BCASemester 22024-25Discrete MathematicsBBC202

Discrete Mathematics (BBC202) - AKTU Question Paper 2024-25

BCA · Semester 2 · Free PDF Download

This is the official AKTU Discrete Mathematics Previous Year Question Paper for BCA Semester 2, academic session 2024-25. Published by Dr. A.P.J. Abdul Kalam Technical University (AKTU/UPTU), Lucknow. Free PDF download — no login required.

Course:BCA

Semester:Semester 2

Session:2024-25

University:AKTU / UPTU

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Questions Asked in 2024-25

Discrete Mathematics (BBC202) — complete question paper · 70 marks · 3 Hours

Section AAttempt all questions in brief. 02 x 7 = 14

a
Define Union and intersection of sets with suitable example. 1 K 2
b
What do you mean by recursively defined function? Give an example
c
Find the generating function for the finite sequence < 3, 3, 3 , 3, 3, 3 >
d
On the set of integers ∗ is defined by 𝑎∗𝑏ൌ𝑎൅𝑏൅2 . Find the inverse
e
Prove that every cyclic gro up is an abelian group
f
Write the statement into symbols: A number x is less than 7 an d greater than 5
g
Define Lattices with suitable example

Section BAttempt any three of the following: 07 x 3 = 21

a
If in a city 1000 families, it was found that 40% families buy newspaper A, 20% families buy Newspaper B, and 10% buy C. Only 5% families buy A and B, 3% buy B and C and 4% buy A and C and 2% families buy all the thre e newspapers. Find the number of families which buy: (a) A only (b) B only (c ) None of A, B and C
b
Define Discrete Numeric functio n with suitable example
c
Show that 𝐺ൌሼ 1 , െ 1 , 𝑖 , െ 𝑖 ሽ is a finite abelian multiplicative group of order four
d
Show that 𝑝↔𝑞 and ሺ𝑝→𝑞 ሻ˄ሺ𝑞 → 𝑝ሻ are logically equivalent
e
Draw the Hasse diagram, for the partial ordering ሼሺ𝐴,𝐵 ሻ :𝐴 ⊆𝐵 ሽ on the power set ℘ሺ𝑆ሻ, where 𝑆 ൌ ሼ 𝑎 ,𝑏 ,𝑐 ሽ

Section CAttempt any one part of the following: 07 x 1 = 07

a
Let 𝑓:𝑅 → 𝑅 be a function defined by 𝑓ሺ𝑥ሻ ൌ 𝑎𝑥 ൅ 𝑏 𝑤ℎ𝑒𝑟𝑒 𝑎, 𝑏, 𝑥𝜖𝑅 and 𝑎്0 . Show that f is invertible and find inverse of f
b
Given 𝐴 ൌ ሼ1,2,3,4ሽ. Consider the following relation in A
a
Draw its directed graph
b
Is R (i) reflexive (ii) symmetric, (iii) transitive
a
Use Mathematical Induction to prove that ଶ୬ାଵ for n ൒ 1
b
Solve the recurrence relation𝑎௥ െ7 𝑎௥ିଵ ൅1 0 𝑎௥ିଶ ൌ0 withconditions𝑎଴ ൌ3 , 𝑎ଵ ൌ3
a
Let ℚ be the set of rational numbers and defined 𝑎∗𝑏ൌ𝑎൅𝑏െ 𝑎𝑏,thenshow that the structure ሺ ℚ, ∗ሻ is Semi-group
b
If 𝑓:𝐺 → 𝐺ᇱ is a homomorphism, then prove that 𝑓ሺ𝑒ሻ ൌ𝑒 ᇱ, where e and 𝑒ᇱ are identity element of G and𝐺ᇱ
a
Show that ሾ𝑝→ሺ 𝑞→𝑟 ሻሿ → ሾሺ𝑝→𝑞 ሻ → ሺ𝑝→𝑟 ሻሿ is a tautology
b
Write the contrapositive, conve rse and inverse of statement “Indian team wins whenever match played in Kolkata, home town of Ganguly”
a
Prove that the set of integers with usual ordering ൑ read as “less than or equal to” is a poset
b
Show that every chain is a Lattice

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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