BC0039-Discrete Mathematics-MQP.pdf

8/10/2019 BC0039-Discrete Mathematics-MQP.pdf

1/26


2/26

B) 2 2

C) 2 5

D) 2 6

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

2 ba

D)2

2ba

6. The n th term of an arithmetic progression a + (a + d) + (a + 2d) + . is

A) a + nd

B) a + (n 1)d


3/26

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

r aS

n

n 1)1(

B)r r a

S n

n 1)1(

C)r r a

S n

n 1)1(

D)r r a

S 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 .


4/26

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) nm

B) mn

C) m + n

D) m n

11. The value of r n P =

A))!(

!r n

n

B))!(

!r n

n

C))!()!(

r nr n

D))!()!1(

r nn


5/26

12. Consider n objects of which m 1 are of first kind, m 2 are of second kind,.., m k are of k th

kind, thenk

iim

1

A) n 3

B) n 2

C) n

D) i

13. A recurrence relation of the form )(.......22110 r f aC aC aC aC k r k r r r where sC i ' are

constants, is called a .

A) Quadratic linear relation

B) Quadratic recurrence relation

C) Linear recurrence relation

D) Cubic recurrence relation

14. r r r aa 232 1 is a order linear recurrence

A) second

B) first

C) third

D) fourth


6/26

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

n xa xa xaa x f 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 x x x f

B) .......321)( 2 x x x f

C) .......321)( 2 x x x f

D) .......642)( 2 x x x f

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

A) n A A A ....21

B) n A A A ....21

C) n A A A ....21

D) n A A A ....21

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


7/26

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,

c S we have

A) cbacba )()(


8/26

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, un der the operation , where },max{ y x y x . 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


9/26

D) superset of

25. If for any ring R, a.b = b.a for all a, b R 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 x x 2 for all R x .

A) permutation ring

B) commutative ring

C) Boolean ring

D) identity ring

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


10/26

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


11/26

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 y B there exists atleast one

element x A 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


12/26

35. The set }:{ b xa R x is denoted by

A) [a, b)

B) (a, b]

C) (a, b)

D) {a, b}

36. The domain of the function65

)(2 x x

x x f is

A) {2, 3}

B) {3, 2}

C) R {3, 2}

D) R {2, 3}

37. The range of x

x x f

1)( =

A) R {1}

B) R { 1}

C) R {2}

D) R {3}

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

A) f(x) = f( )


13/26

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)


14/26

C)

D)

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

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 n th 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


15/26

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

m 1 ways, second object in m 2 ways, and so on,is

A)!!......!

!

21 k mmmn

B)!!......!

!

21

2

k mmm

n

C)!!......!

!

21

3

k mmm

n

D)!......!!

!21

3

k mmmn

46. r nC

A)!)!(

!r r n

n

B)!)!(

!r r n

n

C)!)!(

!2

r r nn

D)!)!(

!r r n

n

47. If ...........1)( 2 n x x x x f and .....)1(......1)( 32 nn x x x x x g then

)()( x g x f

A) ......1 642 x x x


16/26

B) ......1 642 x x x

C) ......642 x x x

D) ......1 642 x x x

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


17/26

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. T he semigroup S/R is called the ..

A) totally ordered

B) quotient semigroup

C) not ordered

D) completely ordered

53. A finite integr al domain is a .

A) subfield

B) vector

C) field

D) ring


18/26

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. P Q is called the of P and Q.

A) conditional

B) conjunction

C) bi-conditional

D) disjunction

56.In the implication Q P , 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 }/),{( bdividesa B Aba R then

the set R =

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


19/26

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 4 th, 7 th and 10 th 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


20/26

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) R y x ),(

D) R x y ),(

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


21/26

B)6

)12)(1( nnn

C)6

)12)(1( nnn

D)6

)12)(1(2 nnn

64. The value of )23()13(

1........

1181

851

521

mm

A)46

2

mm

B)46 m

m

C)46 2

2

m

m

D)46 2

2

m

m

65. .......32 t t t

A)t

t

1

B)t

t

1

C)1t

t


22/26

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) 2 x

D) 2 x

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

A) )3(22 nnna

B) )3(22 nnna

C) )3(22 nnna


23/26

D) )3(22 nnna

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

A) x

B) 2 x

C) 3 x

D) x1

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, b G. Then aH = bH if and only if

A) H ba 11

B) H ab

C) H ab 1

D) H ba 1


24/26


25/26

75.The compound proposition pq p p )]([ is a

A) contradiction

B) tautology

C) neither (a) nor (b)

D) predicate


26/26

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

BC0039-Discrete Mathematics-MQP.pdf

Documents

Transcript of BC0039-Discrete Mathematics-MQP.pdf