FINALTERM EXAMINATION
Fall 2009
MTH202- Discrete Mathematics
Time: 120 min
Marks: 80
Question No: 1 ( Marks: 1 ) - Please choose one
The negation of “Today is Friday” is
► Today is Saturday
► Today is not Friday
► Today is Thursday
Question No: 2 ( Marks: 1 ) - Please choose one
In method of proof by contradiction, we suppose the
statement to be proved is false.
► True
► False
Question No: 3 ( Marks: 1 ) - Please choose one
Whether the relation R on the set of all integers is reflexive,
symmetric, antisymmetric, or transitive, where (x, y)ÎR if and
only if xy ³1
► Antisymmetric
► Transitive
► Symmetric
► Both Symmetric and transitive
Question No: 4 ( Marks: 1 ) - Please choose one
The inverse of given relation R = {(1,1),(1,2),(1,4),(3,4),
(4,1)} is
► {(1,1),(2,1),(4,1),(2,3)}
► {(1,1),(1,2),(4,1),( 4,3),(1,4)}
► {(1,1),(2,1),(4,1),(4,3),(1,4)}
Question No: 5 ( Marks: 1 ) - Please choose one
A circuit with one input and one output signal is called.
► NOT-gate (or inverter)
► OR-
► AND- gate
► None of these
Question No: 6 ( Marks: 1 ) - Please choose one
A sequence in which common difference of two consecutive
terms is same is called
► geometric mean
► harmonic sequence
► geometric sequence
► arithmetic progression page147
Question No: 7 ( Marks: 1 ) - Please choose one
If the sequence { } 2.( 3) 5 n n
n a = - + then the term ! a is
► -1
► 0
► 1
► 2
Question No: 8 ( Marks: 1 ) - Please choose one
How many integers from 1 through 100 must you pick in order
to be sure of getting one that is divisible by 5?
► 21
► 41
► 81
► 56
Question No: 9 ( Marks: 1 ) - Please choose one
What is the probability that a randomly chosen positive
two-digit number is a multiple of 6?
► 0.5213
► 0.167 pg252
► 0.123
Question No: 10 ( Marks: 1 ) – Please choose one
If a pair of dice is thrown then the probability of getting a
total of 5 or 11 is
► 1
18
► 1
9
►
1
6
pg256
Question No: 11 ( Marks: 1 ) - Please choose one
If a die is rolled then what is the probability that the
number is greater than 4
►
1
3
►
3
4
►
1
2
Question No: 12 ( Marks: 1 ) - Please choose one
If a coin is tossed then what is the probability that the
number is 5
► 1
2
► 0
► 1
Question No: 13 ( Marks: 1 ) - Please choose one
If A and B are two sets then The set of all elements that
belong to both A and B , is
► A B
► A U B
► A--B
► None of these
Question No: 14 ( Marks: 1 ) - Please choose one
If A and B are two sets then The set of all elements that
belong to A but not B , is
► A B
► A B
► None of these
► A-B
Question No: 15 ( Marks: 1 ) - Please choose one
If A, B and C are any three events, then
P(ABC) is equal to
► P(A) + P(B) + P(C)
► P(A) + P(B) + P(C)- P(AB) - P (A C) - P(B C) + P(A B
C)
► P(A) + P(B) + P(C) - P(AB) - P (A C) - P(B C)
► P(A) + P(B) + P(C) + P(A B C)
Question No: 16 ( Marks: 1 ) - Please choose one
If a graph has any vertex of degree 3 then
► It must have Euler circuit
► It must have Hamiltonian circuit
► It does not have Euler circuit
Question No: 17 ( Marks: 1 ) - Please choose one
The contradiction proof of a statement pq involves
► Considering p and then try to reach q
► Considering ~q and then try to reach ~p
► Considering p and ~q and try to reach contradiction
► None of these
Question No: 18 ( Marks: 1 ) - Please choose one
How many ways are there to select a first prize winner a
second prize winner, and a third prize winner from 100
different people who have entered in a contest.
► None of these
► P(100,3)
► P(100,97)
► P(97,3)
Question No: 19 ( Marks: 1 ) - Please choose one
A vertex of degree 1 in a tree is called a
► Terminal vertex
► Internal vertex
Question No: 20 ( Marks: 1 ) - Please choose one
Suppose that a connected planar simple graph has 30 edges.
If a plane drawing of this graph has 20 faces, how many
vertices does the graph have?
► 12
► 13
► 14
Question No: 21 ( Marks: 1 ) - Please choose one
How many different ways can three of the letters of the
word BYTES be chosen if the first letter must be B ?
► P(4,2)
► P(2,4)
► C(4,2)
► None of these
Question No: 22 ( Marks: 1 ) - Please choose one
For the given pair of graphs whether it is
► Isomorphic
► Not isomorphic
Question No: 23 ( Marks: 1 ) - Please choose one
On the set of graphs the graph isomorphism is
► Isomorphic Invariant
► Equivalence relation pg304
► Reflexive relation
Question No: 24 ( Marks: 1 ) - Please choose one
A matrix in which number of rows and columns are equal is
called
► Rectangular Matrix
► Square Matrix
► Scalar Matrix
Question No: 25 ( Marks: 1 ) - Please choose one
If the transpose of any square matrix and that matrix are
same then matrix is called
► Additive Inverse
► Hermition Matrix
► Symmetric Matrix
Question No: 26 ( Marks: 1 ) - Please choose one
The number of k-combinations that can be chosen from a set
of n elements can be written as
► nCk pg223
► kCn
► nPk
► kPk
Question No: 27 ( Marks: 1 ) - Please choose one
The value of C (n, 0) =
► 1
► 0
► n
► None of these
Question No: 28 ( Marks: 1 ) - Please choose one
If the order does not matter and repetition is not allowed
then total number of ways for selecting k sample from n. is
► P(n,k)
► C(n,k) pg228
► nk
► C(n+k-1,k)
Question No: 29 ( Marks: 1 ) - Please choose one
If A and B are two disjoint sets then which of the following
must be true
► n(AB) = n(A) + n(B)
► n(AB) = n(A) + n(B) - n(AB)
► n(AB)= o
► None of these
Question No: 30 ( Marks: 1 ) - Please choose one
Among 200 people, 150 either swim or jog or both. If 85
swim and 60 swim and jog, how many jog?
► 125 pg239
► 225
► 85
► 25
Question No: 31 ( Marks: 1 ) - Please choose one
If two sets are disjoint, then PQ is
►
► P
► Q
► PQ
Question No: 32 ( Marks: 1 ) - Please choose one
Every connected tree
► does not have spanning tree
► may or may not have spanning tree
► has a spanning tree
Question No: 33 ( Marks: 1 ) - Please choose one
When P(k) and P(k+1) are true for any positive integer k,
then P(n) is not true for all +ve Integers.
► True
► False
Question No: 34 ( Marks: 1 ) - Please choose one
When 3k is even, then 3k+3k+3k is an odd.
► True
► False
Question No: 35 ( Marks: 1 ) - Please choose one
5n -1 is divisible by 4 for all positive integer values of n.
► True
► False
Question No: 36 ( Marks: 1 ) - Please choose one
Quotient –Remainder Theorem states that for any positive
integer d, there exist unique integer q and r such that n=d.q+
r and _______________.
► 0≤r<d
► 0<r<d
► 0≤d<r
► None of these
Question No: 37 ( Marks: 1 ) - Please choose one
The given graph is
► Simple graph
► Complete graph
► Bipartite graph
► Both (i) and (ii)
► Both (i) and (iii)
Question No: 38 ( Marks: 1 ) - Please choose one
An integer n is even if and only if n = 2k for some integer k.
► True
► False
► Depends on the value of k
Question No: 39 ( Marks: 1 ) - Please choose one
The word "algorithm" refers to a step-by-step method for
performing some action.
► True
► False
► None of these
Question No: 40 ( Marks: 1 ) - Please choose one
The adjacency matrix for the given graph is
►
0 1 1 0 0
1 0 0 1 0
1 0 0 1 1
0 0 1 0 1
1 0 0 1 0
é ù
ê ú
ê ú
ê ú
ê ú
ê ú
êë úû
►
0 1 1 0 1
1 0 0 0 0
1 0 0 1 1
0 0 1 0 1
1 0 1 1 0
é ù
ê ú
ê ú
ê ú
ê ú
ê ú
êë úû
►
0 1 0 0 1
1 0 0 0 0
1 0 0 1 0
0 0 1 0 1
0 0 1 1 0
é ù
ê ú
ê ú
ê ú
ê ú
ê ú
êë úû
► None of these
Question No: 41 ( Marks: 2 )
Let A and B be events with
( ) 1 , ( ) 1 and ( ) 1
2 3 4
P A = P B = P AÇB =
Find
P(B | A)
Ans =
P(A ∩ B) = P(A) P(B|A)
P(B|A)= P(A ∩ B)/ P(A)
= 0.5
Question No: 42 ( Marks: 2 )
Suppose that a connected planar simple graph has 15 edges.
If a plane drawing of this graph has 7 faces, how many
vertices does this graph have?
Vertices-edges+faces=2
V - 15 +7=2
V -8 = 2
V =10
Question No: 43 ( Marks: 2 )
Find integers q and r so that a=bq+r , with 0≤r<b.
a=45 , b=6.
Question No: 44 ( Marks: 3 )
Draw a graph with six vertices, five edges that is not a tree.
Asn:
Here is the graph with six vertices, five edges that is not a
tree
Question No: 45 ( Marks: 3 )
Prove that every integer is a rational number.
Ans:
Every integer is a rational number, since each integer n can
be written in the form n/1. For example 5 = 5/1 and thus 5
is a rational number. However, numbers like 1/2,
45454737/2424242, and -3/7 are also rational; since they
are fractions whose numerator and denominator are integers.
Question No: 46 ( Marks: 3 )
b. Evaluate P(5,2)
c. How many 4-permutations are there of a set of seven
objects?
Question No: 47 ( Marks: 5 )
Find the GCD of 500008, 78 using Division Algorithm.
Question No: 48 ( Marks: 5 )
There are 25 people who work in an office together. Four
of these people are selected to attend four different
conferences. The first person selected will go to a
conference in New York Chicago
third to San Franciso, and the fourth to Miami
such selections are possible?
Ans= 12650
Question No: 49 ( Marks: 5 )
Consider the following graph
(a) How many simple paths are there from 1 v to 4 v ====1
(b) How many paths are there from 1 v to 4 v ?
===========3
(c) How many walks are there from 1 v to 4 v ?==========3
Question No: 50 ( Marks: 10 )
In the graph below, determine whether the following walks
are paths, simple paths, closed walks, circuits,
simple circuits, or are just walk?
vi) v0 e1 v1 e10 v5 e9 v2 e2 v1== paths
vii)v4 e7 v2 e9 v5 e10 v1 e3 v2 e9 v5========, circuits
viii) v2========== closed walks
ix) v5 v2 v3 v4 v4v5=========== closed walks
x) v2 v3 v4 v5 v2v4 v3 v2========= paths
By ADEEL ABBAS, Bhakkar. AdeelAbbasbk@gmail.com
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