MCASemester 12022-23Discrete MathematicsKCA-104
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Discrete Mathematics (KCA-104) - AKTU Question Paper 2022-23

MCA · Semester 1 · Free PDF Download

This is the official AKTU Discrete Mathematics Previous Year Question Paper for MCA Semester 1, academic session 2022-23. 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:2022-23
University:AKTU / UPTU

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Questions Asked in 2022-23

Discrete Mathematics (KCA-104) — complete question paper

Section AAttempt all questions in brief. 2 x 10 = 20
  • a
    State the Distributive and As sociative laws of set theory
  • b
    Write down the properties of Equivalence Relation
  • c
    Define the Hasse diagram with example
  • d
    What do you mean by Normal Form in Boolean algebra?
  • e
    Define the term Proposition
  • f
    Negate the statement “ He is poor and laborious”
  • g
    Define Monoid with example
  • h
    Define the Commutative Ring with unity. (i) Solve the recurrence relation: 𝑎௡ െ 3 𝑎௡ିଵ ൅ 2 𝑎௡ିଶ = 0. (j) Write down the properties of Generating function
Section BAttempt any three of the following: 10x3=30
  • a
    If 𝑋ൌ ሼ1,2,3ሽ,𝑌 ൌሼ𝑝, 𝑞ሽ and 𝑍ൌሼ 𝑎 , 𝑏 ሽ and the functions f and g are define as 𝑔 ∶ 𝑌 → 𝑍 be 𝑔ൌ ሼ ሺ𝑝, 𝑞ሻ , ሺ𝑞, 𝑏ሻሽ then find 𝑓𝑜𝑔 𝑎𝑛𝑑 𝑔𝑜𝑓
  • b
    Let L be the set of all factor of 12 and let ‘/’ be the divisibility relation on L. Then show that (L, ‘/’) is a lattice
  • c
    Show that: (p ⟷𝑞 ሻ∧ሺ𝑞⟷𝑟 ሻ ⟶ሺ 𝑝⟷𝑟 ሻ is a Tautology
  • d
    What do mean by Order of an element in a group? Find the order of each element of the multiplicative group g= {1,-1,i,-i}
  • e
    Solve the recurrence 𝑎௡ାଶ െ4 𝑎௡ାଵ ൅4 𝑎௡ ൌ2 ௡
Section CAttempt any one part of the following: 10x1=10
  • a
    Define the function and explain the difference between function and relation with exam
  • b
    For any set A and B, Prove that ∶ 𝑃ሺ𝐴 ∩𝐵 ሻ ൌ 𝑃 ሺ𝐴ሻ ∩ 𝑃ሺ 𝐵ሻ
  • a
    Define Modular Lattice. Also Prove that: Every Distributive lattice is Modular
  • b
    Solve using K-map:𝐹ሺ𝐴,𝐵 ,𝐶 ,𝐷 ሻ ൌ∑ሺ0,1,2,3,4,5,6,7,8,9,11 ሻ
  • a
    Show that s is a valid conclusion from the premises
  • b
    If 𝐾ሺ𝑥ሻ ∶𝑥 𝑖 𝑠 𝑠 𝑡 𝑢 𝑑 𝑒 𝑛 𝑡 , 𝑀ሺ𝑥ሻ: 𝑥 𝑖𝑠 𝑐𝑙𝑒𝑣𝑒𝑟, 𝑁ሺ𝑥ሻ ∶ 𝑥 𝑖𝑠 𝑠𝑢𝑐𝑐𝑒𝑠𝑠𝑓𝑢𝑙. Express the following using quantifiers: (i) There exists a student (ii) Some students are clever (iii) Some students are not successful
  • a
    Define the permutation group. If A= {1, 2, 3, 4, 5} then find
  • b
    Show that G= {0,1,2,3,4} is a cyclic group under addition modulo 5
  • a
    Determine the numeric function corresponding to the following G enerating function
  • b
    Prove by mathematical induction that 𝑛ଷ ൅2 𝑛 is divisible by 3 for each positive integer 𝑛

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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