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

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Older exam Dec 2018 - CBSGS Semester-end · Applied Mathematics II → Newer exam May 2019 - CBSGS Semester-end · Applied Mathematics II →

Questions asked in this paper

Q2 Answer any three questions from remaining questions
Q3 Figures to the right indicate full marks
- b) Find the circumference of a circle of radius r by using 3 parametric equations of the circle x = rcos@, y =
- c) Solve 3 Solve = with initial condition = by 4 Euler’s method. Find the approximate value of yat x = 0.4 with h = 0.1
- a) Solve = + x? 6 Show that dx log(1 + a) Change the order of integration and evaluate xydydx. 8 Evaluate x*yzdxdydz throughout the volume bounded by 6 the planes x = 0,y = 0,z = 0 and
- b) Find the mass of lamina of a cardioid r = a(1 + cos@) If the density at any point varies as the square of its distance from its axis of symmetry. 6
- c) Solve (3x + 2)? 5(3x + =x? 8
Q4 a) Find by double integration the area common to the circles r = 6 marks
- b) Solve 6 Solve with initial conditions 8 = 0 at at x=0.2 in steps of h=0.1 by Runge Kutta method of
- a) Evaluate f dx and find the value of B (Z,5). 6
- b) The differential equation of a moving body opposed by a force 6 per unit mass of value cx and resistance per unit mass of value where x and v are the displacement and velocity of the particle at that time is given by = —cx — Find the velocity of the particle in terms of x, if it starts from the rest and iii) Simpsons (3/8)th rule
Q6 a) volume of the region that lies under the paraboloid z = y? and above the triangle enclosed by the lines y = x,x = 0 and x + y = 2 in the xy plane 6 marks
- b) Change to polar coordinates and evaluate { y*dxdy Over the 6
- c) Solve by method of variation of parameters 8

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