B.TechSemester 22021-22Engineering Mathematics IiKAS203T

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
  • g
    question in brief Marks (10×2=20) CO
  • a
    Find the differential equation which represents the family of straight lines passing through the origins?
  • b
    State 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 ൌ𝑧൅2 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
  • b
    Assuming Γ𝑛 Γሺ1െ𝑛 ሻ ൌ𝜋 𝑐 𝑜 𝑠 𝑒 𝑐 𝑛 𝜋 , 0൏𝑛൏1 , show that ׬ Test the series If 𝑓ሺ𝑧ሻ ൌ𝑢൅𝑖 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
  • a
    Use the variation of parameter method to solve the differential equation
Section CAttempt an y one of the following questions Marks (1×10=10) CO
  • a
    The arc of the cardioid 𝑟 ൌ 𝑎ሺ1 ൅ cos 𝜃ሻ included between െ ଶ is rotated about the line ൌ ଶ . Find the area of surface generated
  • b
    Evaluate ∭ 𝑥𝑦𝑧 sin ሺ𝑥൅𝑦൅𝑧 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
  • a
    Test 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
  • a
    Prove 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?
  • b
    Find 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
  • b
    Find 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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