MC0063 Discrete Mathematics Model Question Paper

Model Question Paper Subject Code: MC0063 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. If A is the arithmetic mean between the extremes a and b then A = a)

a b 2

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b)

c)

d)

a b 2

a  2b 2

a  2b 2

4. 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

5. Combinatorics is the branch of discrete mathematics concerned with …………. a) counting problems b) abstract algebra c) derivative problems d) integrated problems

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











b) mn c) m + n d) m – n

7. A recurrence relation of the form C 0 ar  C 1ar 1  C 2 ar 2  ....... C k ar k  f (r ) where C i ' s are constants, is called a ……………………….

a) Quadratic linear relation b) Quadratic recurrence relation r elation c) Linear recurrence relation d) Cubic recurrence relation

8. 2a r  3ar 1  2 r is a ………… order linear recurrence a) second b) first c) third d) fourth

9. The relation R between the sets A1 , A2 , ......, An is a subset of a) A1  A2  ....  An











d) A1  A2  ....  An

10. A relation means …………….. on a set S. a) dual relation b) binary relation c) reflexive relation d) symmetric relation r elation

11. 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) a  (b  c)  (a  b)  c b) b  c  c  b c) (b  c)  (a  b) d) a  b  c

12. Let (A, ) be an algebraic system where semigroup if it satisfies the a) closure law b) associative law

 is a binary operation on A. Then (A, ) is called a











d) closure and associative law

13. 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

14. A commutative ring is said to be an integral domain if it has no ……………….. a) zero divisors b) inverse c) multiples d) identity

15. Reasoning is a special kind of thinking called as ………………… a) inferring b) logics c) bijective d) contradictive











a) prime divisor b) prime statement c) bijective statement d) statement

17. A set is a collection of ……………….. a) well defined objects b) undefined objects c) objects d) only numbers

18. Two sets A and B are said to be …………., if A is a subset of B and B is a subset o f A. a) proper subsets b) void c) equal d) unequal

19. “Any non-empty subset of the set of all positive integers contains a smallest element”. This principle is called as a) well ordering principle













d) ungrouping principle

20. If d n , then

n d

is called the ………………… to d

a) addition conjugate b) subtractive conjugate c) divisor conjugate d) multiplicative multiplicative conjugate

21. A language L can be considered as a subset o f the free …………… on an alphabet. a) group b) Monoid c) ring d) vector













a) logic b) sets c) rings d) groups

24. If S is a poset and a , b are b are in S such S such that a > a > b and b and there is no c in c in S such that a > a > c and c and c > c > b then b then we say that a) b covers a b) a covers b c) a uncovers b d) b uncovers a

25. A finite- state machine is an abstract model of a machine with a primitive ……………………. a) circuit b) internal memory











d) functions

27. Suppose that x1......... xn  Z 2n and y  y1............. y n  Z 2n then the distance between x and x and y is y is a)  ( x, y )  { j  1,....,n : x j  y j } b)  ( x, y)  { x  1,....,n : x j  y j } c)  ( x, y )  { j  1,....,n : x j  y j } d)  ( x, y)  { y  1,....,n : x j  y j }

28. The probability of the string e  Z 2n having exactly k 1’s is ………..

 n  a)   p k (1  p) n  k   n  b)   p k (1  p) nk  k 

 n  c)   p k (1 p ) nk











b) 2 c) 2

A

 A

d)  2

A

30. Let

 and  be any two fuzzy subsets of a set S. Then  is said to be contained in  if

……………..

a)  ( x)   ( x)  x  S b)  ( x)   ( x)  x  S c)  ( x)   ( x)  x  S d)  ( x)   ( x)  x  S

31. An edge having the same vertex as both its end vertices is called a ………………. a) self edge b) self loop











d) 4 – complex

33. A tree without any edge is called as a ……………… a) group tree b) self tree c) branch d) null tree

34. A connected graph without circuits is called a ……………. a) unique tree b) vertex c) decision tree d) mail tree

35. A given connected graph G is an Euler graph

 all the vertices of G are of …………….













a)

b)

c)

d)

(n  k ) (n  k  1) 2 (n  k ) (n  k  1) 2 (n  k ) (n  k  1) 2

(n  k  1) 2

37. A graph G is said to be a …………………….. if there exists some geometric representation of G which can be drawn on a plane such that no two of its edges intersect. a) non-planar graph b) planar graph











a) unity b) non-zeroes c) real numbers d) zeroes

40. Two graphs G 1 and G2 are isomorphic if and only if their incidence matrices I(G 1) and I(G2) differ only by …………. of rows and columns

a) combinations b) shuffling c) permutations d) cyclic permutation permutation











b) 2n + 1 c) 2n – 1 d) 1 – 2n

43. In how many ways can a lady wear five rings on the fingers (not the thumb) of her right hand? a) 6620 b) 6720 c) 6520 d) 6700











d) least element

46. Square roots of unity is an abelian group with respect to a) division b) addition c) multiplication d) subtraction subtraction

47. A finite integral domain is a …………. a) subfield b) vector











49. If S  n, then A(S )  a) (n – 2)! b) n! c) (n – 3)! d) (n – 1)!

50. If d n and n d then ………….. a) d  n b) d  n c) d  n













b) n c) n – 2 d) n – 3

53. Let A = {a, { a, b }, }, if L1 consists of all words beginning with an a and a and followed by zero or more s, b’ s,

then the language over A is











c)  d)  + 

56. State whether true(T) or false(F) (i) A tree is a connected graph without any circuits (ii) A single vertex in a graph G is not a sub-graph of G











i) An Euler graph G is arbitrarily traceable from vertex v in G if and only if every circuit in G contains v ii) If a graph has exactly has exactly two vertices of odd degree, then there exists a path joining these two vertices. a) i) F ii)T b) i) T ii)F c) i) T ii)T











b) i) T ii)F c) i) T ii)T d) i) F ii)F

Part C (Four mark questions)











c) L(G)={1, 110, 11110, 1010110,….} d) L(G)={0, 110, 11110, 1111110,….}

64. In a Boolean algebra for all a, b a) a

B, a  (a  b) 













c) 0.00036 d) 0.000306











(i) The number of labeled trees with n vertices is n ( n2) . (ii) Every disconnected graph has atleast one spanning tree.











c) (i) T

(ii) T

d) (i) F (ii) F











74. The compound proposition [ p  ( p  q)]  p is a











MC0063 Discrete Mathematics Model Question Paper

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