B.TechSemester 22024-25Engineering Mathematics IiBAS203

Engineering Mathematics Ii (BAS203) - AKTU Question Paper 2024-25

B.Tech · Semester 2 · Free PDF Download

This is the official AKTU Engineering Mathematics Ii Previous Year Question Paper for B.Tech 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:B.Tech

Semester:Semester 2

Session:2024-25

University:AKTU / UPTU

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Questions Asked in 2024-25

Engineering Mathematics Ii (BAS203) — complete question paper · 70 marks · 3 Hours

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

a
Find the general solution of the following differential equation
b
Find the Particular Integral for the following differential equation
c
Find Laplace Transform of f(t) = sin 2𝑡 cos 3𝑡
d
Find inverse Laplace Transform of 𝐹(s) =

Test the convergence of the following sequence:

𝑎𝑛 = {
  1  if 𝑛 = 2𝑝 for some 𝑝 ∈ 𝑁
𝑛  otherwise

f
Show that the following function is harmonic
g
Find the residue at the simple pole of the following function

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

a
Find the general solution of the differential equation
b
Solve the following differential equations using Laplace Transform
c
Test the convergence of the following series If 𝑓(𝑧) = 𝑢 + 𝑖𝑣 is analytic, and cos sin cosh cos ye x xuv yx −+−= − , find 𝑓(𝑧) such that cos sin cosh cos ye x xuv yx
e
Evaluate the following integral using contour integration. where, cis the circle

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

a
Find the general solution of the differential equation
b
Solve the following set of simultaneous linear differential equations
a
Find the Laplace Transform of the following function: 𝑒𝑡 sin 𝑡
b
Use convolution theorem to evaluate
a
Examine the convergence of the following series
b
Obtain the Fourier series for the function 𝑓(𝑥) = 𝑥2, −𝜋 ≤ 𝑥 ≤ 𝜋. Hence, or otherwise show that

𝑓(𝑧) = {
show that
()fz  is not analytic at
0z=  even if Cauchy -Riemann
equations are satisfied at origin

b
Show that 𝑓(𝑧) = 𝑧|𝑧| is nowhere analytic
a
State Cauchy’s Integral Theorem. Verify Cauchy’s theorem for () izf z e= integrated along the boundary of the rectangle in counterclockwise direction
b
Use contour integral to evaluate: 2 cos 2 5 4cos

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.