MCASemester 12025-26Discrete MathematicsBMC104

Discrete Mathematics (BMC104) - AKTU Question Paper 2025-26

MCA · Semester 1 · Free PDF Download

This is the official AKTU Discrete Mathematics Previous Year Question Paper for MCA Semester 1, academic session 2025-26. 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:2025-26

University:AKTU / UPTU

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Questions Asked in 2025-26

Discrete Mathematics (BMC104) — complete question paper · 70 marks · 3 Hours

Section AAttempt all q u e s t i o n s i n b r i e f . 02 x 7 = 14

a
Is function 𝒇:𝑹 → 𝑹 , defined as 𝒇ሺ𝒙ሻ ൌ |𝒙| ൅𝒙 , one to one? Reason?
b
Define Multiset with an example
c
Define Lattice and Com plete lattice
d
Use quantifiers to express the statement “All students in the class have taken a course in Discrete Mathematics” and also write its negation
e
State the Lagrange’s theorem w ith reference to Group theory. 4 K 1
f
Test whether the permutation ቀ𝟏 𝟐 𝟑 𝟒 𝟓 𝟔 𝟏 𝟒 𝟑 𝟓 𝟐 𝟔ቁ is even permutation or odd permutation?
g
Use Pigeonhole principle to find the minimum number of student s in a class to be sure that four out of them are born in the same month

Section BAttempt any three o f t h e f o l l o w i n g : 07 x 3 = 21

a
Let 𝑹 be a relation in a set of integers 𝒁, defined by 𝑹ൌሼ ሺ𝒙, 𝒚ሻ: 𝒙 െ 𝒚 is divisible by 𝟔 , 𝒙∈𝒁 , 𝒚∈𝒁 ሽ. Justify that 𝑹 is an equivalence relation or partially ordered relation in 𝑍
b
Convert the Boolean expression ሾሺ𝒙𝒚ᇱ ൅𝒙 𝒛 ሻᇱ ൅𝒙 ᇱሿ into Disjunctive normal form and Conjunctive normal form
c
Check the validity of t he following argument: If 2 is an odd number then 4 does not divide 10. Either 11 is n ot a prime number or 4 divides 10. But 11 is a prime number, therefore 2 i s an even number
d
Prove that the set of all positive rational numbers 𝑄ା forms an abelian group under the operation ′ ∗ ′, defined as 𝒂∗𝒃ൌ
e
Solve the followi ng Recurrence relation: 𝒂𝒓 െ𝟕 𝒂𝒓ି𝟏 ൅ 𝟏𝟎𝒂𝒓ି𝟐 ൌ𝒓൅𝟐 given 𝒂𝟎 ൌ𝟏 , 𝒂𝟏 ൌ𝟏

Section CAttempt any one p a r t o f t h e f o l l o w i n g : 07 x 1 = 07

a
ሺ𝑖ሻ is function 𝒇: 𝑹 → 𝑹 , given by 𝒇ሺ𝒙ሻ ൌ𝐜 𝐨 𝐬 𝒙 , bijective? Justify. ሺ𝑖𝑖ሻ Let a function : 𝑹 → 𝑹 , given by 𝒇ሺ𝒙ሻ ൌ𝒙 𝟐 then find 𝒇ି𝟏ሺ𝟏𝟔ሻ and 𝒇ି𝟏ሺെ𝟏𝟔ሻ
b
If 𝑨,𝑩 ,𝑪 are three sets then show that ሺ𝑨 െ𝑩 ሻ 𝑿 𝑪 ൌሺ𝑨 𝑿 𝑪ሻ െሺ 𝑩 𝑿 𝑪ሻ
a
Let 𝑨 ൌ ሼ𝟏, 𝟐, 𝟑, 𝟒, 𝟔, 𝟖, 𝟗, 𝟏𝟐, 𝟏𝟖, 𝟐𝟒ሽ be any set. The relation ′≼′ in set 𝑨 is defined as 𝒙≼𝒚 when 𝒙 divides 𝒚. diagram for this poset and hence list all the maximal, minimal, g r e a t e s t and least elements of the poset
b
Draw a logic gate circuit f or the following Boolean expression: Also draw a circuit for the minimized form of above Boolean expression
a
T e s t w h e t h e r t h e s t a t e m e n t 𝒑 ⇒ሺ~𝒒 ⋁ 𝒓ሻ is a tautology or a contradiction or a contingency. Also, test whether 𝒑 ⇒ሺ~𝒒 ⋁ 𝒓ሻ ≡ ሺ𝒑⇒~ 𝒒ሻ ⋁ሺ𝒑 ⇒ 𝒓ሻ
b
Define quantifiers and its type s with suitable examples. Tra nslate each of the following statements into sy mbols using quantifiers, variab les and predicate symbols: ሺ𝑖ሻ There is a student who can speak Tamil and who knows C ൅ ൅ ሺ𝑖𝑖ሻ There is a student who can speak Tamil but does not know C ൅ ൅ ሺ𝑖𝑖𝑖ሻ Every student either can speak Tamil or knows C ൅ ൅ ሺ𝑖𝑣ሻ No student can speak Tamil or knows C ൅ ൅
a
If 𝑹 be a group of real numbers under addition and let 𝑹ା be the group of positive real numbers under multiplication. Let 𝒇: 𝑹 → 𝑹ା be defined as 𝒇ሺ𝒙ሻ ൌ𝒆 𝒙 then show that 𝒇 is an isomorphism
b
Prove that the set 𝑹ൌሼ 𝒂൅𝒃√𝟓 ∶ 𝒂, 𝒃 are integersሽ is a commutative ring with unity with respect to usual addition and multiplication
a
Show that 𝒏𝟐 ൐ ሺ𝟐𝒏 ൅ 𝟏ሻ for 𝒏൒𝟑 by Mathematical Induction
b
Find Generating functions of t he following numeric functions

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.

Repeated Questions — BMC104

Questions that appeared in more than one session, found by comparing 2 years of Discrete Mathematics papers (2024-25, 2025-26)

Solve the followi ng Recurrence relation: 𝒂𝒓 െ𝟕 𝒂𝒓ି𝟏 ൅ 𝟏𝟎𝒂𝒓ି𝟐 ൌ𝒓൅𝟐 given 𝒂𝟎 ൌ𝟏 , 𝒂𝟏 ൌ𝟏

Appeared in: 2024-25 · 2025-26

Find Generating functions of t he following numeric functions

Appeared in: 2024-25 · 2025-26

Discrete Mathematics — Other Year Papers

AKTU Discrete Mathematics PYQs from other sessions

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