Numerical Analysis Multiple Choice Questions Answers

NA MCQs 01 consist of 68 multiple choice questions. These multiples are very important for all kinds of tests. So attempt these questions to get better results.

This page consist of mcq on numerical methods with answers , mcq on bisection method, numerical methods objective, multiple choice questions on interpolation, mcq on mathematical methods of physics, multiple choice questions on , ,trapezoidal rule , computer oriented statistical methods mcq and mcqs of gaussian elimination method
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1. The rate of convergence of bisection method is

1.67

2.00

2.2

1.00

2. Newton-Raphson method to solve equation having formula

$\dpi{120} \small x_{n}=x_{n+1}-\frac{f(x_{n+1})}{f'(x_{n+1})}$

$\dpi{120} \small x_{n+1}=x_n-\frac{f'(x_n)}{f(x_n)}$

$\dpi{120} \small x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$

$\dpi{120} \small x_{n+1}=x_n+\frac{f(x_n)}{f'(x_n)}$

3. The % error in approximating $\dpi{120} \small \frac{4}{3}$ by 1.33 is ________%

0.20

0.25

0.15

0.10

4. The Newton-Raphson method fails if in the neighborhood of root

f(x)=0

f'(x)=0

f”(x)=0

f'(x)=

5. To solve $\dpi{120} \small x^2 - x -2=0$ by Newton-Raphson method we choose $\dpi{120} \small x_o=1$ , then value of $\dpi{120} \small x_2$ is

9/5

11/5

19/5

6. The error in Simpson’s rule when approximating $\dpi{120} \small \int_{1}^{3} \frac{dx}{x}$ is less than

1/70

1/80

1/20

1/60

7. Which of the followong is modefication of Guass-Jocobi method

None

Guass-Jarden method

Guass Seidal method

Guass-Elimination

8. The fixed point iteration method defined as $\dpi{120} \small x_{n+1}=g(x_n)$ converges if

| g'(x)| < 1

| g'(x)| = 0

| g'(x)| > 1

| g'(x)| = 1

9. The Approximate value of $\dpi{120} \small \int_{0}^{1} x^3 dx$ when n=3 using Trapezoidal rule is

0.234

0.246

0.265

0.242

10. To find the root of equation f(x)=0 in (a,b) , the false position method is given as

$\dpi{120} \small \frac{bf(a)-af(b)}{f(b)-f(a)}$

None

$\dpi{120} \small \frac{af(b)-bf(a)}{f(b)-f(a)}$

$\dpi{120} \small \frac{af(b)-bf(a)}{f(a)-f(b)}$

11. To solve $\dpi{120} \small x^3 -x-9=0$ for x near 2 ,with Newton’s method, the correct answer up to three decimal places is

2.241

2.242

2.273

None of these

12. By using Newton-Raphson method the root b/w 0 and 1 by first approx. of $\dpi{120} \small x^3-6x+4=0$ is

0.7306

0.7410

0.7316

0.7319

13. The method of false position is also known as

secant method

bisection method

Regula False method

Iteration method

14. If $\dpi{120} \small f(x_n).f(x_{n-1})<0,$ then compute New iteration $\dpi{120} \small x_{n+1}$ when lies b/w

$\dpi{120} \small f( x_{n-1}) , f(_{n+1})$

$\dpi{120} \small x_n \,\,\,\,\,\, , \,\,\, x_{n+1}$

$\dpi{120} \small x_n \,\,\,\,\,\, , \,\,\, x_{n-1}$

$\dpi{120} \small f( x_n) , f(_{n+1})$

15. By v using iterative process $\dpi{120} \small x_{n+1}=\frac{1}{2}(x_o + \frac{N}{x_n}),$ the positive square root of 102 correct to four decimal places is

10.0995

10.2225

10.1995

10.2995

16. The value of $\dpi{120} \small \int_{1}^{10} x^2$ using Trapezoidal rule is

335

333.5

334.8

334.5

17. The symbol used for shift operator

∇

18. Bisection method is also known as

Bolzano method

Interval halving method

bolzano and Interval Halving method

successive method

19. The rate of convergence of secant method is

2.00

1.00

2.67

1.67

20.

If $\dpi{120} \small \frac{5}{6}$ ≅ 0.8333 then percentage error is __________ %

0.003

0.004

0.0003

0.0004

21. Every square matrix can be expressed as product of lower triangular and unit upper triangular matrix _________ method based on this fact

Choleski method

LU decomposition method

Crout’s method

All of these

22. The order of convergence of iteration method is

23. The False position 2nd approximation of $\dpi{120} \small x^3-9x+1=0$ between 2 and 4 is

2.729

2.735

2.740

2.730

24. Sum of roots of equation $\dpi{120} \small x^3 - 7x^2+14x-8=0$ is

-1/2

-7

25. The smallest +ve root of $\dpi{120} \small x^3-5x+3=0$ lies between

None of these

2 and 3

0 and 1

1 and 2

26. By using False position 2nd approximation of $\dpi{120} \small x^2-x-1=0$ is

1.16154

1.50

1.60

1.70

27. The number of significant digits in 8.00312

28. Round off error occurers when 2.987654 is rounded off up to 5 significant digits is

None of these

-0.000048

-0.00048

0.000046

29. Relative error = ?

None

Truncation error

Error/ True value

Approximate error

30. The formula $\dpi{120} \small \int_{x_o}^{x_o + nh} f(x)dx=h[ny_o+\frac{n^2}{2}\Delta y_o+\frac{1}{2}(\frac{n^3}{3}-\frac{n^2}{2})\Delta^2 y_o+ \frac{1}{6}(\frac{n^4}{4}-n^3+n^2)\Delta^2 y_o+...]$ is known as

Trapezoidal rule

Weddle’s rule

Newton-Cote’s Quadrature formula

Simpson’s 1/3 rule

31. The method of successive approximation is known as

None

secant method

convergent method

iteration method

32. The symbol used for backward difference operator

$\dpi{120} \small \Delta$

∇

33. Which of the following is the modification of Guass Elimination method

Guass Seidal method

Guass Jordan Method

Guass Jocobi method

Crout’s method

34. The root of $\dpi{120} \small x^4 -x-10=0$ by using Newton-Raphson 2nd approximation correct answer up to three decimal places is

1.857

1.7421

1.7315

1.7265

35. The roots of equation $\dpi{120} \small x^3-x-9=0$ near x= 2 correct to three decimal places by using Newton-Raphson method

2.273

2.240

2.241

2.242

36. By solving $\dpi{120} \small x^2-2x-4=0$ for x near 3 using iterative process , the correct answer up to three decimal places is

3.136

3.236

3.139

None of these

37. Simpson’s rule was exact when applied to any polynomial of

degree 4

degree 3 or less

degree 5

degree 6

38. In Simpson’s 1/3 rule , curve of y= f(x) is considered to be a

circle

Hyperbola

parabola

None of these

39. Newton’s method fails to find the root of f(x)=0 if

f'(x) ≤ 0

f'( x) > 0

f'(x) < 0

f'(x) ≥ 0

40. Gauss- Serial iterative method is used to solve

system of non-linear equations

system of linear equations

partial differential Equation

differential equation

41. The symbol used for forward diffefence operator is

∇

42. Which of the following is iterative method

Guass Seidal method

Guass Jardan method

Crout’s method

Guass-Elimination method

43. Method of factorization is also known as

All of above

Choleski method

LU-decomposition method

triangularization method

44. Numerical solutions of linear algebraic equations can be obtained by

Euler’s modified method

Ranga Kutta Method

Euler’s method

None of these

45. The fixed iterative method has ________ converges

None of these

linear

cubic

quadratic

46. Relaxation method is known as

algebraic method

Iterative method

Direct method

simple method

47. The number of significant figures in 48.710000

48. By using False position method , the 2nd approximation of root of f(x)=0 is

$\dpi{120} \small \frac{x_of(x_1)-x_1f(x_o)}{f(x_1)-f(x_o)}$

$\dpi{120} \small \frac{x_of(x_o)-x_1f(x_1)}{f(x_1)-f(x_o)}$

$\dpi{120} \small x_o - \frac{f(x_o)}{f(x_1)-f(x_o)}$

$\dpi{120} \small x_1-\frac{f(x_o)}{f(x_1)-f(x_o)}$

49. Newton’s method has ____________ convergence

quadratic

None of these

cubic

linear

50. To evaluate $\dpi{120} \small \int_{0}^{1} f(x) dx$ approximately which of the following method is used when the value of f(x) is given only at $\dpi{120} \small x=0,\frac{1}{3},\frac{2}{3}, 0$

both of above

None

Trapezoidal rule

Simpson’s rule

51. which method is known as Regula-Falsi method

secant method

Bisection method

Method of interpolation

Method of iteration

52. By using iterative process $\dpi{120} \small x_{n+1}=\frac{1}{2}(x_n + \frac{N}{x_n}),$ the positive root of 278 to five significant figures is

16.670

16.672

16.673

16.671

53. The symbol used for average operator

54. $\dpi{120} \small sin x + e^x$ is

transcendental equation

polynomial equation

All of above

algebraic equation

55. Using bisection method , the real roots of $\dpi{120} \small x^3 -9x+1=0$ between x=2 and x=4 is near to

3.5

2.75

2.2

4.0

56. The process of convergence in iterative method is faster than in

Bisection method

tri-section

Newton Method

None

57. In simpson 1/3 rule, if the interval is reduced by 1/3 rd then the truncation error is reduced to

1/9

1/22

1/81

1/3

58. By using Newton-Raphson method to solve $\dpi{120} \small \sqrt{12}$ , the correct answer up to three decimal places is

3.465

3.412

3.461

None of these

59. The rate of convergence of Guass-Seidal is twice that of

Guass Jocobi method

Guass Elimination method

none

Guass Jordan Method

60. The number of significant figures in 0.021444 is

61. The Regula False method is somewhat similar to

none

iteration method

bisection method

secant method

62. The error in Simpson’s 1/3 rule is of order of

$\dpi{120} \small h^{1/2}$

$\dpi{120} \small h^2$

$\dpi{120} \small h^3$

$\dpi{120} \small h^5$

63. The equation $\dpi{120} \small x^3 - log_{10}x + sin x =0$ is known as

transcendental equation

algebraic equation

none

polynomial equation

64. The error in Trapezoidal rule is of order of

$\dpi{120} \small h$

$\dpi{120} \small h^2$

$\dpi{120} \small h^3$

$\dpi{120} \small h^{1/2}$

65. Newton Raphson Formula is derived from

Taylor’s Theorem

Binomial Theorem

Roll’s Theorem

Bisection Formula

66. The equation $\dpi{120} \small x^2 +3x+1=0$ is known as

cubic equation

transcendental equation

algebraic equation

polynomial equation

67. By using Simpson’s rule, the value of integral $\dpi{120} \small \int_{0}^{1} \frac{1}{1+x^2}dx=$ =

0.785

0.781

None of these

0.788

68. To find the roots of equation f(x) , Newton’s Iterative formula is

$\dpi{120} \small x_{n+1}=x_n+\frac{f'(x_n)}{f(x_n)}$

$\dpi{120} \small x_{n+1}=x_n-\frac{f'(x_n)}{f(x_n)}$

$\dpi{120} \small x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$

None

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  20/04/2019 at 1:28 AM
  
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