Whether the relation R on the set of
all integers is reflexive, symmetric, antisymmetric, or transitive, where 
if and only if 
if and only if
► 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 
then R is
* ► Antisymmetric
► Symmetric
► Irreflexive
Question No: 3 ( Marks: 1 ) - Please choose one
If (
) = A, then (
) = B
► True
► False
► Cannot be determined
Question No: 4 ( Marks: 1 ) - Please choose one
Let
►-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 
►
46
► 29
► 49
6(9-1)+1
=> 6(8)+1 => 49
Question No: 7 ( Marks: 1 ) - Please choose one
In
probability distribution random variable f satisfies the conditions
► 
► 
► 
► 
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
► 
► 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 È (B È C) = (A È B) È C
► A Ç (B Ç C) = (A Ç B) Ç C
► A È (B Ç C) = (A È B) Ç (A È B)
► None of these
Question No: 13 ( Marks: 1 ) - Please choose one
The
indirect proof of a statement pàq 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
72 = 27 · 2 + 18 => 27 = 18 · 1 + 9 => 18 = 9 · 2 + 0 =>(72, 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
to 
to
► 2
► 3
► 4
Question No: 22 ( Marks: 1 ) - Please choose one
The
value of 
is
► 0
► n(n-1)
► 
► 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(AÈB) = n(A) + n(B)
► n(AÈB) = n(A) +
n(B) - n(AÇB)
► n(AÈB)= ø
► 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 
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
► ~
(pÙq)
► ~ pÚq
► ~ pÙq
► 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 
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
= v =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.
Question No: 39 ( Marks: 5 )
Find n
if
P(n,2) = 72
n.(n-1)=72
n²-n=72
n²-n-72=0
n=9,-8
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