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. 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

0.7410

0.7316

0.7319

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

1.16154

1.70

1.50

1.60

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

f”(x)=0

f(x)=0

f'(x)=0

f'(x)=

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

333.5

334.5

334.8

335

5. The number of significant figures in 48.710000

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

0.0003

0.0004

0.003

0.004

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

2.740

2.735

2.729

2.730

8. The number of significant digits in 8.00312

9. The rate of convergence of bisection method is

2.2

1.00

1.67

2.00

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

None of these

circle

Hyperbola

parabola

11. 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

12. 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

Trapezoidal rule

Simpson’s rule

both of above

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

0.242

0.234

0.246

0.265

14. Bisection method is also known as

successive method

bolzano and Interval Halving method

Interval halving method

Bolzano method

15. The order of convergence of iteration method is

16. The symbol used for backward difference operator

∇

$\dpi{120} \small \Delta$

17. Relative error = ?

Approximate error

Truncation error

None

Error/ True value

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

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

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

None

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

19. The symbol used for average operator

20. 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

16.673

16.671

16.670

16.672

21. 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

22. 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

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

Guass-Jarden method

None

Guass Seidal method

Guass-Elimination

24. 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

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

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

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

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

25. The Regula False method is somewhat similar to

bisection method

iteration method

secant method

none

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

-7

-1/2

27. Which of the following is iterative method

Guass Seidal method

Guass Jardan method

Crout’s method

Guass-Elimination method

28. 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

2.241

2.273

2.242

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

none

Guass Jordan Method

Guass Elimination method

Guass Jocobi method

30. Newton-Raphson method to solve equation having formula

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

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

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

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

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

3.412

3.461

3.465

None of these

32. Newton Raphson Formula is derived from

Bisection Formula

Roll’s Theorem

Taylor’s Theorem

Binomial Theorem

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

1/3

1/81

1/9

1/22

34. Gauss- Serial iterative method is used to solve

differential equation

system of linear equations

partial differential Equation

system of non-linear equations

35. 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

10.1995

10.0995

10.2225

36. The rate of convergence of secant method is

1.00

2.00

1.67

2.67

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

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

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

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

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

38. 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

Newton-Cote’s Quadrature formula

Trapezoidal rule

Simpson’s 1/3 rule

Weddle’s rule

39. which method is known as Regula-Falsi method

Method of iteration

Method of interpolation

secant method

Bisection method

40. 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

3.236

3.136

None of these

41. The symbol used for shift operator

∇

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

None of these

-0.000048

-0.00048

0.000046

43. The error in Trapezoidal rule is of order of

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

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

$\dpi{120} \small h$

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

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

3.5

2.75

4.0

2.2

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

degree 3 or less

degree 5

degree 6

degree 4

46. The method of false position is also known as

secant method

Regula False method

bisection method

Iteration method

47. Method of factorization is also known as

triangularization method

All of above

Choleski method

LU-decomposition method

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

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

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

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

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

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

polynomial equation

transcendental equation

algebraic equation

none

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

Euler’s modified method

Ranga Kutta Method

None of these

Euler’s method

51. 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

1.857

1.7315

1.7265

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

0.781

None of these

0.788

0.785

53. Newton’s method has ____________ convergence

linear

cubic

quadratic

None of these

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

transcendental equation

polynomial equation

algebraic equation

All of above

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

None of these

0 and 1

1 and 2

2 and 3

56. The method of successive approximation is known as

iteration method

secant method

convergent method

None

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

0.15

0.25

0.20

0.10

58. Relaxation method is known as

algebraic method

Iterative method

simple method

Direct method

59. 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

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

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

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

algebraic equation

polynomial equation

cubic equation

transcendental equation

61. 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

2.242

2.240

2.273

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

1/60

1/70

1/20

1/80

63. The fixed iterative method has ________ converges

None of these

cubic

quadratic

linear

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

tri-section

Bisection method

None

Newton Method

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

Guass Seidal method

Guass Jordan Method

Crout’s method

Guass Jocobi method

66. The symbol used for forward diffefence operator is

∇

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

Crout’s method

LU decomposition method

Choleski method

All of these

68. The number of significant figures in 0.021444 is

Vector and tensor analysis mcqs with answers

Numerical Analysis Multiple Choice Questions Answers

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