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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
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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
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 .
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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) 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
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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
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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.
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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,
c S 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, 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
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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 .
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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 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
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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( )
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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 )( 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
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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
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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
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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. 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
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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. 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{(
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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 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
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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) 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
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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........
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
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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) 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
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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
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75.The compound proposition pq p p )]([ 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