B.TechSemester 22022-23Engineering Mathematics IiBAS203

Engineering Mathematics Ii (BAS203) - AKTU Question Paper 2022-23

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 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 2

Session:2022-23

University:AKTU / UPTU

Rate this paper

Questions Asked in 2022-23

Engineering Mathematics Ii (BAS203) — complete question paper

Section AAttempt all questions in brief. 2 x 7 = 14

a
Solve: .,)32( 23 dDeyDDD x 
b
Explain the first shifting property of the Laplace transform with example
c
Discuss the convergence of sequence {un}, where )./1(sin nun ᮓ {un} ᭅ ᱶ, )./1(sin nun
d
Show that the function 2||)( zzf  is not analytic at origin
e
Classify the singularity of .)(
f
Find the inverse Laplace transform of .22 1)( 2  sssF
g
Find the invariant points of the transformation .7

Section BAttempt any three of the following: 7 x 3 = 21

a
Solve the following differential equation: .log122 3 2 xxydx dyxdx ydx  (b) Find the Laplace transform of the function xxxf sin)( 3 . Hence, prove that .0sin3  xdxxe x 0sin3  xdxxe x
c
Test the convergence of following series:  xx Where x is a real number
d
Show that the function f(z) defined by 0)0(,0,)()( 106  fzyx iyxyxzf is not analytic at the origin even though it satisfies Cauchy-Riemann equations at the origin.  fzyx
e
Using Cauchy-integral formula, evaluate ,)1)(3( 2sin dzzz z where C is a rectangle with vertices at .2,3 ii  dzzz

Section CAttempt any one part of the following: 7 x 1 = 7

a
Solve the following differential equation by the variation of parameters: .cos2 xecydx
b
Solve the differential equation by the changing the independent variable: .sin84 233 xxyxdx ydx 
a
State convolution theorem of the Laplace transforms. Hence, find inverse Laplace transform of .)1(
b
Using Laplace transform, solve the following differential equation: .1)0('&3)0(,2cos62  yyxydx
a
Find a Fourier series to represent .,)( 2   xxxxf Hence, show that  clear
b
Find the half range cosine series for the function 2)1()(  xxf in the interval (0,1). Hence, prove that  clear
a
Determine an analytic function f(z)=u+iv in terms of z whose real part u(x,y) is )sincos( yyyxex  and f(1)=e
b
Find the bilinear transformation which maps the points iz ,1,0 onto .,0, iw Also, find the image of the unit circle |z|=1
a
Expand zzz zzf 2  in the following regions: zzf 2 .2||)(2||1)(1||0)(  ziiiziizi
b
Using contour integration, evaluate the real integral .0,sin0

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.