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

334.5

333.5

334.8

335

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

Hyperbola

parabola

None of these

circle

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

0.003

0.004

0.0004

0.0003

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

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

None

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

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

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

0.242

0.246

0.234

0.265

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

Guass Elimination method

Guass Jocobi method

none

Guass Jordan Method

7. The symbol used for shift operator

∇

8. The fixed iterative method has ________ converges

linear

None of these

quadratic

cubic

9. The order of convergence of iteration method is

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

algebraic equation

transcendental equation

polynomial equation

none

11. 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

0.7306

0.7319

0.7316

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

Guass Jordan Method

Guass Seidal method

Guass Jocobi method

Crout’s method

13. The symbol used for average operator

14. The rate of convergence of bisection method is

2.00

2.2

1.00

1.67

15. The symbol used for forward diffefence operator is

∇

16. Newton-Raphson method to solve equation having formula

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

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

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

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

17. The number of significant digits in 8.00312

18. 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

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

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

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

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

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

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

0.000046

None of these

-0.00048

-0.000048

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

0.10

0.25

0.20

0.15

22. 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

23. which method is known as Regula-Falsi method

Method of interpolation

Bisection method

Method of iteration

secant method

24. 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

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

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

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

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

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

26. Bisection method is also known as

Interval halving method

bolzano and Interval Halving method

successive method

Bolzano method

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

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

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

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

None

28. The error in Trapezoidal rule is of order of

$\dpi{120} \small h$

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

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

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

29. Method of factorization is also known as

LU-decomposition method

Choleski method

All of above

triangularization method

30. 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

1.7265

1.7315

1.7421

31. The method of false position is also known as

Regula False method

Iteration method

bisection method

secant method

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

4.0

2.75

2.2

3.5

33. 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

10.1995

10.2995

10.2225

10.0995

34. 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

35. The method of successive approximation is known as

secant method

convergent method

iteration method

None

36. 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

Newton-Cote’s Quadrature formula

Simpson’s 1/3 rule

Weddle’s rule

37. Gauss- Serial iterative method is used to solve

partial differential Equation

differential equation

system of linear equations

system of non-linear equations

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

1/81

1/3

1/9

1/22

39. 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

19/5

9/5

11/5

40. The Regula False method is somewhat similar to

none

bisection method

iteration method

secant method

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

All of these

Choleski method

Crout’s method

LU decomposition method

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

1/70

1/20

1/80

1/60

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

Guass-Elimination

Guass-Jarden method

None

Guass Seidal method

44. 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

None of these

3.461

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

degree 5

degree 4

degree 3 or less

degree 6

46. Newton Raphson Formula is derived from

Taylor’s Theorem

Roll’s Theorem

Binomial Theorem

Bisection Formula

47. The symbol used for backward difference operator

∇

$\dpi{120} \small \Delta$

48. 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

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

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

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

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

49. Relative error = ?

Truncation error

Approximate error

Error/ True value

None

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

None of these

Ranga Kutta Method

Euler’s method

Euler’s modified method

51. 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 $\dpi{120} \small x=0,\frac{1}{3},\frac{2}{3}, 0$

Simpson’s rule

both of above

Trapezoidal rule

None

52. Newton’s method has ____________ convergence

cubic

linear

quadratic

None of these

53. The number of significant figures in 0.021444 is

54. 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

None of these

2.241

2.242

2.273

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

2.735

2.730

2.740

2.729

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

f'(x)=0

f”(x)=0

f'(x)=

f(x)=0

57. 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

3.139

3.236

None of these

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

algebraic equation

transcendental equation

cubic equation

polynomial equation

59. 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

16.671

16.672

16.673

16.670

60. Relaxation method is known as

Iterative method

algebraic method

Direct method

simple method

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

1.50

1.16154

1.60

1.70

62. Which of the following is iterative method

Crout’s method

Guass-Elimination method

Guass Seidal method

Guass Jardan method

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

Newton Method

tri-section

Bisection method

None

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

0.788

0.781

None of these

0.785

65. The rate of convergence of secant method is

2.67

1.67

1.00

2.00

66. The number of significant figures in 48.710000

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

All of above

algebraic equation

polynomial equation

transcendental equation

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

-7

-1/2

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9 comments

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- admin
  20/04/2019 at 1:28 AM
  
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