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 symbol used for shift operator

∇

2. Which of the following is iterative method

Crout’s method

Guass Seidal method

Guass-Elimination method

Guass Jardan method

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

Guass Seidal method

Guass-Jarden method

None

Guass-Elimination

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

2.730

2.740

2.735

2.729

5. 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

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

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

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

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

6. Method of factorization is also known as

triangularization method

Choleski method

All of above

LU-decomposition method

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

Hyperbola

parabola

None of these

circle

8. 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

16.671

16.670

16.673

9. 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

10. The Regula False method is somewhat similar to

bisection method

secant method

iteration method

none

11. Newton Raphson Formula is derived from

Binomial Theorem

Taylor’s Theorem

Roll’s Theorem

Bisection Formula

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

None of these

0.000046

-0.000048

-0.00048

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

none

polynomial equation

algebraic equation

transcendental equation

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

3.412

None of these

3.465

3.461

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

2.75

4.0

3.5

2.2

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

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

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

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

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

17. 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

18. Gauss- Serial iterative method is used to solve

system of non-linear equations

partial differential Equation

system of linear equations

differential equation

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

Guass Elimination method

none

Guass Jordan Method

Guass Jocobi method

20. The rate of convergence of secant method is

2.00

1.67

2.67

1.00

21. 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

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

0.20

0.10

0.15

0.25

23. 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

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

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

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

None

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

25. 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

26. Bisection method is also known as

Interval halving method

bolzano and Interval Halving method

successive method

Bolzano method

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

transcendental equation

polynomial equation

All of above

algebraic equation

28. Relaxation method is known as

simple method

Iterative method

algebraic method

Direct method

29. 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

19/5

9/5

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

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

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

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

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

31. 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

None

Trapezoidal rule

Simpson’s rule

32. The symbol used for forward diffefence operator is

∇

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

None of these

0.785

0.788

0.781

34. The number of significant figures in 48.710000

35. 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

2.241

2.273

None of these

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

f'(x)=

f'(x)=0

f”(x)=0

f(x)=0

37. Newton-Raphson method to solve equation having formula

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

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

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

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

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

None

Bisection method

Newton Method

tri-section

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

1/80

1/60

1/20

1/70

40. The method of successive approximation is known as

convergent method

secant method

None

iteration method

41. 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

0.7319

0.7306

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

1/22

1/3

1/9

1/81

43. 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

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

0.265

0.242

0.246

0.234

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

334.8

335

334.5

333.5

46. 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

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

0 and 1

2 and 3

None of these

1 and 2

48. Newton’s method has ____________ convergence

None of these

linear

cubic

quadratic

49. 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

3.139

3.236

3.136

50. Relative error = ?

None

Approximate error

Error/ True value

Truncation error

51. The symbol used for average operator

52. The method of false position is also known as

Iteration method

secant method

bisection method

Regula False method

53. which method is known as Regula-Falsi method

Method of interpolation

Method of iteration

Bisection method

secant method

54. The number of significant figures in 0.021444 is

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

None of these

Euler’s method

Ranga Kutta Method

Euler’s modified method

56. 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

2.240

2.242

2.273

57.

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

0.004

0.0004

0.0003

0.003

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

-1/2

-7

59. The rate of convergence of bisection method is

2.00

2.2

1.00

1.67

60. The fixed iterative method has ________ converges

cubic

linear

quadratic

None of these

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

polynomial equation

transcendental equation

algebraic equation

cubic equation

62. The order of convergence of iteration method is

63. The error in Trapezoidal rule is of order of

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

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

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

$\dpi{120} \small h$

64. The symbol used for backward difference operator

∇

$\dpi{120} \small \Delta$

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

degree 6

degree 5

degree 3 or less

degree 4

66. The number of significant digits in 8.00312

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

Crout’s method

Guass Jocobi method

Guass Jordan Method

Guass Seidal method

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

1.50

1.60

1.16154

1.70

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Numerical Analysis Multiple Choice Questions Answers

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