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

  • Advanced Engineering Mathematics - AEM
  • 2011
  • PYQ
  • I K G Punjab Technical University - IKGPTU
  • Automobile Engineering
  • B.Tech
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Roll No' Total No. of Qucstions [Total No. of Pagcs : 02 : 091 B. Tech. (Sem. - 1"t) I ENGINEERING MATHEIVIATICS' SUB'IECT CODE: AM - 101 Paper [Notc : Plcast f l ID : [A01111 subjcct c(xle and papcr ID ou ONff l Maximum Marks : 60 Time : 03 Hours Instruction to Candidatcs: 1) Section - A is ComPulsorY' 2) Attempt any l-ive questions fronr Scction - B & C' 3) Sclccting atleast Tlvo qucstions liom Section - B & C' scction-A lMarks:2Ilachl Ql) a) b) c) point (x, y). Find the radius of cur.vature of \2 = 4ax at the 2' Find the length of arc -,t' = x2 from x = 0 to x = curve 1, = -r-r and the lines Fincl the area of the region enclosed by the x=0,.v=0andx=2. d) e) r) o\ of lf z = .f (x, y) is a surtace' then what is Geornetrical rneaning (partial derivative w.r't. x)' If r(x, -v) = xr, find (l ll *ay at ( l, dz ; 2)' to 2 terms' Wlite down the maclaurin's theorein of e'siny up that the locus of A plane passes thlough a fixecl point (a' b' c)' Show is the sphere the tbot of perpendicular to it from the origin i+y2+z'-ax-bY-cz=0' h) Evaluate the integlal i) lf j) Firrcl the cube roots n-1263 a series )a"l lr tt J,)rf# ru,, is convergent' then I-im lr,, = 0' of unity using De Moivre's theorem' P.T,O,

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Sectior - Ii [Marks : 8 EachJ Q2) Trace rhe curve, = (y - 1) (y - 2) Q3) Fincl the length /"2\ tv Q4) lt u - tan-r | ; _ 3). of a loop of the cun e l. ,r,o* ttut \ ^ ,, 05) Cv *'** dx- gayz - 3a)2, a > 0. 24,-!+ + y=*= dxdY dy' Find the minimum value of the function ar+by+cz-a+b+c. = a(a sin2rr sin2rr. I t y, + z, subject ro the condition Section - C . tMarks:gEachl .K' passes through the origin and meets the Q6) A sphere of constant radius axes in A, B, c. Prove that the centroid of the triangle lies on the sphere 9(i+f+22)=4y.z. Q7) Evaluate lJe-t''*:'"' dxdt,whereD is the region bounde dby D changing in polar coordinate. Q8) Test for convergence the series a __! l+a (l+a)Q+a\ .. . J F t+f (t+B1e+B)' - _-]- Q9) Show that 25 sina0 cos20 = cos6 0 - 2 cos4 0 - cos2 0 + 2. tt** R-1263 I f +f = a2 by

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