B.TechSemester 32022-23Mathematics IiiKAS-303

Mathematics Iii (KAS-303) - AKTU Question Paper 2022-23

B.Tech · Semester 3 · Free PDF Download

This is the official AKTU Mathematics Iii Previous Year Question Paper for B.Tech Semester 3, academic session 2022-23. Published by Dr. A.P.J. Abdul Kalam Technical University (AKTU/UPTU), Lucknow. Free PDF download — no login required.

Course:B.Tech

Semester:Semester 3

Session:2022-23

University:AKTU / UPTU

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Questions Asked in 2022-23

Mathematics Iii (KAS-303) — complete question paper

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

c
Write the formula for Fourier integral representation of a func tion 𝑓ሺ𝑥ሻ w i t h appropriate properties of 𝑓ሺ𝑥ሻ
d
Find Fourier transform of 𝑓ሺ𝑥ሻ ൌ ቄ1, െ1 ൑ 𝑥 ൑ 1
f
Sate Lagrange’s theorem
g
Write the conditions for a relation to be an equivalence relat ion
h
If 𝑓ሺ𝑥ሻ ൌc o sሺlog 𝑥ሻ, then prove that𝑓ሺ𝑎ሻ𝑓ሺ𝑏ሻ െ (i) Draw Hasse diagram for the POSET ሺ𝐴,൑ ሻ, where 𝐴 ൌ ሼ1,2,3,9,18ሽ and relation “൑” is the “divides” relation. (j) Let 𝐴 ൌ ሼ2, 3, 4, 6, 8, 24, 48ሽ with partial ordering of divisibility. Determine all the maximal and minimal elements of 𝐴

Section BAttempt any three of the following: 10x3=30

a
If 𝐿ሼ𝑓ሺ𝑡ሻሽ ൌ𝐹 ሺ 𝑠 ሻ, then prove that
b
Find inverse Fourier sine transform of
c
Show that the set 𝐺ൌሼ 1 , െ 1 , 𝑖 , െ 𝑖 ሽof all 4th roots of unity forms a multiplicative abelian group. Also find the order of each element of 𝐺
d
Establish the following formula by the method of mathematical induction
e
Determine the disjunctive normal form of the following Boolean expression

Section CAttempt any one part of the following: 10x1=10

a
By using the method of Laplace transform, solve the initial value problem
b
Use convolution theorem to find inverse Laplace transform of
a
If𝑓ሺ𝑥ሻ ൌ𝑒 ି|௫|, then prove that the Fourier transform 𝐹ሼ𝑓ሺ𝑥ሻሽ ൌ
b
Solve the following difference equation by using Z- transform
a
Show that the proposition 𝑝∨ ∼ሺ 𝑝∧𝑞 ሻ is tautology
b
Find the congruent solutions of the following
a
Find the solution for the recurrence relation
b
Find the coefficient of 𝑥ଶ଴଴ହ in the generating function 𝐺ሺ𝑥ሻ ൌ
a
Given the Boolean expression 𝑓 ൌ 𝐴𝐵𝐶 ൅ 𝐵𝐶̅𝐷൅ 𝐴̅𝐵𝐶. Then, (i) Make a truth table, (ii) Simplify using 𝑘െ map, (iii) Make a switching circuit of the expression
b
Define distributive lattices. Prove that in a distributive latt ice ሺ𝐿, ∧, ∨ሻ,ሺ𝑎∧𝑏 ሻ ∨ ሺ𝑏∧𝑐 ሻ ∨ ሺ𝑐∧𝑎 ሻ ൌሺ 𝑎∨𝑏 ሻ∧ሺ 𝑏∨𝑐 ሻ∧ሺ 𝑐∨𝑎 ሻ holds for all 𝑎, 𝑏, 𝑐 ∈ 𝐿

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 — KAS-303

Questions that appeared in more than one session, found by comparing 2 years of Mathematics Iii papers (2021-22, 2022-23)

Find Fourier transform of 𝑓ሺ𝑥ሻ ൌ ቄ1, െ1 ൑ 𝑥 ൑ 1

Appeared in: 2021-22 · 2022-23

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