DISCRETE STRUCTURE
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BS PROGRAM
GRAND ASSESSMENT TEST
Let A and B be any two arbitrary events then which one of the following is true ?
P( A intersection B) = P(A). P(B)
P(A union B) = P(A) + P(B)
P(AB) = P(A intersection B). P(B)
P(A union B) >= P(A) + P(B)
If X and Y be the sets. Then the set ( X - Y) union (Y- X) union (X intersection Y ) is
equal to?
X union Y
Xc union Yc
X intersection Y
Xc intersection Yc
If G is an undirected planer graph on n vertices with e edges then ?
e<=n
e<=2n
e<=3n
None of these
Which of the following statement is false ?
G is connected and is circuitless
G is connected and has n edges
G is minimally connected graph
G is circuitless and has n-1 edges
Probability that two randomly selected cards from a set of two red and two black
cards are of same color is ?
1/2
1/3
2/3
None of these
The number of circuits that can be created by adding an edge between any two
vertices in a tree is ?
Two
Exactly one
At least two
None
In a tree between every pair of vertices there is ?
Exactly one path
A self loop
Two circuits
n number of paths
The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52
cards to guarantee that three cards are from some same suit is ?
8
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3
9
12
Context free languages are closed under ?
union, intersection
Intersection , complement
union , kleene star
Complement , kleene star
Let R be a symmetric and transitive relation on a set A. Then ?
R is reflexive and hence a partial order
R is reflexive and hence an equivalence relation
R is not reflexive and hence not an equivalence relation
None of above
A graph is a collection of.... ?
Row and columns
Vertices and edges
Equations
None of these
The degree of any vertex of graph is .... ?
The number of edges incident with vertex
Number of vertex in a graph
Number of vertices adjacent to that vertex
Number of edges in a graph
If for some positive integer k, degree of vertex d(v)=k for every vertex v of the graph
G, then G is called... ?
K graph
K-regular graph
Empty graph
All of above
A graph with no edges is known as empty graph. Empty graph is also known as... ?
Trivial graph
Regular graph
Bipartite graph
None of these
Length of the walk of a graph is .... ?
The number of vertices in walk W
The number of edges in walk W
Total number of edges in a graph
Total number of vertices in a graph
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If the origin and terminus of a walk are same, the walk is known as... ?
Open
Closed
Path
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None of these
A graph G is called a ..... if it is a connected acyclic graph ?
Cyclic graph
Regular graph
Tree
Not a graph
Eccentricity of a vertex denoted by e(v) is defined by.... ?
max { d(u,v): u belongs to v, u does not equal to v : where d(u,v) is the distance between
u&v}
min { d(u,v): u belongs to v, u does not equal to v }
Both A and B
None of these
Radius of a graph, denoted by rad(G) is defined by.... ?
max {e(v): v belongs to V }
min { e(v): v belongs to V}
max { d(u,v): u belongs to v, u does not equal to v }
min { d(u,v): u belongs to v, u does not equal to v }
The complete graph K, has... different spanning trees?
nn-2
n*n
nn
n2
A tour of G is a closed walk of graph G which includes every edge G at least once. A
..... tour of G is a tour which includes every edge of G exactly once ?
Hamiltonian
Planar
Isomorphic
Euler
Which of the following is not a type of graph ?
Euler
Hamiltonian
Tree
Path
Choose the most appropriate definition of plane graph ?
A graph drawn in a plane in such a way that any pair of edges meet only at their end
vertices
A graph drawn in a plane in such a way that if the vertex set of graph can be partitioned
into two non - empty disjoint subset X and Y in such a way that each edge of G has one
end in X and one end in Y.
A simple graph which is Isomorphic to Hamiltonian graph
None of these
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A continuous non - intersecting curve in the plane whose origin and terminus
coincide ?
Planer
Jordan
Hamiltonian
All of these
Polyhedral is.... ?
A simple connected graph
A plane graph
A graph in which the degree of every vertex and every face is atleast 3
All of above
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A path in graph G, which contains every vertex of G once and only once ?
Eulartour
Hamiltonian Path
Eular trail
Hamiltonian tour
A minimal spanning tree of a graph G is.... ?
A spanning sub graph
A tree
Minimum weights
All of above
A tree having a main node, which has no predecessor is.... ?
Spanning tree
Rooted tree
Weighted tree
None of these
Diameter of a graph is denoted by diam(G) is defined by.... ?
max (e(v) : v belongs to V)
max( d(u,v) )
Both A and B
None of these
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A vertex of a graph is called even or odd depending upon ?
Total number of edges in a graph is even or odd
Total number of vertices in a graph is even or odd
Its degree is even or odd
None of these
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Let A and B be any two arbitrary events then which one of the following is true ?
P( A intersection B) = P(A). P(B)
P(A union B) = P(A) + P(B)
P(AB) = P(A intersection B). P(B)
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P(A union B) >= P(A) + P(B)
If X and Y be the sets. Then the set ( X - Y) union (Y- X) union (X intersection Y ) is
equal to?
X union Y
Xc union Yc
X intersection Y
Xc intersection Yc
If G is an undirected planer graph on n vertices with e edges then ?
e<=n
e<=2n
e<=3n
None of these
Which of the following statement is false ?
G is connected and is circuitless
G is connected and has n edges
G is minimally connected graph
G is circuitless and has n-1 edges
Probability that two randomly selected cards from a set of two red and two black
cards are of same color is ?
1/2
1/3
2/3
None of these
The number of circuits that can be created by adding an edge between any two
vertices in a tree is ?
Two
Exactly one
At least two
None
In a tree between every pair of vertices there is ?
Exactly one path
A self loop
Two circuits
n number of paths
The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52
cards to guarantee that three cards are from some same suit is ?
8
3
9
12
Context free languages are closed under ?
union, intersection
Intersection , complement
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union , kleene star
Complement , kleene star
Let R be a symmetric and transitive relation on a set A. Then ?
R is reflexive and hence a partial order
R is reflexive and hence an equivalence relation
R is not reflexive and hence not an equivalence relation
None of above
How many bytes are required to encode 2000 bits of data:
A. 2
B. 1
C. 3
D. 10
A collection of graph is:
A. row and coloumn
B. Equation
C. vertices and columns
D. None of above
The number of edges in a complete graph with „n‟ vertices is equal to:
A. 2n-1
B. n(n-1)
C. n^2
D. n(n-1)/2
Error correcting code is a _____:
A. hamming code
B. gray code
C. error deducting code
D. none of above
5. The symbol II is ASCII stands for:
A. international information
B. information interchange
C. American Standard Code for Information Interchange
D. none of above
6. What is domain of function f(x)= x1/2:
A. [0, ∞)
B. (2, ∞)
C. (-∞, 1)
D. none of above
7. ordered collection of objects is:
A. Relation
B. set
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C. proposition
D. Function
8. A function is a Domain of:
A. it is set of natural numbers for which a function is defined
B. the maximal set of numbers for which a function is defined
C. the maximal set of numbers which a function can take values
D. none of above
9. Range of a function is :
A. the maximal set of numbers for which a function is defined
B. the maximal set of numbers which a function can take values
C. it is set of natural numbers for which a function is defined
D. none of above
10. In an undirected graph the number of nodes with odd degree must be:
A. odd
B. prime
C. even
D. zero
11. What is the cardinality of the set of odd positive integers less than 10?
A. 5
B. 10
C. 3
D. 20
2. The Gray code of a number whose binary representation is 1000 is:
A. 0100
B. 1100
C. 0111
D. 0110
1. The function q ∨ r is equal to the function:
A. ((p ∨ r) ∨ q) ∧ (p ∨ r)
B. (p ∧ q) ∨ (p ∧ r)
C. (p ∨ q) ∧ ∼(p ∨ r)
D. (p ∨ (r ∨ q)) ∧ ∼(∼q ∧ ∼r)
2. The truth table for (p ∨ q) ∨ (p ∧ r) is the same as the truth table for:
A. p ∨ q
B. (p ∨ q) ∧ r
C. (p ∨ q) ∧ (p ∧ r)
D. (p ∨ q) ∧ (p ∨ r)
3. How many have all the vowels together in word MISAPPREHENSION:
A. 15!/2!2!2!2!2!
B. 10!/2!2!2! × 6!/2!2!
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C. 13!/2!2!2!2!
D. None of the above
4. The Boolean function [∼(∼p∧q)∧∼(∼p∧∼q)]∨(p∧r) is equal to the Boolean
function:
A. q
B. p ∧ r
C. p
D. None of the above
5. In how many ways can a hungry student choose 3 toppings for his prize from a
list of 10 delicious possibilities?
A. 123
B. 220
C. 130
D. 120
6. Which of the following statements is FALSE:
A. (P ∧ Q) ∨ (∼P ∧ Q) ∨ (P ∧ ∼Q) is equal to ∼Q ∧ ∼P
B. (P ∧ Q) ∨ (∼P ∧ Q) ∨ (P ∧ ∼Q) is equal to Q ∨ P
C. (P ∧ Q) ∨ (∼P ∧ Q) ∨ (P ∧ ∼Q) is equal to Q ∨ (P ∧ ∼Q)
D. (P ∧ Q) ∨ (∼P ∧ Q) ∨ (P ∧ ∼Q) is equal to [(P ∨ ∼P) ∧ Q] ∨ (P ∧ ∼Q)
7. In any, undirected graph the sum of degrees of all the nodes
A. Must be even
B. Are twice the number of edges
C. Must be odd
D. Need not be even
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8. The walk of a graph length is:
A. The number of vertices in walk W
B. Total number of vertices in a graph
C. Total number of edges in a graph
D. The number of edges in walk W
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9. Definition of a plane graph is:
A. A graph, drawn in a plane in such a way that any pair of edges meet only at their end
vertices
B. A graph, drawn in a plane in such a way that if the vertex set of the graph can be
partitioned into two non – empty disjoint subset X and Y in such a way that each edge of
G has one end in X and one end in Y
C. A simple graph which is Isomorphic to Hamiltonian graph
D. None of the above
10. A continuous non-intersecting curve in the plane whose origin and terminus
coincide :
A. Jordan
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B. Planer
C. Hamiltonian
D. All of these
o V is an isolated vertex in a graph, then the degree of v is:
A. 2
B. 1
C. 0
D. 3
12. Hasse diagrams are drawn
A. Partially ordered sets
B. Lattices
C. Boolean algebra
D. None of these
Default values in programming are
o global variables
o functions calls
o constants
o all of the above
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We use return statement to return
o numeric value
o a value calling function
o single value
o none
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Which statement is true about inline functions?
o it is not a user-defined function
o with this function , the size of program becomes small
o prototype is omitted
o none
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The local variables are known as
o external variables
o static variables
o dynamic variables
o automatic variables
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When a program is terminated which variable isdestroyed?
o auto variables
o global variables
o register
o local variables
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Data shared among the functions is done with the help of
o register variable
o static variables
o local variables
o global variables
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Which functions are the part of ” math.h” file?
o log
o log()
o tan
o tan(10)
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Which one is not included in “conio.h” file?
o kbhit(10)
o getche()
o gotoxy()
o none
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Which fuction is used by the programmars to convert lowercase letters to uppercase
letters?
o isupper()
o toascii()
o tolower()
o toupper()
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The sequential search in C++ is caleed to be
o binary search
o table search
o linear search
o none of these
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An array has a starting address that is known as
o original address
o base address
o memory address
o all of the above
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Each index is ——-,when the multidimensional array is being accessed
o separated by commas
o surronded by brackets
o separated by colon
o none