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

None

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

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

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

2. 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

3. The number of significant figures in 48.710000

4. Relative error = ?

None

Error/ True value

Approximate error

Truncation error

5. The rate of convergence of bisection method is

2.00

1.00

1.67

2.2

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

-7

-1/2

7. The rate of convergence of secant method is

2.00

1.00

2.67

1.67

8. 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

10.2225

10.0995

10.2995

10.1995

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

None of these

Ranga Kutta Method

Euler’s modified method

Euler’s method

10. The number of significant figures in 0.021444 is

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

Guass-Elimination

None

Guass Seidal method

Guass-Jarden method

12. Newton-Raphson method to solve equation having formula

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

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

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

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

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

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

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

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

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

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

9/5

11/5

15. Newton’s method has ____________ convergence

cubic

quadratic

linear

None of these

16. The method of successive approximation is known as

convergent method

secant method

None

iteration method

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

Guass Jocobi method

none

Guass Jordan Method

Guass Elimination method

18. which method is known as Regula-Falsi method

secant method

Method of iteration

Method of interpolation

Bisection method

19. The Regula False method is somewhat similar to

bisection method

secant method

none

iteration method

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

0.15

0.20

0.25

0.10

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

1/80

1/70

1/60

1/20

22. Which of the following is iterative method

Guass Jardan method

Crout’s method

Guass-Elimination method

Guass Seidal method

23. 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

24. 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

25.

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

0.004

0.0004

0.0003

0.003

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

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

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

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

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

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

Newton Method

tri-section

Bisection method

None

28. The symbol used for backward difference operator

∇

$\dpi{120} \small \Delta$

29. The symbol used for shift operator

∇

30. The number of significant digits in 8.00312

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

1/22

1/9

1/3

1/81

32. Bisection method is also known as

successive method

Bolzano method

bolzano and Interval Halving method

Interval halving method

33. The fixed iterative method has ________ converges

cubic

None of these

quadratic

linear

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

f'(x)=0

f'(x)=

f(x)=0

f”(x)=0

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

1.857

1.7265

1.7315

1.7421

36. The order of convergence of iteration method is

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

-0.00048

-0.000048

None of these

0.000046

38. The symbol used for forward diffefence operator is

∇

39. 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

40. 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

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

degree 5

degree 4

degree 6

degree 3 or less

42. 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

Simpson’s 1/3 rule

Newton-Cote’s Quadrature formula

Weddle’s rule

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

Crout’s method

Guass Jocobi method

Guass Jordan Method

Guass Seidal method

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

transcendental equation

none

polynomial equation

algebraic equation

45. Gauss- Serial iterative method is used to solve

system of linear equations

system of non-linear equations

partial differential Equation

differential equation

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

2.740

2.729

2.735

2.730

47. 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

2.2

4.0

48. 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

0.7319

0.7316

0.7306

0.7410

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

0.781

0.788

0.785

None of these

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

334.8

335

333.5

334.5

51. 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

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

0.242

0.265

0.234

0.246

53. 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

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

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

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

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

None

55. 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

56. Newton Raphson Formula is derived from

Bisection Formula

Binomial Theorem

Roll’s Theorem

Taylor’s Theorem

57. 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

3.139

None of these

3.136

58. The symbol used for average operator

59. The error in Trapezoidal rule is of order of

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

$\dpi{120} \small h$

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

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

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

algebraic equation

transcendental equation

cubic equation

polynomial equation

61. Relaxation method is known as

simple method

Direct method

Iterative method

algebraic method

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

All of above

transcendental equation

algebraic equation

polynomial equation

63. The method of false position is also known as

bisection method

Regula False method

Iteration method

secant method

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

All of these

LU decomposition method

Choleski method

Crout’s method

65. 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

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

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

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

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

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

circle

None of these

Hyperbola

parabola

67. Method of factorization is also known as

triangularization method

All of above

LU-decomposition method

Choleski method

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

1.70

1.60

1.16154

1.50

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Numerical Analysis Multiple Choice Questions Answers

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