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Download Maths and English me full movie download and more Schemes and Mind Maps Mathematics in PDF only on Docsity! PAPER ID-421872 Printed Page: 1 of 2 Subject Code: KAS203T Roll No: BIECH (SEM IID) THEORY EXAMINATION 2021-22 ENGINEERING MATHEMATICS-II Time:3 Hours Total Marks: 100 Notes- e Attempt all sections and assume any missing data. e Appropriate marks are allotted to each question, answer accordingly. SECTION -A Attempt all of following question in brief Marks (10x2=20) | CO (Q.1(a) [Find the differential equation which represents the family of straight lines passing through the 1 origins? (Q.1(b) [State the criterion for linearly independent solutions of the homogeneous linear nth order 1 differential equation. 1 pt _dx 2 Q-1(¢) Evaluate: So “Togs (Q.1(d) {Find the volume of the solid obtained by rotating the ellipse x? + 9y? = 9 about the x-axis. 2 (Q-1(e) [Test the series Ueassin=. 3 (Q.1(f) {Find the constant term when f(x) = 1 + |x| is expanded in Fourier series in the interval (-3, 3).|_ 3 (Q.1(g) |Show that f(z) = z + 22 is not analytic anywhere in the complex plane. 4 (Q.1(h) [Find the image of |z — 2i|=2 under the mapping w = : . 4 2-10) Expand f(z) = e /@-2) in a Laurent series about the pointz =2. 5 (Q-1(j) [Discuss the nature of singularity of a atz = aandz =.” 5 SECTION -B Attempt any three of the following questions Marks (3x10=30) | CO Q.2(a) exe =et, SY_ye& = si 1 Solve: Sty t3xse'. F747 t3y =sin2t. . (Q.2(b) Assuming [nT(1 —n) = 2 cosecnn, 0 <n <1, show that {ax = a 50<p<1. 2 Q.2¢6) ies ep ep pee 3 (Test the series atsatsetzet Q.2(d) If f(z) = w+ iv is an analytic function, find f(z) nterm of z ifu-—v = cates when 4 m) — 3t f () 72" (Q.2(e) {Evaluate by contour integration: fo" e= cos cos(n@ + sin 6) d@ ; nel. 5