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Previous Year Exam Questions of Advanced Engineering Mathematics of IKGPTU - AEM by Ravichandran Rao

  • Advanced Engineering Mathematics - AEM
  • 2010
  • PYQ
  • I K G Punjab Technical University - IKGPTU
  • Automobile Engineering
  • B.Tech
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Roll No. V,Ifi,-v.ailsUbj9ets4l'prr"cgnl Total No, of Questions i 091 lTotal No. of Pages: 04 I].Tech. (Sem. - 1") E,NGINEERING MATHEMATICS - I SUIIJECT 9ODE : AM - l0r QK4 & Onwards) Paper ID : [A01I1] fill subjectcodeandpaperID on OMRI lNote: Please hQ.cft 7-eL?.//-s<$1icU 4Vq, Time: 03 Hours y U Instruction to Candidates: \.., Q.ortu__ MaximumMarks:60 l) Section- A is Compulsory. 2) Attempt any Five questionsfrom Section- B & C. 3) Selectat lcastTwo questionsfrom Section- B & C. Section- A (Marks:2Eoch) QI) a) Irind thc cntirc lengthofthe cardiode r -- a(l + cosd) b) Use Eulo''s [heoremto show that '- +)'?:2tttosn, "'::1 cr o.y w h e r eu : e " + ; . \- c) If x : r cos2,y: r sind,then showthat d(r',O) - l. 8(x,l') r d) Find the pcrcentageelror in the areaof an ellipse when an error of +l percentis madein measuringthe major and minor axes. e) For whatvaluc(s)of kwill the plane x - 2y -- 2z : t touch the sphere x, * yt * z2-2x + 4y - 6z * 5 : 0. 0 tn,,Jti," . .\ EvaluateJJ' to polarco-ordinates. \*' + y')dx dy, bychanging 00 R-807 pTO.

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susr$to64ydl'Goll wuurfl g) Statecauchyroot test and use it testthe convergenceof thc series: t :,tt2 rl\ n+l +l/ h) Examine the convergenceof llll lrgr- ltg3 r) * aro l"g5 +' "" "'' lf sin(A + iB) = x * ry, thenprovethat f v' -, - - - L . cost A sin2A Find all thc valuesof (1 - i)'*'. ) Section - I| (Marks : I Each) = giving all its fcatures.in dctail. Q2) (a) Tracethe curvey2(2n x) x3,by g' (b) Provc that the radiusof curvaturcof thc cu1c tn = ctncosn n = | ' 2' " " e" ;. at any point (r, 0) is --(n+l)r'-' c'rve .r(r2+ .),2)= a(f - f). e3) tq) Find the areaof onc loop of thc solid gencratedby levolving (b) Obtain the volumc of thc spindle-shaped the asteroid x2tz* yt't = o'o aboutthe x-axis' show that Q4 @) lf u = log,(x3+ t' + 2.3 3xyz),then (a a - a)'- - l - + - +- - l u I\ (,, ar a',' v.ar) / ,l.r' s (x+.y+z)2 - 0, into polarlbrm' .'. (b) Transfonnthc Laplacianequation ' + S Dx" dv' R-807 2

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bJeCt3.iir+U.GC r.r;vw.3iiSu ri'! powersof (x - l) and (y + 2) OS) (a) Expand/(x,},) = ly + 3y 2 in ascending usingTaylor's theorcmfor severalvariables' , (b) Provcthat a rectangularsolidof maximumvolumewhich canbe inscribed in a sphereis a cube. Section - C (a, b, c) and cuts axesin A, B and Qd) (a) A plane passesthrough a fixed point C. Show that locus of thc c6nterof the sphereOABC is abc ;.;*;=, \/ (b) Find thc cquationof thc conewhoscvertexis (1, 2, 3) and guidingcurve is thc circlc. f +y'+2,2-4,,r+y+z=1. Q7) (a) Evaluatcthc intcgral r ---1: ..- I f Jt J 0 r f v ', j dvdr {.r-+Y- by changingthe ordcr of integration. (b) Establishthc lesult. lt p1"',n), i t,,- a)rn-r(b-x)n-r6-(b-ayt+n-t \-, u tn, n) a, b arepositiveconstants of thc scrics QS) (a) Discussthe ConvcrgcncclDivergcnce € (tnn)' (i) Ln=l 0'!)" (ii) $ ,!_r(,* lI '' of thc scrics. (b) Findtheradiusald intcrvalof cottvcrgcnce -,(3" + l)'' L"/ 2n+2 Further,for what valucsof x (i{'any) docsthe scriesconvcrgcs (i) R-807 6i) conditionally' absolutcly 3

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tI Q9) (a) Findthe sumof theseries: sin2 0- 1 ,in Z0 sinz e + lsin3d sin3d ----oo 23 (b) UscDe-Moivrc'stheoremto solvethc equation(x - 1),+ x5= 0. $${w.alrsublsds4You'com R-807 4

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