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- Advanced Engineering Mathematics - AEM
- 2015
- PYQ
**I K G Punjab Technical University - IKGPTU**- Automobile Engineering
- B.Tech
**2 Views**- Uploaded 3 months ago

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 n1) 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

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 . xy 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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