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Engineering FE Engineering Common Sem 2 Applied Mathematics II Dec 2019 R16 Question Paper - Mumbai University | munotes

Applied Mathematics II Question Paper, Dec 2019.pdf
HAS · 670 KB · 1 May 2025

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Older exam May 2019 - CBSGS Semester-end · Applied Mathematics II → Newer exam Dec 2019 - CBSGS Semester-end · Applied Mathematics II →

Questions asked in this paper

  1. Q2 Answer any three questions from remaining questions
  2. Q3 Figures to the right indicate full marks
  3. Q1 a) Evaluate dx. 3 marks
    • b) Find the length of the arc of the curve r = asin? (5) 3 from = 0 to any point P(@)
    • c) Solve (D* 3
    • f) Solve = x? + y with initial condition = 1, yp = 1 4 by Taylors method. Find the approximate value of y for
  4. Q2 a) —4y = + — sin2x. Show that gy = > 0) 6 6 marks
    • c) Change the order of integration and evaluate 8
  5. Q3 a) Evaluate {ff zdxdydz over the volume of tetrahedron bounded by the planes x =0,y =0,z 6 marks
    • b) Find the mass of the lamina bounded by the curves 6 y* = 4x and x* = 4y if the density of the lamina at any point varies as the square of its distance from the origin
  6. Q4 a) Find by the double integration the area between the Solve with initial conditions yo = 1, 8 Xo at at x=0.2 in steps of h=0.1 by Runge Kutta method of fourth order 6 marks
  7. Q5 a) 1 x? pt ax 6 marks
    • b) The distance x descended by a parachute satisfies the 6 differential equation = where k and g are constants. If x=0 when t=0, show that
  8. Q6 Find the volume in the first octant bounded by the cylinder x? + y? = 2 and the planesz=x+y,y =X, Change to polar coordinates and evaluate Jf, over one loop of the lemniscates (x? + = x2 — y? 6 marks
    • c) Solve by method of variation of parameters 8

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