FINALTERM EXAMINATION
Spring 2010
MTH202- Discrete Mathematics (Session - 1)
Time: 90 min
Marks: 60
Question No: 1 ( 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: 2 ( Marks: 1 ) - Please choose one
For a binary relation R defined on a set A , if for all
t Î A,(t,t)ÏR then R is
► Antisymmetric
► Symmetric
► Irreflexive
Question No: 3 ( Marks: 1 ) - Please choose one
If ( AÈB ) = A, then ( AÇB ) = B
► True
► False
► Cannot be determined
Question No: 4 ( Marks: 1 ) - Please choose one
Let
0 1 2
2
0
1, 2 3
j
j
a a and a
then a
=
= = - =
å =
►-6
►2
►8
Question No: 5 ( Marks: 1 ) - Please choose one
The part of definition which can be expressed in terms of smaller
versions of itself is called
► Base
► Restriction
► Recursion
► Conclusion
Question No: 6 ( Marks: 1 ) - Please choose one
What is the smallest integer N such that 9
6
éN ù = êê úú
► 46
► 29
► 49
Question No: 7 ( Marks: 1 ) - Please choose one
In probability distribution random variable f satisfies the
conditions
►
1
( ) 0 ( ) 1
n
i i
i
f x and f x
=
£ å ¹
►
1
( ) 0 ( ) 1
n
i i
i
f x and f x
=
³ å =
►
1
( ) 0 ( ) 1
n
i i
i
f x and f x
=
³ å ¹
►
1
( ) 0 ( ) 1
n
i i
i
f x and f x
=
p å =
Question No: 8 ( Marks: 1 ) - Please choose one
What is the probability that a hand of five cards contains
four cards of one kind?
► 0.0018
► 1
2
► 0.0024
Question No: 9 ( Marks: 1 ) - Please choose one
A rule that assigns a numerical value to each outcome in a
sample space is called
► One to one function
► Conditional probability
► Random variable
Question No: 10 ( Marks: 1 ) - Please choose one
A walk that starts and ends at the same vertex is called
► Simple walk
► Circuit
► Closed walk
Question No: 11 ( Marks: 1 ) - Please choose one
The Hamiltonian circuit for the following graph is
► abcdefgh
► abefgha
► abcdefgha
Question No: 12 ( Marks: 1 ) - Please choose one
Distributive law of union over intersection for three sets
► A E (B E C) = (A E B) E C
► A C (B C C) = (A C B) C C
► A E (B C C) = (A E B) C (A E B)
► None of these
Question No: 13 ( Marks: 1 ) - Please choose one
The indirect proof of a statement paq involves
►Considering ~q and then try to reach ~p
►Considering p and ~q and try to reach contradiction
*►Both 2 and 3 above
►Considering p and then try to reach q
Question No: 14 ( Marks: 1 ) - Please choose one
The square root of every prime number is irrational
► True
► False
► Depends on the prime number given
Question No: 15 ( Marks: 1 ) - Please choose one
If a and b are any positive integers with b≠0 and q and r are non
negative integers such that a= b.q+r then
► gcd(a,b)=gcd(b,r)
► gcd(a,r)=gcd(b,r)
► gcd(a,q)=gcd(q,r)
Question No: 16 ( Marks: 1 ) - Please choose one
The greatest common divisor of 27 and 72 is
► 27
► 9
► 1
► None of these
Question No: 17 ( Marks: 1 ) - Please choose one
In how many ways can a set of five letters be selected from the
English Alphabets?
► C(26,5)
► C(5,26)
► C(12,3)
► None of these
Question No: 18 ( Marks: 1 ) - Please choose one
A vertex of degree greater than 1 in a tree is called a
► Branch vertex
► Terminal vertex
► Ancestor
Question No: 19 ( Marks: 1 ) - Please choose one
For the given pair of graphs whether it is
► Isomorphic
► Not isomorphic
Question No: 20 ( Marks: 1 ) - Please choose one
The value of (-2)! Is
► 0
► 1
► Cannot be determined
Question No: 21 ( Marks: 1 ) - Please choose one
In the following graph
How many simple paths are there from 1 v to 4 v
► 2
► 3
► 4
Question No: 22 ( Marks: 1 ) - Please choose one
The value of ( )
( 1)!
1 !
n
n
+
- is
► 0
► n(n-1)
► n2 + n
► Cannot be determined
Question No: 23 ( Marks: 1 ) - Please choose one
If A and B are finite (overlapping) sets, then which of the
following must be true
► n(AEB) = n(A) + n(B)
► n(AEB) = n(A) + n(B) - n(ACB) page238
► n(AEB)= o
► None of these
Question No: 24 ( Marks: 1 ) - Please choose one
Any two spanning trees for a graph
► Does not contain same number of edges
► Have the same degree of corresponding edges
► contain same number of edges
► May or may not contain same number of edges
Question No: 25 ( Marks: 1 ) - Please choose one
When 3k is even, then 3k+3k+3k is an odd.
► True
► False
Question No: 26 ( 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: 27 ( Marks: 1 ) - Please choose one
The value of éêxùú for x = -3.01 is
► -3.01
► -3
► -2
► -1.99
Question No: 28 ( Marks: 1 ) - Please choose one
If p= A Pentium 4 computer,
q= attached with ups.
Then "no Pentium 4 computer is attached with ups" is denoted
by
► ~ (pUq)
► ~ pUq
► ~ pUq
► None of these
Question No: 29 ( Marks: 1 ) - Please choose one
An integer n is prime if and only if n > 1 and for all positive
integers r and s, if
n = r·s, then
►r = 1 or s = 2.
►r = 1 or s = 0.
►r = 2 or s = 3.
►None of these
Question No: 30 ( Marks: 1 ) - Please choose one
If P(AÇB) ¹ P(A)P(B) then the events A and B are called
►Independent
►Dependent
►Exhaustive
Question No: 31 ( Marks: 2 )
Let A and B be the events. Rewrite the following event using set
notation
“Only A occurs”
Question No: 32 ( 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?
Answer:
Given,
Edges = e =15
Faces = f = 7
Vertices = v =?
According toEuler Formula, we know that,
f= e – v +2
Putting values, we get
7 = 15 – v + 2
7 = 17 – v
Simplifying
v =1 7-7 =10
Question No: 33 ( Marks: 2 )
How many ordered selections of two elements can be made from
the set {0,1,2,3}?
Answer
The order selection of two elements from 4 is as
P(4,2) = 4!/(4-2)!
= (4.3.2.1)/2!
= 12
Question No: 34 ( Marks: 3 )
Consider the following events for a family with children:
A={children of both sexes}, B={at most one boy}.Show that A and
B are dependent events if a family has only two children.
Question No: 35 ( Marks: 3 )
Determine the chromatic number of the given graph by
inspection.
Question No: 36 ( Marks: 3 )
A cafeteria offers a choice of two soups, five sandwiches, three
desserts and three drinks. How many different lunches, each
consisting of a soup, a sandwiche, a dessert and a drink are
possible?
Question No: 37 ( Marks: 5 )
A box contains 15 items, 4 of which are defective and 11 are good.
Two items are selected. What is probability that the first is good
and the second defective?
Answer
Question No: 38 ( Marks: 5 )
Draw a binary tree with height 3 and having seven terminal
vertices.
Given height=h=3
Any binary tree with height 3 has almost 23=8 terminal vertices.
But here terminal vertices are 7 and Internal vertices=k=6 so
binary trees exist:
Question No: 39 ( Marks: 5 )
Find n if
P(n,2) = 72
(a) P(n,2) = 72
SOLUTION:
(a) Given P(n,2) = 72
Þ n × (n-1) = 72 (by using the definition of permutation)
Þ n2 -n = 72
Þ n2 - n - 72 = 0
Þ n = 9, -8
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