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Engineering FE Engineering Common Sem 2 Applied Mathematics II Dec 2018 R16 Question Paper - Mumbai University | munotes

Applied Mathematics II Question Paper, Dec 2018.pdf
HAS · 362 KB · 1 May 2025

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Older exam None: this is the earliest we hold
Newer exam Dec 2018 - 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
    • b) Find the length of the curve x = = + 3
    • c) Solve (D? + D)y = 3
    • e) Solve 4
    • f) Solve = 1+ xy with initial condition 4 Xo = = 0.2 by Taylors series method. Find the approximate value of y for x=0.4 (step size 0.4)
  3. Q2 a) Solve — 16y = + — cos3x + 2*. 6 marks
    • b) Show that gx = 6 Change the order of integration and evaluate J,
  4. Q3 a) Evaluate + y + z) dxdydz over the tetrahedron bounded by 6 marks
    • b) Find the mass of the lamina bounded by the curves y = — 3x and y = 2x if the density of the lamina at any point is given by
  5. Q4 a) Find by double integration the area bounded by the parabola y* = 4x and the line y = 2x — 4 6 marks
    • b) Solve + xsin2y = 6
    • C) Solve = x? + y with initial conditions y(0) = 2 at x=0.2 in 8 steps of h=0.1 by Runge Kutta method of fourth order
  6. Q5 a) Byaluate f 1x dx and find the value of B 6 marks
    • b) In a circuit containing inductance L, resistance R, and voltage E, 6 the current i is given by L + Ri = E. Find the current 1 at time t if at and E are constants Evaluate — by using i) Trapezoidal 8
  7. Q6 Find the volume bounded by the paraboloid 6 marks
    • b) Change to polar coordinates and evaluate 6
    • c) Solve by method of variation of parameters 8

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