject Code: BC0039

Subject Name: Discrete Mathematics

Credits: 4 Marks: 140

Part A (One mark questions)

1. If the number of elements in a set is not finite then the set is called an

A) finite set

B) collective set

C) Infinite set

D) arranged set

2. If A = {1,3,5} and B = {1,3,5,7} then A is a ……….. subset of B

A) smaller

B) proper

C) improper

D) normal

3. Consider the set A = {1, 2, 3}, the power set of A has …………. elements

A) 23

B) 22

C) 25

D) 26

4. The cardinality of the set A= {1, 2, 3, 0, 6, 7, 8, 9} is

A) 7

B) 8

C) 6

D) 2

5. If A is the arithmetic mean between the extremes a and b then A =

A) 2

ba

B) 2

ba

C) 2

2ba

D) 2

2ba

6. The nth term of an arithmetic progression a + (a + d) + (a + 2d) + …. is

A) a + nd

B) a + (n–1)d

C) a + (n+1)d

D) 2a + (n+1)d

7. The sum to n terms of a geometric progression is given by

A) r

raS

n

n

1

)1(

B) r

raS

n

n

1

)1(

C) r

raS

n

n

1

)1(

D) r

raS

n

n

1

)1(

8. The sum to infinity of a geometric progression is

A) r

a

1

B) r

a

1

C) r

a

1

D) r

a

1

2

9. Combinatorics is the branch of discrete mathematics concerned with ………….

A) counting problems

B) abstract algebra

C) derivative problems

D) integrated problems

10. If the object A is chosen in m ways and B in n ways then either A or B is chosen in ………

ways

A) n

m

B) mn

C) m + n

D) m – n

11. The value of rnP =

A) )!(

!

rn

n

B) )!(

!

rn

n

C) )!(

)!(

rn

rn

D) )!(

)!1(

rn

n

12. Consider n objects of which m1 are of first kind, m2 are of second kind,…….., mk are of kth

kind, then

k

i

im

1

A) n3

B) n2

C) n

D) i

13. A recurrence relation of the form )(.......22110 rfaCaCaCaC krkrrr where sCi ' are

constants, is called a ……………………….

A) Quadratic linear relation

B) Quadratic recurrence relation

C) Linear recurrence relation

D) Cubic recurrence relation

14. rrr aa 232 1 is a ………… order linear recurrence

A) second

B) first

C) third

D) fourth

15. A …………. function is a polynomial of the form ...........)( 2210 n

nxaxaxaaxf which

has infinitely many non-zero terms

A) irrecursive

B) recursive

C) implicit

D) generating

16. The generating function of the sequence 1, 2, 3,.……of natural numbers is

A) .......321)( 2 xxxf

B) .......321)( 2 xxxf

C) .......321)( 2 xxxf

D) .......642)( 2 xxxf

17. The relation R between the sets nAAA ......,,, 21 is a subset of

A) nAAA ....21

B) nAAA ....21

C) nAAA ....21

D) nAAA ....21

18. A relation means …………….. on a set S.

A) dual relation

B) binary relation

C) reflexive relation

D) symmetric relation

19. A ………………. is a set S with a relation R on it which is reflexive, anti-symmetric and

transitive

A) equivalent set

B) ordered set

C) implicit set

D) Partially ordered set

20. If S is a poset and a, b are in S such that a > b and there is no c in S such that a > c and c >

b, then we say that ……………….

A) b covers b

B) a covers a

C) a covers b

D) b covers a

21. Let S be a non-empty set, then the operation on S is said to be associative if for all a, b,

cS we have

A) cbacba )()(

B) bccb

C) )()( bacb

D) cba

22. Let (A,) be an algebraic system where is a binary operation on A. Then (A,) is called a

semigroup if it satisfies the

A) closure law

B) associative law

C) reflexive law

D) closure and associative law

23. Let N be the set of natural numbers, under the operation „‟, where },max{ yxyx . Then

the set N is a

A) topogroup

B) multigroup

C) semigroup

D) subgroup

24. The set Z with the binary operation „subtraction‟ is ………….. a subgroup

A) not

B) subset of

C) always

D) superset of

25. If for any ring R, a.b = b.a for all a, bR then R is said to be a ……………..

A) integer ring

B) commutative ring

C) cyclic ring

D) non-commutative ring

26. A commutative ring is said to be an integral domain if it has no ………………..

A) zero divisors

B) inverse

C) multiples

D) identity

27. A ring R is said to be a ……………. if xx 2 for all Rx .

A) permutation ring

B) commutative ring

C) Boolean ring

D) identity ring

28. If R is a Boolean ring then R is a …………………….

A) commutative ring

B) subring

C) integral ring

D) integer

29. Reasoning is a special kind of thinking called as …………………

A) inferring

B) logics

C) bijective

D) contradictive

30. The basic unit of our objective language is called a …………………….

A) prime divisor

B) prime statement

C) bijective statement

D) statement

31. The validity of an argument doesnot guarantee the truth of the ……………..

A) permutation

B) commutative value

C) conclusion

D) identity value

32. A …………… is a statement which is either true or false, but not both.

A) argument

B) conclusion

C) bi-conditional

D) proposition

33. A function f: A B is said to be ……………… if for every yB there exists atleast one

element xA such that f(x) = y.

A) surjective

B) bijective

C) injective

D) Automorphism

34. If f is onto then f(A) =

A)

B) B

C) A

D) A B

35. The set }:{ bxaRx is denoted by

A) [a, b)

B) (a, b]

C) (a, b)

D) {a, b}

36. The domain of the function 65

)(2

xx

xxf is

A) {2, 3}

B) {3, 2}

C) R – {3, 2}

D) R – {2, 3}

37. The range of x

xxf

1)( =

A) R – {1}

B) R – {– 1}

C) R – {2}

D) R – {3}

38. A function f:AB is said to be periodic function if …………………

A) f(x) = f()

B) f(x) = f(x – )

C) f(x) = f(x + 2)

D) f(x) = f(x + )

39. f(x) = tanx is a periodic function with period …………..

A)

B) 2

C) 2

D) 3

40. The nth term of the series ..............755331 222 is

A) 2)12()32( nn

B) 2)12()32( nn

C) 2)12()12( nn

D) 2)12()3( nn

Part B (Two mark questions)

41. U

A) U

B)

C)

D)

42. If A = {2, 3, 4}, B = {4, 5, 6} and C = {6, 7} then )( BCA

A) {(2,7) (3,7) (7,4)}

B) {(2,7) (3,3) (4,7)}

C) {(7,2) (3,7) (4,7)}

D) {(2,7) (3,7) (4,7)}

43. The nth term of 1 + 3 + 5 + 7 + ……….

A) 2n

B) 2n + 1

C) 2n – 1

D) 1 – 2n

44. The nth term of ..............1077441

A) )13)(23( nn

B) )13)(23( nn

C) )1)(23( nn

D) )1)(23( nn

45. The number of distinguishable permutations of n objects in which the first object appears in

m1 ways, second object in m2 ways,… and so on,is

A) !!......!

!

21 kmmm

n

B) !!......!

!

21

2

kmmm

n

C) !!......!

!

21

3

kmmm

n

D) !......!!

!

21

3

kmmm

n

46. rnC

A) !)!(

!

rrn

n

B) !)!(

!

rrn

n

C) !)!(

!2

rrn

n

D) !)!(

!

rrn

n

47. If ...........1)( 2 nxxxxf and .....)1(......1)( 32 nn xxxxxg then

)()( xgxf

A) ......1 642 xxx

B) ......1 642 xxx

C) ......642 xxx

D) ......1 642 xxx

48. If x = 2.52 then 52.2

A) 0

B) 1

C) 2

D) 3

49. The elements in level-1 are called …………

A) electrons

B) atoms

C) neutrons

D) molecules

50. A Poset S is said to be ……………………. Set if for a, b in S exactly one of the conditions, a

> b, a = b or b > a holds

A) totally ordered

B) ordered

C) not ordered

D) completely ordered

51. Let (S,) be a semigroup and let T be a subset of S. If T is closed under the operation ,

Then (T,) is called a ………………. of (S,)

A) semigroup

B) super group

C) subgroup

D) subsemigroup

52. The semigroup S/R is called the ………………..

A) totally ordered

B) quotient semigroup

C) not ordered

D) completely ordered

53. A finite integral domain is a ………….

A) subfield

B) vector

C) field

D) ring

54. An integral domain D is said to be of characteristic 0 if the relation 0ma where Da0

and m is an integer, can hold only if

A) m = 0

B) m =1

C) m = 2

D) m = – 1

55. PQ is called the ………… of P and Q.

A) conditional

B) conjunction

C) bi-conditional

D) disjunction

56.In the implication QP , P is called the ……….

A) consequent

B) premise

C) conditional

D) statement

57. If A = {2, 3, 5} and B = {4, 6, 9} then if R is defined as }/),{( bdividesaBAbaR then

the set R =

A) )}9,3(),4,3(),6,2(),4,2{(

B) )}9,3(),6,3(),6,2(),4,2{(

C) )}9,3(),6,3(),9,2(),4,2{(

D) )}9,3(),6,3(),6,2(),2,4{(

58. If R = {(2,1), (3,1), (5,1), (5,4)} then R-1 =

A) {(2,1), (3,1), (5,1), (4,5)}

B) {(2,1), (3,1), (5,1), (5,4)}

C) {(1,2), (1,3), (1,5), (4,5)}

D) {(2,1), (3,1), (5,1), (4,5)}

59. If 4th, 7th and 10th terms of G.P. are a, b, c respectively then

A) 22 acb

B) cab 2

C) 222 cab

D) acb 2

60. n....321

A) 2

)1( nn

B) 2

)1( nn

C) 2

)1(2 nn

D) 2

)1( 22 nn

Part C (Four mark questions)

61. A relation R on a set A is said to be symmetric if Rba ),(

A) Rab ),(

B) Rab ),( 22

C) Ryx ),(

D) Rxy ),(

62. Consider the set of all straight lines in a plane. If the relation R is defined as

“parallel to” then R is

A) reflexive

B) symmetric

C) transitive

D) A), B) and C)

63. 2222 ..............321 n

A) 6

)12)(1( nnn

B) 6

)12)(1( nnn

C) 6

)12)(1( nnn

D) 6

)12)(1(2 nnn

64. The value of

)23()13(

1........

118

1

85

1

52

1

mm

A) 46

2

m

m

B) 46 m

m

C) 46 2

2

m

m

D) 46 2

2

m

m

65. .......32 ttt

A) t

t

1

B) t

t

1

C) 1t

t

D) t

t

1

66. The next permutation to 4123 in the reverse Lexicographic order is

A) 3412

B) 3421

C) 2413

D) 4312

67. x

A) 1

B) x

C)

2x

D) 2x

68. The solution of the recurrence relation 4,1,2,65 1021 aagivennaaa nnn is

A) )3(22 nnna

B) )3(22 nnna

C) )3(22 nnna

D) )3(22 nnna

69. Let ),,( L be an algebraic lattice and xL then xx

A) x

B) 2x

C) 3x

D) x

1

70. If L is a finite lattice then L is

A) supremum

B) infimum

C) bounded

D) unbounded

71. If H is a subgroup of G and a, bG. Then aH = bH if and only if

A) Hba 11

B) Hab

C) Hab 1

D) Hba 1

72. If is a homomorphism of G into G with kernel K then K is a ……………… of G

A) normal subgroup

B) subgroup

C) bounded subgroup

D) unbounded subgroup

73. If RR : is a homomorphism then )( a

A) )( 2a

B) )(a

C) )(a

D) a

74. A field F is said to have ………………. if there exist a positive integer n such that

nx = 0 for all xF

A) characterstic

B) finite characteristic

C) finite bound

D) least upper bound

75.The compound proposition pqpp )]([ is a

A) contradiction

B) tautology

C) neither (a) nor (b)

D) predicate

Answer Keys

Part - A Part - B Part - C

Q. No. Ans. Key Q. No. Ans. Key Q. No. Ans. Key Q. No. Ans. Key

1 C 21 A 41 B 61 A

2 B 22 D 42 D 62 D

3 A 23 C 43 C 63 A

4 B 24 A 44 B 64 B

5 B 25 B 45 A 65 A

6 B 26 A 46 D 66 C

7 C 27 C 47 D 67 B

8 A 28 A 48 C 68 A

9 A 29 A 49 B 69 A

10 C 30 B 50 A 70 C

11 B 31 C 51 D 71 D

12 C 32 D 52 B 72 A

13 C 33 A 53 C 73 C

14 C 34 B 54 A 74 B

15 D 35 C 55 B 75 B

16 A 36 D 56 B

17 C 37 B 57 B

18 B 38 D 58 C

19 D 39 A 59 D

20 C 40 C 60 A