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

  • Advanced Engineering Mathematics - AEM
  • 2015
  • PYQ
  • I K G Punjab Technical University - IKGPTU
  • Automobile Engineering
  • B.Tech
  • 2 Views
  • Uploaded 3 months ago
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Roll No. Total No. of Pages : 02 Total No. of Questions : 09 B.Tech.(2008-2010 Batches) (Sem.–1) ENGINEERING MATHEMATICS–I Subject Code : AM-101 Paper ID : [A0111] Time : 3 Hrs. Max. Marks : 60 INSTRUCTIONS TO CANDIDATES : 1. 2. 3. 4. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each. SECTION - B & C. have FOUR questions each. Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each. Select atleast TWO questions from SECTION - B & C. SECTION - A l. Solve the following : (a) State De-Moivre’s theorem. (b) Prove that ii  e –(4 n1)  2 . (c) Define Cauchy’s Integral Test.  (d) Show that  x71/ 4 0 e– x dx  8  . 3 (e) Write an equation for ellipsoid. (f ) If u yz xy , v  zx , w  x y z . Find   u , v , w   x, y, z  (g) Find the equation of the tangent plane and the normal to xyz = a 2 at (x 1 , y 1, z 1 ). (h) Find the area of the circle of radius r. (i) Define Uniform Convergence. (j) Expand x2y + 3y – 2 in powers of x – 1 and y + 2 using Taylor’s theorem. [M - 54001 ] (S-1) 9

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SECTION - B 2. Trace the curve, y2 = (x + 1)3. 3. Find the whole length of the curve, x2/3 + y2/3 = a 2/3. 4. If u = cosec –1  x1/ 2  y1/ 2   1/ 3  x  y1/ 3  1/ 2 , then prove that 2 2 2 2   x 2  u2  2 xy  u  y 2  u2  tan u  13  tan u  . xy 12  12 12  x y 5. Find the point on the surface z2 = xy + 1 nearest to the origin. SECTION - C 6. Find the equation of the cone whose vertex is at origin and guiding curve is 2 x 2  y  z 2  1, x  y  z  1. 4 9 1 2 x 2  y  z 2  1. 7. Find the volume of the ellipsoid 2 a b2 c2 3 5 8. Test the convergence of the series x  1 · x  1 · 3 · x  ............. 1 2 3 2 4 5 9. Prove that the nth roots of unity form the geometric progression. Also show that the sum of these n roots is zero and their product is (–1)n–1. [M - 54001 ] (S-1) 9

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