This is a downloaded MCQ (multiple choice question) exam for Lovely Professional University's (LPU) MTH401 Discrete Mathematics course. Sets, ETP (Elementary Theory of Poles), and other course-related subjects are among the topics addressed in the paper's questions. The objective of the MCQ format is to assess the student's comprehension of the core ideas in discrete mathematics.
Lovely Professional University (LPU) is a well-known private university in India that offers a wide range of undergraduate and postgraduate courses, including a course on Discrete Mathematics (MTH401). A large part of computer science and information technology use discrete mathematics, a subfield of mathematics that deals with discrete structures like sets, graphs, and algorithms.
UNIT-WISE Questions - 6 Unit - 20 Questions Per Unit | 120 Questions |
UNIT I LOGIC AND PROOFS
1. What is the negation of the statement "All cats can fly"?
a) No cats can fly
b) Some cats can't fly
c) All cats can't fly
d) Some cats can fly
Answer: c) All cats can't fly
2. Which of the following is a propositional variable?
a) 2+2=4
b) p implies q
c) (x+1)(x-1)=x^2-1
d) There are no unicorns.
Answer: b) p implies q
3. Which of the following is a tautology?
a) p xor q
b) p implies q
c) p and (not p)
d) p or (not p)
Answer: d) p or (not p)
4. What is the contrapositive of the statement "If it rains, then I stay inside"?
a) If I don't stay inside, then it doesn't rain.
b) If I stay inside, then it doesn't rain.
c) If it doesn't rain, then I don't stay inside.
d) If it doesn't rain, then I stay inside.
Answer: b) If I don't stay inside, then it doesn't rain.
UNIT II RECURRENCE RELATIONS
21. What is a recurrence relation?
A) A mathematical equation that describes a sequence of numbers
B) A function that maps elements of one set to another set
C) A binary operation on a set that is associative, commutative, and has an identity element
D) A relation between two sets that assigns to each element of the first set a set of elements from the second set
Answer: A
22. Which of the following is an example of a recurrence relation?
A) f(x) = 3x + 2
B) g(x) = x^2 + 1
C) h(n) = h(n-1) + 3
D) i(x) = sin(x)
Answer: C
23. How can recurrence relations be used to model real-world phenomena?
A) By describing the behavior of a system over time
B) By mapping the inputs and outputs of a function
C) By creating a graph of a set of data points
D) By computing the average of a set of numbers
Answer: A
24. What is a homogeneous linear recurrence relation with constant coefficients?
A) A recurrence relation where all the coefficients are equal
B) A recurrence relation where all the terms are of the same degree
C) A recurrence relation where the coefficients are constants and the non-homogeneous term is zero
D) A recurrence relation where the coefficients depend on the previous terms
Answer: C
The purpose of this MCQ paper is to aid students in getting ready for their exams for the LPU subject MTH401 Discrete Mathematics. It contains a range of questions relating to the core ideas in discrete mathematics, such as sets, ETP, and other subjects. Due to the paper's MCQ format, students can test their topic knowledge in a time-limited manner and build confidence before sitting the final exam.
UNIT III COUNTING PRINCIPLES AND RELATIONS
41. Which principle of counting is used to find the number of elements in the union of two sets A and B
when A and B have some elements in common?
A. Principle of Inclusion-Exclusion
B. Pigeonhole Principle
C. Generalized Pigeonhole Principle
D. None of the above
Answer: A. Principle of Inclusion-Exclusion
42. In how many ways can 5 books be arranged on a shelf if 2 of the books must always be together?
A. 60
B. 120
C. 240
D. 480
Answer: B. 120
43. What is the maximum number of pigeons that can be placed in 4 pigeonholes if each hole can hold at
most 2 pigeons?
A. 4
B. 6
C. 8
D. 10
Answer: C. 8
44. Which principle is used when there are more pigeons than pigeonholes?
A. Principle of Inclusion-Exclusion
B. Pigeonhole Principle
C. Generalized Pigeonhole Principle
D. None of the above
Answer: C. Generalized Pigeonhole Principle
UNIT IV GRAPH 1
61. Which of the following is not a special type of graph?
A) Complete graph
B) Cycle graph
C) Bipartite graph
D) Linear graph
Answer: D) Linear graph
62. Which of the following graphs is not a regular graph?
A) Complete graph
B) Cycle graph
C) Bipartite graph
D) Wheel graph
Answer: D) Wheel graph
63. What is a graph with n vertices and no edges called?
A) Null graph
B) Complete graph
C) Cycle graph
D) Regular graph
Answer: A) Null graph
64. In a complete graph with n vertices, how many edges are there?
A) n
B) n(n-1)/2
C) n(n+1)/2
D) n^2
Answer: B) n(n-1)/2
UNIT V GRAPH THEORY 2
81. Which of the following is a characteristic of planar graphs?
a) Every edge is connected to exactly two vertices
b) Every vertex has an even degree
c) There are no cycles of odd length
d) They can be drawn on a flat surface without any edges crossing
Answer: d) They can be drawn on a flat surface without any edges crossing
82. What is the Euler formula for planar graphs?
a) V - E + F = 1
b) V + E = F + 2
c) E - V + F = 2
d) V + E - F = 1
Answer: c) E - V + F = 2
83. In a graph, what is the chromatic number?
a) The number of edges in a spanning tree
b) The minimum number of colors needed to color the vertices
c) The maximum number of edges in a tree graph
d) The number of connected components in a graph
Answer: b) The minimum number of colors needed to color the vertices
84. What is a tree graph?
a) A graph with no cycles
b) A graph with a single vertex
c) A graph with only two vertices
d) A graph with only three vertices
Answer: a) A graph with no cycles
UNIT VI NUMBER THEORY AND ITS APPLICATION IN CRYPTOGRAPHY
101. Which of the following is not a property of modular arithmetic?
A) Commutativity
B) Associativity
C) Distributivity
D) Transitivity
Answer: D) Transitivity
102. What is the remainder when 1001 is divided by 7?
A) 0
B) 1
C) 2
D) 3
Answer: D) 3
103. Which of the following is not true for a prime number?
A) It is divisible by itself and 1 only
B) It is an odd number
C) It is a natural number
D) It has no positive divisors other than 1 and itself
Answer: B) It is an odd number
104. Which of the following is not a prime number?
A) 2
B) 3
C) 5
D) 6
Answer: D) 6