Engineering Mathematics Ii (KAS203T) - AKTU Question Paper 2021-22
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 2021-22. 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:2021-22
University:AKTU / UPTU
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Questions Asked in 2021-22
Engineering Mathematics Ii (KAS203T) — complete question paper
Section AAttempt all of followin
- gquestion in brief Marks (10×2=20) CO
- aFind the differential equation which represents the family of straight lines passing through the origins?
- bState the criterion for linearly independent solutions of the homogeneous linear nth order differential equation. Evaluate: Find the volume of the solid obtained by rotating the ellipse 𝑥ଶ 9 𝑦ଶ ൌ9 about the 𝑥-axis. 2 Test the series ∑ 𝟏 Find the constant term when 𝑓ሺ𝑥ሻ ൌ1 |𝑥| is expanded in Fourier series in the interval (-3, 3). 3 Show that 𝑓ሺ𝑧ሻ ൌ𝑧2 𝑧̅ is not analytic anywhere in the complex plane. 4 Find the image of |𝑧െ2 𝑖|=2 under the mapping 𝑤ൌ Expand 𝑓ሺ𝑧ሻ ൌ𝑒 ௭ ሺ௭ିଶሻൗ in a Laurent series about the point 𝑧ൌ2 . 5 Discuss the nature of singularity of
Section BAttempt any three of the following questions Marks (3×10=30) CO
- bAssuming Γ𝑛 Γሺ1െ𝑛 ሻ ൌ𝜋 𝑐 𝑜 𝑠 𝑒 𝑐 𝑛 𝜋 , 0൏𝑛൏1 , show that Test the series If 𝑓ሺ𝑧ሻ ൌ𝑢𝑖 𝑣 is an analytic function, find 𝑓ሺ𝑧ሻ in term of 𝑧 if 𝒖െ𝒗ൌ 𝐜𝐨𝐬𝐡 𝒚ି𝐜𝐨𝐬 𝒙 when Evaluate by contour integration: 𝑒ି ୡ୭ୱ ఏଶగ cosሺ𝑛𝜃 sin 𝜃ሻ 𝑑𝜃 ; 𝑛𝜖𝐼 . 5
Section CAttempt any one of the followin g questions Marks (1×10=10) CO
- aUse the variation of parameter method to solve the differential equation
Section CAttempt an y one of the following questions Marks (1×10=10) CO
- aThe arc of the cardioid 𝑟 ൌ 𝑎ሺ1 cos 𝜃ሻ included between െ ଶ is rotated about the line ൌ ଶ . Find the area of surface generated
- bEvaluate ∭ 𝑥𝑦𝑧 sin ሺ𝑥𝑦𝑧 ሻ𝑑𝑥 𝑑𝑦 𝑑𝑧 , the integral being extended to all positive values of the variables subject to the condition 𝑦 𝑧
Section CAttempt an y one of the following questions Marks (1×10=10) CO
- aTest for convergence of the series Obtain Fourier series for the function 𝑓ሺ𝑥ሻ ൌ ቐ Hence deduce that
Section CAttempt an y one of the following questions Marks (1×10=10) CO
- aProve that 𝑤ൌ ଵି௭ maps the upper half of the z-plane onto upper half of the w-plane. What is the image of the circle |𝑧| ൌ1 under this transformation?
- bFind a bilinear transformation which maps the points 𝑖, െ𝑖, 1 of the 𝑧െ plane into 0, 1, ∞ of the 𝑤െ𝑝 𝑙 𝑎 𝑛 𝑒 respectively
Section CAttempt an y one of the following questions Marks (1×10=10) CO
- bFind the Taylor’s and Laurent’s series which represent the function ሺ௭ାଶሻሺ௭ାଷሻ when ሺ𝑖ሻ |𝑧| ൏2
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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