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# Computer Oriented Numerical Analysis 1

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Assignment – A

Question 1: Define error, relative error and absolute error. Give example of each

Question 2: Find the rate of convergence of Newton Raphson Method.

Question 3: By using Regula Falsi method find the root of 15 correct up to 2 decimal places.

Question 4: Solve the following set of equations by using Gauss Elimination Method.

Question 5: Solve the following set of equations by Gauss Seidal Method.

Assignment – B

Question 1(a): Round off and truncate the following numbers to four decimal places.

(a) 132.59839

(b) 0.073729

(c) 9528.26058

Question 1(b): Find the root of the equation 2x3-5x-1=0 by using Bisection method. Perform 5 steps.

Question 2: Solve the following problem by Jacobi Method. Perform three steps.

Question 3(a): For the given data

 X f(x) 1 33 2 50 3 69 4 90 5 129

Find the value of f(x) at 1.4

Question 3(b): Choose 4 cards at-random from a standard 52 card deck. What is the probability that two kings and two ace will be chosen.

Assignment – C

1. Round off the number 0.859378 to four significant digits.

(a) 0.8594 (b) 0.8593 (c) 8593 (d) 8.593

2. Truncate the number 0.859378 to four significant digits.

(a) 0.8594 (b) 0.8593 (c) 8593 (d) 8.593 (e) None

3. The formula for Regula Falsi method is

(a) x2=x1-(f(x0)(x1-x0)/(f(x1)-f(x0))

(b) x2=x1-(f(x0) (f(x1)-f(x0))/(x1-x0)

(c) x2=x0-(f(x0)(x1-x0)/(f(x1)-f(x0))

(d) x2=x0-(f(x0) (f(x1)-f(x­))/(x1-x0)

4. Solve the following equation by Regula Falsi Method upto 2 steps by taking the initial value x0=1 and x1=2

X3-X-4=0

(a) 1.234 (b) 1.666 (c) 1.9823 (d) None of the above

5. Choose the initial values of the Bisection Method to solve the following equation

x5+5x+1=0

(a) x0=1, x1=2 (b) x0=0, x1=1 (c) x0=0, x1=-1 (d) x0=-1, x1=-2

6. Solve x3-2x-5=0 by Newton Raphson Method upto 2 decimal places of accuracy by taking x0=2

(a) 2.3568 (b) 2.995 (c) 2.09 (d) 2.135

7. Solve x=1/(x+1)2 by iteration method. Take x0=0.5. Perform two steps only.

(a) .479 (b) .3854 (c) .4053 (d) .793

8. Which method has the fastest convergence?

(a) Bisection method (b) Newton Raphson Method (c) Regula Falsi Method

(d) Iterative Method

9. In Bisection method the initial approximation x0 and x1 are chosen such that

(a) f(x0).f(x1)<0

(b) f(x0).f(x1)>0

(c) f(x0).f(x1)=0

(d) f(x0)-f(x1) is negative.

10. The basic iteration formula to solve 12 is

(a)1/2(xn-12/xn)

(b) 1/2(xn+12/xn)

(c) 1/2(1/xn-12/xn)

(d) None

11. The equation 3-x=e(x-1) is an example of

(a) Transcendental equation

(b) Algebraic Equation

(c) Polynomial Equation

(d) None of the above

12. Δ4 Y0=

(a) y4-4y3+6y2-4y1+y0

(b) = y4-4y3+6y2-4y1+y0

(c) y4+4y3-6y2+4y1-y0

(d) None of these

13. Which one is true?

(a) E+ Δ =1 (b) E- Δ =1 (c) E* Δ =1 (d) E/ Δ =1

14. If ei+1/eip = 1 then rate of convergence is said to be

(a) Linear (b) Quadratic (c) p (d) None

15. Rate of convergence of Newton Raphson method is

(a) 1 (b) 2 (c) 3 (d) Can’t be determined

16. Inverse of inverse of a matrix A is

(a) A-1 (b) 1/A (c) A (d) None of these

17. For Matrix A and B of same order, AB=BA

(a) True (b) False (c) Can’t be determined (d) None of these

18. Which one is true?

(a) y1=y0-h

(b) y1=y0/h

(c) y1=y0+h

(d) None

19. Which one is an integration method?

(a) Trapezoidal Method

(b) Newton Raphson Method

(c) Jacobi Method

(d) None

20. Which one is not an interpolation method?

(a) Lagrange’s Method

(b) Newton Forward Method

(c) Newton Divided Difference Formula

(d) Bisection Method

21. Round off the number 0.259378 to four significant digits.

(a) 0.2594 (b) 0.2593 (c) 2593 (d) 2.593 (e) None

22. Truncate the number 0.159378 to four significant digits.

(a) 0.1594

(b) 0.1593

(c) 1593

(d) 1.593

(e) None

23. The formula for Bisection method is

(a)

(b)

(c.)

(d) None

23. Cramer’s rule fails for

(a) Δ= 2 (b) Δ= 1 (c) Δ=0 (d) None

24. To solve a set of linear algebraic equations, the method is:

a) Gauss Jordan (b) Jacobi (c) Gauss Elimination (d) All (e) None

25. Eigen values for will be

(a) (1,6)

(b) (2,3)

(c) (2,2)

(d) None

26. Equation of line is:

(a) y= c

(b) y=ax2+c

(c) y=ax+c

(d) None

27. Δ2 Y0 is

28. Runga Kutta method is used for

(a) Differentiation (b) Integration (c) Differential Equation

(d) None of these

29. Trapezoida formula is

30. For Simpson’s 3/8 rule, the value of n is

(a) 1 (b) 2 (c) 3 (d) 4

31. Accuracy of Simpson’s method is better than Trapezoidal method.

(a) True (b) False (c) Can’t say

32. Divided Difference formula can also be used for equi-distant points:

(a) True (b) False (c) Can’t say

33.

(a) 0

(b) 1

(c) Δ

(d) None

34. Given the data

 x 1 2 3 F(x) 2 5 8

What is the value of F(x) at x=1.5

(a) 3 (b) 4.3 (c) 2.9 (d) None of these

35. In Question 34, what is the value of F(x) at x=2.3

(a) 6.2 (b) 7.3 (c) 6.9 (d) None of these

36. In Question 34, what is the value of F’f(x) at x=0

(a) 1 (b) 2 (c) 3 (d) None of these

37. For getting the solution of non-linear equation, which method uses the tangent

(a) Bisection (b) Iterative (c) Newton Raphson (d) Regula Falsi

38. Jordan method is a refinement over Gausee’s method

(a) True (b) False (c) Can’t say

39. Numerical Solutions always give accurate solution

(a) True (b) False

40. What will be the relative error if 2/3 is approximated to 0.667?

(a) 0.0005 (b) 0.0006 (c) 0.005 (d) None