Numerical Analysis Multiple Choice Questions Answers

Dive into NA MCQs 01, a collection of 68 crucial multiple-choice questions. Mastery of these questions is highly advantageous for success in various assessments. Engage with them to significantly enhance your test performance.

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 Trapezoidal rule is of order of

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

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

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

$\dpi{120} \small h$

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

1/80

1/70

1/20

1/60

3. 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

4. The fixed iterative method has ________ converges

None of these

cubic

quadratic

linear

5. The method of successive approximation is known as

convergent method

iteration method

None

secant method

6. 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

Trapezoidal rule

Newton-Cote’s Quadrature formula

7. 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

0.7316

0.7319

0.7306

0.7410

8. Relative error = ?

Truncation error

None

Approximate error

Error/ True value

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

Crout’s method

All of these

LU decomposition method

Choleski method

10. The rate of convergence of bisection method is

2.00

1.67

2.2

1.00

11. 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

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

f'(x)=0

f(x)=0

f'(x)=

f”(x)=0

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

1.50

1.60

1.16154

1.70

14. 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

15. which method is known as Regula-Falsi method

Method of interpolation

secant method

Method of iteration

Bisection method

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

Guass-Jarden method

Guass-Elimination

Guass Seidal method

None

17. The number of significant figures in 48.710000

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

Guass Seidal method

Guass Jocobi method

Crout’s method

Guass Jordan Method

19. The number of significant digits in 8.00312

20. 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

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

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

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

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

21. Newton Raphson Formula is derived from

Roll’s Theorem

Bisection Formula

Taylor’s Theorem

Binomial Theorem

22. Newton-Raphson method to solve equation having formula

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

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

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

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

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

none

Guass Jocobi method

Guass Jordan Method

Guass Elimination method

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

0.265

0.234

0.246

0.242

25. 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

26. Newton’s method has ____________ convergence

None of these

cubic

linear

quadratic

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

None of these

circle

Hyperbola

parabola

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

polynomial equation

algebraic equation

transcendental equation

All of above

29.

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

0.0003

0.004

0.003

0.0004

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

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

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

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

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

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

degree 6

degree 5

degree 4

degree 3 or less

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

None of these

3.465

3.461

3.412

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

-7

-1/2

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

333.5

334.5

335

334.8

35. 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

1.7315

1.7421

1.7265

1.857

36. The number of significant figures in 0.021444 is

37. 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

10.0995

10.2225

10.2995

38. 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

2.2

3.5

2.75

39. 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

2.273

2.241

2.242

40. Which of the following is iterative method

Guass Jardan method

Guass Seidal method

Crout’s method

Guass-Elimination method

41. 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

None of these

0.788

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

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

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

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

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

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

2 and 3

0 and 1

1 and 2

None of these

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

None

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

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

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

45. The symbol used for shift operator

∇

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

None

Bisection method

tri-section

Newton Method

47. The method of false position is also known as

secant method

bisection method

Regula False method

Iteration method

48. Relaxation method is known as

simple method

algebraic method

Iterative method

Direct method

49. 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

2.242

2.241

50. The Regula False method is somewhat similar to

secant method

none

iteration method

bisection method

51. The symbol used for backward difference operator

∇

$\dpi{120} \small \Delta$

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

0.15

0.20

0.25

0.10

53. 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

54. 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

16.673

16.671

16.670

55. 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

56. 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

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

None of these

-0.00048

-0.000048

0.000046

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

None

Simpson’s rule

Trapezoidal rule

both of above

59. Bisection method is also known as

bolzano and Interval Halving method

Bolzano method

Interval halving method

successive method

60. Gauss- Serial iterative method is used to solve

partial differential Equation

system of linear equations

differential equation

system of non-linear equations

61. The order of convergence of iteration method is

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

Euler’s method

Ranga Kutta Method

None of these

Euler’s modified method

63. Method of factorization is also known as

Choleski method

LU-decomposition method

All of above

triangularization method

64. The rate of convergence of secant method is

2.00

2.67

1.00

1.67

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

algebraic equation

polynomial equation

none

transcendental equation

66. The symbol used for average operator

67. The symbol used for forward diffefence operator is

∇

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

polynomial equation

transcendental equation

algebraic equation

cubic equation

Vector and tensor analysis mcqs with answers

Numerical Analysis Multiple Choice Questions Answers

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