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.

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1. The fixed iterative method has ________ converges

quadratic

linear

None of these

cubic

2. 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

1/3

1/9

3. 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

4. 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

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

-0.00048

None of these

-0.000048

0.000046

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

Newton-Cote’s Quadrature formula

Simpson’s 1/3 rule

Trapezoidal rule

7. Gauss- Serial iterative method is used to solve

system of non-linear equations

system of linear equations

partial differential Equation

differential equation

8. The number of significant figures in 0.021444 is

9. The method of successive approximation is known as

convergent method

secant method

None

iteration method

10. Bisection method is also known as

successive method

bolzano and Interval Halving method

Interval halving method

Bolzano method

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

Hyperbola

None of these

circle

parabola

12. The symbol used for average operator

13. Relaxation method is known as

Iterative method

Direct method

simple method

algebraic method

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

Guass Jocobi method

none

Guass Elimination method

Guass Jordan Method

15. The symbol used for backward difference operator

∇

$\dpi{120} \small \Delta$

16. Method of factorization is also known as

triangularization method

LU-decomposition method

Choleski method

All of above

17. Which of the following is iterative method

Guass Seidal method

Crout’s method

Guass-Elimination method

Guass Jardan method

18. The rate of convergence of secant method is

1.00

2.00

1.67

2.67

19. 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

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

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

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

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

20. The error in Trapezoidal rule is of order of

$\dpi{120} \small h$

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

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

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

21. The number of significant digits in 8.00312

22. The rate of convergence of bisection method is

1.67

2.2

1.00

2.00

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

Bisection method

tri-section

Newton Method

None

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

Guass Seidal method

Guass Jordan Method

Crout’s method

Guass Jocobi method

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

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

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

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

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

26. 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

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

none

transcendental equation

polynomial equation

algebraic equation

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

Ranga Kutta Method

Euler’s modified method

None of these

Euler’s method

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

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

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

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

None

30. Newton-Raphson method to solve equation having formula

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

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

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

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

31. 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

3.5

4.0

2.2

32. which method is known as Regula-Falsi method

secant method

Method of interpolation

Method of iteration

Bisection method

33. 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

None of these

3.465

34. The Regula False method is somewhat similar to

secant method

bisection method

none

iteration method

35. The number of significant figures in 48.710000

36. 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

16.670

16.672

16.671

16.673

37. 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

None of these

3.136

3.236

38. The symbol used for shift operator

∇

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

algebraic equation

cubic equation

polynomial equation

transcendental equation

40. 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

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

1.70

1.16154

1.60

1.50

42. 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

10.0995

10.2995

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

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

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

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

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

44. 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

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

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

45. 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

2.242

2.240

2.241

2.273

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

degree 3 or less

degree 4

degree 5

degree 6

47. 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

both of above

Trapezoidal rule

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

f”(x)=0

f(x)=0

f'(x)=0

f'(x)=

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

None

Guass-Elimination

Guass Seidal method

Guass-Jarden method

50. The symbol used for forward diffefence operator is

∇

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

0.25

0.20

0.15

0.10

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

LU decomposition method

All of these

Crout’s method

Choleski method

53. Newton Raphson Formula is derived from

Binomial Theorem

Roll’s Theorem

Bisection Formula

Taylor’s Theorem

54. Newton’s method has ____________ convergence

quadratic

linear

None of these

cubic

55. 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

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

0 and 1

1 and 2

2 and 3

None of these

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

1/20

1/80

1/70

1/60

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

algebraic equation

All of above

polynomial equation

transcendental equation

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

334.8

335

334.5

333.5

60. 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

1.7265

1.7315

1.7421

1.857

61. The order of convergence of iteration method is

62. 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

2.273

2.241

None of these

2.242

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

-1/2

-7

64. 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

65. 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

66.

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

0.0003

0.003

0.0004

0.004

67. Relative error = ?

Approximate error

None

Truncation error

Error/ True value

68. The method of false position is also known as

Iteration method

Regula False method

secant method

bisection method

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Numerical Analysis Multiple Choice Questions Answers

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