SRM University 2007 B.Tech Food Process Engineering MA – 252 NUMERICAL METHODS - Question Paper

II B. Tech FOOD PROCESSING
MA – 252 NUMERICAL METHODS
UNIT – I
CURVE FITTING AND NUMERICAL SOLUTION OF EQUATIONS.
PART - A
1. What is the principle of lowest squares or the lowest square criterion?
2. What are the normal equations in fitting a straight line?
3. What are the normal equations in fitting a parabola?
4. In fitting a straight line y = ax + b, what is the formula to obtain the sum of the squares of the residuals?
5. In fitting a parabola y = ax2 + bx + c, what is the formula for finding the sum of the squares of the residuals?
6. What are the normal equations in fitting a curve of the form y = abx?
7. What are the normal equations in fitting a curve of the form y = axb?
8. What is the order of convergence of Newton - Raphson method?
9. Does a root of x3 - 3x2 + 2.5 = 0 lie ranging from 1.1 and 1.2 ?
10. What are the 2 methods of solving linear equations?
11. By Gauss – elimination, solve x + y = 2; 2x + 3y = 5
12. By Gauss – Jordan, solve 11x = 3y = 17, 2x + 7y = 16
13. State the condition for convergence of Gauss – seidel method.
14. The rate of convergence in Gauss – seidal method is _________ times greater than of Gauss Jacobi method.
15. Show that the root of the formula sin x = one + x3 lies in the interval (-2, -1)
16. Approximate by using Newton’s method
17. Approximate by using Newton’s methods
18. obtain the root of that lies ranging from two and three using Newton Raphson
method.

19. Distinguish ranging from Gauss Jacobi and Gauss seidal method.

20. describe diagonally dominant matrix.

21. Write down the formulae to solve a system of linear equations by Gauss
seidal method.

22. What is the difference ranging from direct and iterative method of solving a system
of linear algebraic equations

23. elaborate the advantages of iterative methods over direct methods of solving a
system of linear algebraic equations?

24. Solve the equations 10x+ y = seven and x – 10y = 31 by Gauss Seidal iteration
method.
25. Using the iterative formula for finding the reciprocal of N obtain the value of .

PART – B
1. By the method of lowest squares obtain the best fitting straight line to the data provided beneath
X : 5 10 15 20 25
Y : 15 19 23 26 30
2. Fit a parabola, by the method of lowest square, to the subsequent data; also estimate y at x = 6.
X : 1 2 3 4 5
Y : 5 12 26 60 97
3. Fit a curve of the form y = abx to the data
X : 1 2 3 4 5 6
Y : 151 100 61 50 20 8
By the principle of lowest square
4. Obtain the fault of the straight line fit to the subsequent data
X : 1 2 3 4 5
Y : 4 5 6 7 11
5. Find an iterative formula to obtain the reciprocal of a provided number N and hence obtain the value of
6. .Prove that Newton-Raphson’s iterative formula for is .
7. Use Newton-Raphson’s method to obtain the values of (i) (ii) .

8. Use Newton-Raphson’s method to obtain the roots of the formula
(root lying ranging from one and 2) accurate to 4 decimal places.
9. Find the root of 4x = ex that lies ranging from two and 3
10. Solve the system of formula by (i) Gauss elimination method (ii) Gauss – Jordan method
x + 2y + z = three
2x + 3y+3z = 10
3x – y + 2z = 13
11. Solve the system by Gauss – elimination method
2x + 3y – z = five
4x + 4y+3z = three
2x - 3y+2z = 2

12. Solve the subsequent system by Gauss – Jacobi method:
10x - 5y - 2z - three = 0
4x - 10y + 3z + three = 0
x + 6y + 10z + three = 0
13. Fit a straight line and a parabola to the subsequent data and obtain out which 1 is most
improper cause out for your conclusion.
X : 0 1 2 3 4
Y : 1 1.8 1.3 2.5 6.3

14. Solve the subsequent system of linear equations by Gauss elimination method :
5x – y – 2z = 142 ; x – 3y – z = -30 , 2x – y – 3z = 5.

15. Solve the subsequent system of equations by Gauss Jacobi method
10x – 5y – 2z = three ; 4x – 10y + 3z = -3 ; x + 6y + 10z = -3.

16. Solve the subsequent equations by Gauss Seidal method
20x + 4y – z = 32 ; x + 3y + 10z = 24 ; 2x + 17 y + 4z = 35.

17. Find by Newton’s method the root of the formula which is
ranging from one and 2.

18. Find by Newton’s method the root of the formula ,correct to
3 places of decimals.

19. Solve by Gauss elimination method the subsequent equations accurate to three decimal places.
2x + y + 4z = 12 ; 8x – 3y + 2z = 20 ; 4x + 11y – z = 33.

20. .Solve the subsequent system of equations accurate to three places of decimals by
Gauss Jacobi method.
5x – y – z = three ; -x + 10 y – 2z = seven and –x – y + 10z = 8.

21. . Solve the subsequent system of equations accurate to 3 places of decimals by
Gauss Seidal iteration method.
x + y + 54 z=110 ; 27x + 6y – z = 85 ; 6x + 15y + 2z = 72.

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Earning:   Approval pending.