Download PTU B.Tech 2020 March Civil 6th Sem BTCE 604 Numerical Methods In Civil Engineering Question Paper

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Roll No. Total No. of Pages : 02
Total No. of Questions : 09

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B.Tech.(CE) (2012 to 2017) (Sem.-6)
NUMERICAL METHODS IN CIVIL ENGINEERING
Subject Code : BTCE-604
M.Code : 71085
Time : 3 Hrs. Max. Marks : 60

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INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.

SECTION-A

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Q1. Answer the following :

1. Write a short note of Boundary Value problem.
2. Write normal equation for fitting second degree polynomial.
3. Write a short note on Bisection method.
4. Find a polynomial which takes values
   

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   X: 0 1 2 3 4
   y: 1 2 1 1 10
5. Evaluate ?² (ab^x), the interval of differencing being unity.
6. Find the Eigen values of the matrix
   1 1 3
   

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   1 5 1
   3 1 1
7. Explain interpolation with example.
8. Give any two difference between Galerkin and collocation method.
9. Write the relation between Correlation and Regression coefficient.

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10. What is the classification of the equation?
    ?²u/?x² + ?²u/?x?y + ?²u/?y² = ?u/?x + ?u/?y

SECTION-B

1. Determine the largest Eigen values and Eigen vector of the matrix
   2 -1 0
   

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   -1 2 -1
   0 -1 2
2. A curve passes through the points (0, 18), (1, 10), (3, -18), (6, 90). Find the slope of the curve at x = 2.
3. Apply Runge Kutta method to find an approximate root of y for x = 0.2 in steps of 0.1 of dx/dy = x + y² given y = 1 where x = 0.
4. Explain the Newmark's method for solving non-linear problems.

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5. Solve the equation y"" = x + y boundary conditions y (0) = y (1) = 0

SECTION-C

1. Solve the system of equation using Gauss Jordan method
   x + y + z = 9
   2x - 3y + 4z = 13
   

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   3x + 4y + 5z = 40
2. Solve the boundary value problem defined by y" - x = 0 and y (0) = 0, y (1) = 71 by Galerkin’s method.
3. Obtain the iterative-formula for finding the vN using Newton Raphson method and hence find the value of v5.

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