Download JNTUA M.Tech 1st Sem 2016 Feb Reg-Supple 9D12103 Numerical Methods Question Paper

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Code: 9D12103

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M.Tech I Semester Regular & Supplementary Examinations February 2016

NUMERICAL METHODS

(Geotechnical Engineering)

(For students admitted in 2011, 2012, 2013, 2014 & 2015 only)

Time: 3 hours

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Max Marks: 60

Answer any FIVE questions

All questions carry equal marks

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1. (a) State Lagrange's interpolation method and use it to find the value of y at x = 6 from the following data.
   

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   X	3	7	9	10
   y	168	120	72	63

   (b) Explain interpolation by central difference method.
2. Find & $\frac{dy}{dx}$ $\frac{d^{2}y}{d{x}^2}$ at x = 51 from the following data using Newton's forward difference.
   

   X	50	60	70	80	90
   y	19.96	36.65	58.81	77.21	94.61

3. Using Taylor's series method, find the values of x and y for t = 0.4 satisfying equations: $\frac{d^{2}y}{d{t}^2}$ = x - t, with initial condition y = 0, $\frac{dy}{dt}$ = -1 at t = 0.
4. (a) Solve the equations:
   

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   X1 + 2X2 + X3 = 2
   3X1 + 6x2 + x3 = 1
   3x1 + 3x2 + 2x3 = 1
   (i) Using Cramer's rule.
   (ii) Determining the inverse of the coefficient matrix.
   

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   (b) What is pivoting in Gauss elimination method?
5. (a) Solve 2x + y = 3, 2x + 3y = 5 by Gauss Seidel iteration method.
   (b) Solve by Jacobi's method:
   5x - y + z = 10
   2x + 4y = 12
   

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   x + y + 5z = -1 with initial values (2, 3, 0).
6. (a) What are the advantages and disadvantages of FEM over conventional methods?
   (b) Write down analysis steps for 2D element by using FEM.
7. Explain finite element technique using minimization of total potential energy principle.
8. Write short notes on:
   

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   (a) Types of sheet pile walls.
   (b) Stability analysis of sheet piles.
   (c) Failure measurement of sheet piles.

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