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

1/20

1/70

1/60

1/80

2. The fixed iterative method has ________ converges

quadratic

linear

None of these

cubic

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

f'(x)=

f(x)=0

f”(x)=0

f'(x)=0

4. 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

Weddle’s rule

Trapezoidal rule

Newton-Cote’s Quadrature formula

Simpson’s 1/3 rule

5. 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

LU decomposition method

Crout’s method

6. 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

1.7265

1.7421

1.857

1.7315

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

333.5

334.5

335

334.8

8. 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

10.2995

10.2225

10.1995

10.0995

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

1/3

1/22

1/9

1/81

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

Guass Seidal method

None

Guass-Elimination

Guass-Jarden method

11. The order of convergence of iteration method is

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

None of these

Euler’s method

Euler’s modified method

Ranga Kutta Method

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

Guass Jocobi method

Crout’s method

Guass Jordan Method

Guass Seidal method

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

Trapezoidal rule

both of above

Simpson’s rule

None

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

2 and 3

None of these

0 and 1

1 and 2

16. 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

0.7319

0.7410

0.7316

17. 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

None of these

3.136

3.236

18. Newton-Raphson method to solve equation having formula

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

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

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

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

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

None of these

-0.00048

0.000046

-0.000048

20. The number of significant figures in 0.021444 is

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

Newton Method

Bisection method

None

tri-section

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

algebraic equation

transcendental equation

polynomial equation

All of above

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

circle

Hyperbola

parabola

None of these

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

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

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

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

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

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

0.785

0.788

0.781

None of these

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

2.2

3.5

4.0

2.75

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

none

transcendental equation

algebraic equation

polynomial equation

28. 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

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

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

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

Guass Jordan Method

none

Guass Elimination method

Guass Jocobi method

30. The rate of convergence of bisection method is

1.67

2.2

2.00

1.00

31. Newton’s method has ____________ convergence

linear

cubic

None of these

quadratic

32. The error in Trapezoidal rule is of order of

$\dpi{120} \small h$

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

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

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

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

cubic equation

polynomial equation

algebraic equation

transcendental equation

34. Bisection method is also known as

Bolzano method

bolzano and Interval Halving method

successive method

Interval halving method

35. Relaxation method is known as

algebraic method

Direct method

Iterative method

simple method

36. 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

37. The symbol used for shift operator

∇

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

degree 6

degree 4

degree 5

degree 3 or less

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

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

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

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

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

40.

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

0.004

0.0004

0.0003

0.003

41. 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

16.670

16.672

16.673

42. The number of significant digits in 8.00312

43. 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

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

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

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

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

44. Method of factorization is also known as

Choleski method

triangularization method

All of above

LU-decomposition method

45. 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

46. The method of successive approximation is known as

convergent method

None

secant method

iteration method

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

-1/2

-7

48. The rate of convergence of secant method is

1.00

1.67

2.67

2.00

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

0.10

0.20

0.25

0.15

50. which method is known as Regula-Falsi method

Method of iteration

Method of interpolation

Bisection method

secant method

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

0.265

0.234

0.242

0.246

52. 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)| = 0

| g'(x)| = 1

53. The symbol used for backward difference operator

∇

$\dpi{120} \small \Delta$

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

2.242

None of these

2.241

2.273

55. Newton Raphson Formula is derived from

Binomial Theorem

Bisection Formula

Roll’s Theorem

Taylor’s Theorem

56. Which of the following is iterative method

Crout’s method

Guass-Elimination method

Guass Seidal method

Guass Jardan method

57. The Regula False method is somewhat similar to

iteration method

bisection method

secant method

none

58. 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

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

19/5

11/5

9/5

60. The symbol used for forward diffefence operator is

∇

61. The method of false position is also known as

bisection method

Iteration method

Regula False method

secant method

62. Gauss- Serial iterative method is used to solve

system of linear equations

differential equation

partial differential Equation

system of non-linear equations

63. The number of significant figures in 48.710000

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

1.70

1.16154

1.60

1.50

65. Relative error = ?

Approximate error

Error/ True value

Truncation error

None

66. 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

67. The symbol used for average operator

68. 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

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9 comments

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