B.TechSemester 42022-23Mathematics IiiKAS-403

Mathematics Iii (KAS-403) - AKTU Question Paper 2022-23

B.Tech · Semester 4 · Free PDF Download

This is the official AKTU Mathematics Iii Previous Year Question Paper for B.Tech Semester 4, 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 4

Session:2022-23

University:AKTU / UPTU

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Questions Asked in 2022-23

Mathematics Iii (KAS-403) — complete question paper

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

a
Evaluate L[ , where represents the unit step function
b
Describe the sufficient condition for the existence of Laplace transform of any function
c
If , evaluate .Here represents the Z-transform of
d
Write the complex form of Fourier integral representation of a function
e
Test whether the permutation is even permutation or odd permutation?
f
State the Lagrange’s theorem with reference to Group theory
g
In a class of 25 students, 12havetakenMathematics, 8 have taken Mathematics but not Biology. Find the number of students who have taken Mathematics & Biology both and also the number of students who have taken Biology but not Mathematics
h
If function is defined as , find and . (i) Define Lattice and Distributive lattice with examples. (j) Prove the following absorption laws in Boolean algebra

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

a
Apply the Convolution theorem to find the inverse Laplace transform
b
Apply the Fourier transform to solve the Heat equation if is bounded for
c
Check the validity of the following argument: If 2 is an odd number then 4 does not divide 10. Either 11 is not a prime number or 4 divides 10. But 11 is a prime number, therefore 12 is an even number
d
Solve the following Recurrence relation: given
e
Convert the Boolean expression into Disjunctive normal form and Conjunctive normal form

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

a
Solve the following differential equation using Laplace transform: given that
b
Find the Laplace transform of the following function
b
Solve the following difference equation using Z-transform: with
b
Test whether the statement is a tautology or a contradiction or a contingency. Also, test whether
a
Show that for by Mathematical Induction
b
Let be a relation in a set of integers , defined by is divisible by . Justify that is an Equivalence relation or Partially ordered relation in
b
Draw a switching circuit for the following Boolean expression: Also draw a logic gate circuit for the minimized form of above Boolean expression

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.