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. 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

0.7306

0.7316

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

polynomial equation

transcendental equation

algebraic equation

All of above

3. The symbol used for average operator

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

1.50

1.60

1.70

1.16154

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

0.10

0.15

0.20

0.25

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

0.004

0.003

0.0004

0.0003

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

0 and 1

None of these

2 and 3

1 and 2

8. Gauss- Serial iterative method is used to solve

partial differential Equation

system of linear equations

system of non-linear equations

differential equation

9. 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

2.241

2.273

2.240

2.242

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

0.781

0.785

0.788

None of these

11. The rate of convergence of secant method is

2.00

2.67

1.67

1.00

12. The method of false position is also known as

Regula False method

bisection method

Iteration method

secant method

13. 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

1.7315

1.7265

1.857

14. 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

2.75

4.0

3.5

15. 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

Simpson’s rule

None

Trapezoidal rule

16. 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

10.2225

10.2995

10.0995

17. The symbol used for shift operator

∇

18. The number of significant figures in 48.710000

19. Relaxation method is known as

algebraic method

Direct method

Iterative method

simple method

20. The fixed iterative method has ________ converges

linear

None of these

quadratic

cubic

21. Newton’s method has ____________ convergence

linear

None of these

cubic

quadratic

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

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

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

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

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

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

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

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

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

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

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

Hyperbola

circle

parabola

None of these

25. 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

26. Relative error = ?

Approximate error

Error/ True value

None

Truncation error

27. The Regula False method is somewhat similar to

none

bisection method

secant method

iteration method

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

0.000046

-0.00048

None of these

-0.000048

29. 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

16.673

16.672

16.670

30. The symbol used for forward diffefence operator is

∇

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

f'(x)=

f(x)=0

f'(x)=0

f”(x)=0

32. Method of factorization is also known as

Choleski method

triangularization method

All of above

LU-decomposition method

33. 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

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

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

34. Newton-Raphson method to solve equation having formula

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

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

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

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

35. Bisection method is also known as

Bolzano method

successive method

Interval halving method

bolzano and Interval Halving method

36. which method is known as Regula-Falsi method

secant method

Bisection method

Method of interpolation

Method of iteration

37. The rate of convergence of bisection method is

1.67

2.00

2.2

1.00

38. 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

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

2.735

2.729

2.740

2.730

40. Which of the following is iterative method

Guass Jardan method

Crout’s method

Guass-Elimination method

Guass Seidal method

41. The number of significant digits in 8.00312

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

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

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

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

None

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

Ranga Kutta Method

Euler’s method

None of these

Euler’s modified method

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

LU decomposition method

Choleski method

Crout’s method

All of these

45. 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

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

transcendental equation

none

algebraic equation

polynomial equation

47. Newton Raphson Formula is derived from

Binomial Theorem

Taylor’s Theorem

Roll’s Theorem

Bisection Formula

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

Guass-Elimination

Guass Seidal method

None

Guass-Jarden method

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

tri-section

Bisection method

None

Newton Method

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

333.5

334.8

334.5

335

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

Guass Jocobi method

none

Guass Jordan Method

Guass Elimination method

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

cubic equation

algebraic equation

polynomial equation

transcendental equation

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

1/22

1/81

1/9

1/3

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

-7

-1/2

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

1/70

1/60

1/20

1/80

56. The order of convergence of iteration method is

57. The error in Trapezoidal rule is of order of

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

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

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

$\dpi{120} \small h$

58. The method of successive approximation is known as

secant method

convergent method

None

iteration method

59. 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

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

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

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

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

60. The number of significant figures in 0.021444 is

61. The symbol used for backward difference operator

$\dpi{120} \small \Delta$

∇

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

degree 4

degree 6

degree 5

degree 3 or less

63. 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

Simpson’s 1/3 rule

Newton-Cote’s Quadrature formula

Trapezoidal rule

64. 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

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

| g'(x)| = 0

| g'(x)| = 1

| g'(x)| < 1

| g'(x)| > 1

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

Crout’s method

Guass Jocobi method

Guass Seidal method

Guass Jordan Method

67. 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

None of these

3.136

3.139

3.236

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

3.461

None of these

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9 comments

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- admin
  20/04/2019 at 1:28 AM
  
  Dead Dawood israr , Very soon we shall provide inter mcqs and its video lectures.
  thank you for contacting us.
  
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