MCASemester 12024-25Discrete MathematicsKCA104

Discrete Mathematics (KCA104) - AKTU Question Paper 2024-25

MCA · Semester 1 · Free PDF Download

This is the official AKTU Discrete Mathematics Previous Year Question Paper for MCA Semester 1, academic session 2024-25. Published by Dr. A.P.J. Abdul Kalam Technical University (AKTU/UPTU), Lucknow. Free PDF download — no login required.

Course:MCA

Semester:Semester 1

Session:2024-25

University:AKTU / UPTU

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Questions Asked in 2024-25

Discrete Mathematics (KCA104) — complete question paper · 100 marks · 3 Hours

Section AAttempt all questions in brief. 2 x 10 = 20

a
Find the Cartesian product A × B when A = {1, 2, 3} and B = {a , b, c
b
Describe the different types of relations. 1 K1, K2
c
Compare the properties of modul ar and complemented lattices. 2 K2, K3
d
Summarize the importance of Hasse diagrams in representing par tially ordered sets
e
Explain the difference between universal and existential quantifiers. 3 K3, K4
f
Classify Mathemat ical Induction. 3 K3, K4
g
Categorize groups. 4 K3, K4
h
Compare the properties of rings and fields. 4 K3, K4 i. Define Peano’s axioms. 5 K1, K3 j. Define pigeonhole principle. 5 K1, K3

Section BAttempt any three of the following: 10 x 3 = 30

a
Summarize the key properties of functions, including injecti ve, surjective, and bijective functions, and discuss their signific ance in mathematical modeling
b
Explain the significance of l ogic gates in digital circuits. D i s c u s s h o w NAND and NOR gates are functionally complete
c
Solve how truth tables can be used to determine logical equi valences. Provide an example of two logically equivalent statements
d
Simplify the role of homomorphism and isomorphism in group t heory. Provide examples where these concepts are applicable
e
Show how Polya’s counting theorem can be used to determine t he number of distinct colorings of a hexagonal object using 3 colors

Section CAttempt any one part of the following: 10 x 1 = 10

a
Show that if a function f: A → B is both injective and surje ctive, then it is bijective. Provide an example and counterexample
b
Explain the difference between recursively defined functions a n d explicitly defined functions. Provide an example of each
a
Apply the simplified Boolean expression for the function F(A, B , C) = A'B + AB' + ABC using Karnaugh maps. Show all steps
b
Solve and minimize the Boolean function F(A, B, C, D) = A'B + A'CD + BCD. 2 K2, K3
a
Analyze the truth table for the compound proposition (P → Q) ∧ ( ¬ Q →¬P) and determine whether it is a tautology, contradiction, or contingency
b
Inspect the validity of the argument using the rules of inferen ce: Premises: (P ∨ Q), (¬P → R), (¬Q → S), (¬R ∨ ¬S) Conclusion: ¬P ∧ ¬Q
a
Solve the order of a group with 10 elements under modulo additi on and verify whether it forms an Abelian group
b
Inspect whether the set of inte gers under multiplication forms a group. Justify your answer with group properties
a
Compute the sum of the first 50 natural numbers using mathematical induction. 5 K1, K3
b
Determine the number of ways to distribute 10 identical objects among 4 people using combinatorial techniques

Question text is extracted from the official AKTU question paper PDF above. Hindi translations are omitted — every question is printed in English in the original paper. Last verified: 2026-08-23.

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