bc0039-discrete mathematics-model question paper
TRANSCRIPT
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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
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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
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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 ………….
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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
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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
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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.
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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 )()(
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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
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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 …………………….
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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
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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
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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()
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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)
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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
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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
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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
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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
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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{(
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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
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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
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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
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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
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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
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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
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75.The compound proposition pqpp )]([ is a
A) contradiction
B) tautology
C) neither (a) nor (b)
D) predicate
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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