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. Relaxation method is known as

Iterative method

algebraic method

simple method

Direct method

2. 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

2.2

4.0

2.75

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

2.729

2.740

2.735

2.730

4. The Regula False method is somewhat similar to

secant method

iteration method

none

bisection method

5. Relative error = ?

Error/ True value

Truncation error

None

Approximate error

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

transcendental equation

algebraic equation

cubic equation

polynomial equation

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

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

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

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

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

8. The rate of convergence of secant method is

2.00

2.67

1.00

1.67

9. Method of factorization is also known as

All of above

Choleski method

LU-decomposition method

triangularization method

10. 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

10.2225

10.0995

10.2995

10.1995

11. Which of the following is iterative method

Guass Seidal method

Crout’s method

Guass Jardan method

Guass-Elimination method

12. The symbol used for shift operator

∇

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

degree 5

degree 3 or less

degree 4

degree 6

14. Newton’s method has ____________ convergence

linear

cubic

quadratic

None of these

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

Hyperbola

None of these

parabola

circle

16. The fixed iterative method has ________ converges

None of these

linear

cubic

quadratic

17. The method of false position is also known as

Regula False method

bisection method

secant method

Iteration method

18. 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

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

algebraic equation

polynomial equation

none

transcendental equation

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

3.465

3.461

3.412

None of these

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

f”(x)=0

f'(x)=

f(x)=0

f'(x)=0

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

| g'(x)| = 1

| g'(x)| > 1

| g'(x)| < 1

| g'(x)| = 0

23. 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

3.139

3.136

None of these

3.236

24. The number of significant digits in 8.00312

25. 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

16.672

16.670

16.673

16.671

26. 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

Trapezoidal rule

Simpson’s rule

None

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

Guass Jocobi method

none

Guass Elimination method

Guass Jordan Method

28. The rate of convergence of bisection method is

2.2

1.67

1.00

2.00

29. 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

1/3

1/81

30. 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

0.7410

0.7319

0.7316

0.7306

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

1.16154

1.50

1.70

1.60

32. 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

2.273

None of these

2.242

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

1/80

1/60

1/20

1/70

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

transcendental equation

polynomial equation

All of above

algebraic equation

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

Choleski method

Crout’s method

All of these

LU decomposition method

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

334.5

335

334.8

333.5

37. The method of successive approximation is known as

None

convergent method

iteration method

secant method

38. The error in Trapezoidal rule is of order of

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

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

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

$\dpi{120} \small h$

39. which method is known as Regula-Falsi method

secant method

Bisection method

Method of iteration

Method of interpolation

40. The symbol used for backward difference operator

$\dpi{120} \small \Delta$

∇

41. Gauss- Serial iterative method is used to solve

system of linear equations

partial differential Equation

differential equation

system of non-linear equations

42. Newton-Raphson method to solve equation having formula

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

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

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

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

43. 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

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

Newton Method

None

tri-section

Bisection method

45. Newton Raphson Formula is derived from

Binomial Theorem

Taylor’s Theorem

Bisection Formula

Roll’s Theorem

46. 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

2.242

2.240

2.273

2.241

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

0.10

0.15

0.25

0.20

48. The order of convergence of iteration method is

49. The number of significant figures in 48.710000

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

0.246

0.265

0.234

0.242

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

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

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

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

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

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

-1/2

-7

53. Bisection method is also known as

successive method

bolzano and Interval Halving method

Bolzano method

Interval halving method

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

0.788

0.785

0.781

None of these

55. 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

56. The symbol used for forward diffefence operator is

∇

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

None of these

2 and 3

1 and 2

0 and 1

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

Guass Seidal method

Guass Jocobi method

Guass Jordan Method

Crout’s method

59. 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

19/5

11/5

60. The number of significant figures in 0.021444 is

61.

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

0.0003

0.004

0.0004

0.003

62. The symbol used for average operator

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

-0.000048

None of these

-0.00048

0.000046

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

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

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

None

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

65. 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

1.7421

1.857

1.7315

1.7265

66. 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

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

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

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

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

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

Guass-Jarden method

Guass-Elimination

Guass Seidal method

None

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

None of these

Euler’s modified method

Ranga Kutta Method

Euler’s method

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  20/04/2019 at 1:28 AM
  
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