Discrete Mathematics (useful for UGCNET,GATE ,APSET ,Engineering mathematic):Top 50 mcqs

Discrete Mathematics (useful for UGCNET,GATE ,APSET ,Engineering mathematic):Top 50 mcqs

TECHMANACADEMY March 09, 2026

Discrete Mathematics – UGC NET, GATE, APSET & Engineering Mathematics Preparation

Discrete Mathematics is a fundamental subject for competitive exams like UGC NET, GATE, APSET, and Engineering Mathematics courses. This topic covers essential concepts such as logic, set theory, relations, functions, combinatorics, graph theory, and recurrence relations. Understanding discrete mathematics helps in developing strong problem-solving and analytical skills required for computer science, mathematics, and engineering examinations.

In this blog, you will find clear explanations, important formulas, solved examples, practice problems, and exam-oriented notes designed for UGC NET, GATE, APSET, and engineering students. Whether you are preparing for competitive exams or strengthening your mathematical foundation, this guide will help you master discrete mathematics concepts effectively.

Discrete Mathematics – UGC NET, GATE, APSET & Engineering Mathematics Preparation

1. Introduction to Discrete Mathematics

  • Definition of Discrete Mathematics

  • Importance in Computer Science and Engineering

  • Role in competitive exams (UGC NET, GATE, APSET)

  • Real-world applications of discrete mathematics

Keywords: Discrete Mathematics basics, importance of discrete math

2. Why Discrete Mathematics is Important for Competitive Exams

  • Weightage in UGC NET Computer Science

  • Importance in GATE CSE

  • Role in APSET Mathematics / Computer Science

  • Applications in Engineering Mathematics

Exam tips:

  • Focus on logic and combinatorics

  • Practice proof-based problems

3. Propositional Logic

Topics Covered

  • Statements and propositions

  • Logical connectives

  • Truth tables

  • Tautology, contradiction, contingency

  • Logical equivalence

  • Laws of logic

Important Laws

Exam Focus

  • Truth table questions

  • Logical equivalence problems

4. Predicate Logic and Quantifiers

  • Predicates and variables

  • Universal quantifier (∀)

  • Existential quantifier (∃)

  • Negation of quantified statements

Example Problems

  • Translating English sentences into predicate logic

  • Quantifier negation rules

5. Set Theory

Topics Covered

  • Sets and subsets

  • Power set

  • Union, Intersection, Difference

  • Complement of a set

  • Cartesian product

Important Laws

  • Commutative Law

  • Associative Law

  • Distributive Law

  • De Morgan’s Laws for sets

Practice Questions

  • Venn diagram problems

  • Set identities

6. Relations

Types of Relations

  • Reflexive relation

  • Symmetric relation

  • Transitive relation

  • Equivalence relation

Concepts

Exam Focus

  • Checking properties of relations

  • Equivalence class problems

7. Functions

Types of Functions

Important Concepts

  • Inverse functions

  • Composition of functions

  • Identity function

Exam Questions

  • Determining function types

  • Finding inverse functions

8. Counting Techniques (Combinatorics)

Topics Covered

  • Basic counting principles

  • Permutations

  • Combinations

  • Binomial theorem

Important Formulas

  • nPr = n!/(n−r)!

  • nCr = n!/(r!(n−r)!)

Exam Focus

  • Counting problems

  • Binomial expansion

9. Recurrence Relations

Topics Covered

  • Definition of recurrence relations

  • Linear recurrence relations

  • Homogeneous and non-homogeneous recurrence

Methods of Solving

  • Iteration method

  • Characteristic root method

Example Problems

10. Graph Theory

Basic Concepts

  • Graphs and vertices

  • Degree of a vertex

  • Types of graphs

Important Topics

  • Euler graphs

  • Hamiltonian graphs

  • Trees and spanning trees

Applications

  • Network design

  • Shortest path problems

11. Discrete Mathematics Shortcuts for Competitive Exams

  • Memorize logical equivalence laws

  • Practice graph theory problems regularly

  • Focus on combinatorics formulas

  • Solve previous years’ questions

12. Recommended Books

13. Previous Year Question Practice

  • UGC NET Discrete Mathematics questions

  • GATE Discrete Mathematics problems

  • APSET practice questions

14. Tips to Score High in Discrete Mathematics

  • Understand concepts instead of memorizing

  • Practice proofs and logical reasoning

  • Solve mock tests regularly

  • Revise formulas weekly

1. The negation of (p ∧ q) is:
A) ¬p ∧ ¬q
B) ¬p ∨ ¬q
C) p ∨ q
D) p ∧ ¬q
Answer: B

2. Which is a tautology?
A) p ∧ ¬p
B) p ∨ ¬p
C) p → ¬p
D) ¬p → p
Answer: B

3. The contrapositive of p → q is:
A) q → p
B) ¬p → ¬q
C) ¬q → ¬p
D) p ∧ q
Answer: C

4. If p is false and q is true, p → q is:
A) True
B) False
C) Undefined
D) Depends on p
Answer: A

5. (p → q) is equivalent to:
A) ¬p ∨ q
B) p ∨ q
C) ¬p ∧ q
D) p ∧ q
Answer: A

2. Predicate Logic

6. The negation of ∀x P(x) is:
A) ∀x ¬P(x)
B) ∃x ¬P(x)
C) ¬∃x P(x)
D) ∃x P(x)
Answer: B

7. Which is valid?
A) ∀x P(x) → P(a)
B) P(a) → ∀x P(x)
C) ∃x P(x) → ∀x P(x)
D) None
Answer: A

8. The domain of discourse refers to:
A) Variables
B) Constants
C) Set of possible values
D) Functions
Answer: C

9. Existential quantifier means:
A) For all
B) There exists
C) None
D) Exactly one
Answer: B

10. “Some students are intelligent” is:
A) Universal
B) Existential
C) Conditional
D) Biconditional
Answer: B

3. Set Theory

11. If A ⊆ B and B ⊆ A, then:
A) A ∩ B = ∅
B) A = B
C) A ∪ B = ∅
D) A ≠ B
Answer: B

12. Power set of a set with n elements has:
A) n²
B) 2n
C) 2ⁿ
D) n!
Answer: C

13. De Morgan’s law states:
A) (A ∪ B)’ = A’ ∩ B’
B) (A ∩ B)’ = A’ ∪ B’
C) Both
D) None
Answer: C

14. If |A| = 3, number of subsets is:
A) 6
B) 8
C) 9
D) 12
Answer: B

15. Cartesian product A × B consists of:
A) Ordered pairs
B) Unordered pairs
C) Union
D) Intersection
Answer: A

4. Relations

16. A relation R on A is reflexive if:
A) (a,a) ∈ R for all a
B) (a,b) ∈ R
C) (b,a) ∈ R
D) None
Answer: A

17. A relation that is reflexive, symmetric and transitive is:
A) Partial order
B) Equivalence relation
C) Function
D) Injective
Answer: B

18. A partial order must be:
A) Reflexive, symmetric
B) Reflexive, antisymmetric, transitive
C) Symmetric, transitive
D) None
Answer: B

19. Hasse diagram represents:
A) Equivalence relation
B) Partial order
C) Function
D) Set
Answer: B

20. Equivalence relation partitions a set into:
A) Subsets
B) Partitions
C) Ordered pairs
D) None
Answer: B

5. Functions

21. A function is one-one if:
A) f(a1)=f(a2) ⇒ a1=a2
B) Every element of B has pre-image
C) Onto
D) None
Answer: A

22. A function is onto if:
A) Injective
B) Surjective
C) Bijective
D) None
Answer: B

23. Composition of functions is denoted by:
A) f + g
B) f ∘ g
C) f × g
D) f − g
Answer: B

24. A bijective function has:
A) Inverse
B) No inverse
C) Only injective
D) Only surjective
Answer: A

25. Number of functions from m elements to n elements:
A) mⁿ
B) nᵐ
C) mn
D) m+n
Answer: B

6. Combinatorics

26. nPr equals:
A) n!/(n−r)!
B) n!/(r!(n−r)!)
C) r!
D) n!
Answer: A

27. nCr equals:
A) n!/(n−r)!
B) n!/(r!(n−r)!)
C) r!
D) n!
Answer: B

28. Number of ways to arrange n distinct objects:
A) n
B) n²
C) n!
D) 2ⁿ
Answer: C

29. Pigeonhole principle states:
A) At least one box has ≥2 objects
B) No repetition
C) Equal distribution
D) None
Answer: A

30. (a+b)ⁿ has:
A) n terms
B) n+1 terms
C) n² terms
D) 2ⁿ terms
Answer: B

7. Recurrence Relations

31. Fibonacci recurrence is:
A) Fn = Fn−1 + Fn−2
B) Fn = 2Fn−1
C) Fn = Fn−1 − Fn−2
D) None
Answer: A

32. Order of recurrence relation means:
A) Highest power
B) Number of previous terms
C) Degree
D) None
Answer: B

33. Characteristic equation is used in:
A) Linear homogeneous recurrence
B) Set theory
C) Graph theory
D) None
Answer: A

34. A recurrence with constant coefficients is:
A) Linear
B) Non-linear
C) Variable
D) None
Answer: A

35. Initial conditions are also called:
A) Base conditions
B) Boundary
C) Solutions
D) None
Answer: A

8. Graph Theory

36. A simple graph has:
A) No loops and no multiple edges
B) Loops allowed
C) Multiple edges allowed
D) Directed edges
Answer: A

37. Degree of a vertex is:
A) Incoming edges
B) Outgoing edges
C) Total incident edges
D) None
Answer: C

38. Sum of degrees of all vertices equals:
A) E
B) 2E
C) V
D) V²
Answer: B

39. A tree with n vertices has:
A) n
B) n−1
C) n+1
D) n²
Answer: B

40. A graph with no cycles and connected is:
A) Tree
B) Complete
C) Bipartite
D) Null
Answer: A

9. Boolean Algebra

41. Idempotent law:
A) A + A = A
B) A + 0 = A
C) A·1 = A
D) A + A’ = 1
Answer: A

42. Complement law:
A) A + A’ = 1
B) A·A’ = 0
C) Both
D) None
Answer: C

43. Absorption law:
A) A + AB = A
B) A(A+B) = A
C) Both
D) None
Answer: C

44. Dual of A + 0 = A is:
A) A·1 = A
B) A+1=1
C) A·0=0
D) None
Answer: A

45. Boolean algebra is used in:
A) Databases
B) Digital circuits
C) Networking
D) AI
Answer: B

10. Number Theory

46. GCD(12,18) =
A) 2
B) 3
C) 6
D) 9
Answer: C

47. If a|b and b|c, then:
A) a|c
B) c|a
C) a+b
D) None
Answer: A

48. 17 is:
A) Composite
B) Prime
C) Even
D) Perfect
Answer: B

49. If p is prime, φ(p) =
A) p
B) p−1
C) 1
D) 0
Answer: B

50. Modular arithmetic deals with:
A) Division
B) Remainders
C) Factors
D) Roots
Answer: B


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