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 rate of convergence of secant method is

1.00

2.67

1.67

2.00

2. The symbol used for forward diffefence operator is

∇

3. 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

Simpson’s rule

None

both of above

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

transcendental equation

All of above

polynomial equation

algebraic equation

5. Newton’s method has ____________ convergence

cubic

None of these

linear

quadratic

6. The method of successive approximation is known as

convergent method

iteration method

None

secant method

7. which method is known as Regula-Falsi method

Method of iteration

Bisection method

secant method

Method of interpolation

8. 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

9. The number of significant figures in 48.710000

10. 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

11/5

9/5

19/5

11. The symbol used for shift operator

∇

12. The Regula False method is somewhat similar to

secant method

none

iteration method

bisection method

13. The symbol used for backward difference operator

∇

$\dpi{120} \small \Delta$

14. 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

2.240

2.273

2.242

2.241

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

Crout’s method

Guass Jordan Method

Guass Seidal method

Guass Jocobi method

16. Which of the following is iterative method

Guass Jardan method

Guass-Elimination method

Crout’s method

Guass Seidal method

17. The symbol used for average operator

18. Gauss- Serial iterative method is used to solve

system of non-linear equations

partial differential Equation

differential equation

system of linear equations

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

-0.000048

None of these

0.000046

-0.00048

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

0.15

0.10

0.20

0.25

21. The number of significant figures in 0.021444 is

22. Method of factorization is also known as

Choleski method

triangularization method

LU-decomposition method

All of above

23. The order of convergence of iteration method is

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

None

Newton Method

Bisection method

tri-section

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

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

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

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

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

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

Guass-Jarden method

None

Guass-Elimination

Guass Seidal method

27. Bisection method is also known as

Interval halving method

Bolzano method

successive method

bolzano and Interval Halving method

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

f”(x)=0

f'(x)=

f'(x)=0

f(x)=0

29. 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

10.0995

10.1995

10.2225

30. 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

31. Relative error = ?

None

Error/ True value

Truncation error

Approximate error

32. The method of false position is also known as

Regula False method

secant method

bisection method

Iteration method

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

Choleski method

All of these

LU decomposition method

Crout’s method

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

algebraic equation

transcendental equation

cubic equation

polynomial equation

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

Ranga Kutta Method

Euler’s modified method

None of these

Euler’s method

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

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

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

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

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

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

None of these

parabola

circle

Hyperbola

38. 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

39. Newton Raphson Formula is derived from

Roll’s Theorem

Taylor’s Theorem

Binomial Theorem

Bisection Formula

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

0 and 1

2 and 3

1 and 2

None of these

41. Relaxation method is known as

simple method

Direct method

algebraic method

Iterative method

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

-7

-1/2

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

0.265

0.242

0.234

0.246

44. 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

0.7410

0.7306

0.7319

45. The number of significant digits in 8.00312

46. The rate of convergence of bisection method is

2.2

2.00

1.00

1.67

47. The error in Trapezoidal rule is of order of

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

$\dpi{120} \small h$

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

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

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

Guass Jordan Method

Guass Elimination method

Guass Jocobi method

none

49. 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

Weddle’s rule

Simpson’s 1/3 rule

50.

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

0.0003

0.003

0.0004

0.004

51. 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

3.5

4.0

52. 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

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

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

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

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

53. 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

1.7421

1.7265

1.7315

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

transcendental equation

polynomial equation

none

algebraic equation

55. 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

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

335

333.5

334.8

334.5

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

0.788

None of these

0.781

0.785

58. Newton-Raphson method to solve equation having formula

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

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

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

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

59. 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

3.236

3.136

3.139

None of these

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

degree 4

degree 6

degree 5

degree 3 or less

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

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

None

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

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

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

2.730

2.729

2.735

2.740

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

3.461

3.465

None of these

3.412

64. 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

1/81

1/9

65. 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

2.242

None of these

2.273

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

None

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

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

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

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

1.70

1.60

1.50

1.16154

68. The fixed iterative method has ________ converges

quadratic

cubic

linear

None of these

Vector and tensor analysis mcqs with answers

Numerical Analysis Multiple Choice Questions Answers

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