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. Which of the following is iterative method

Guass Jardan method

Guass-Elimination method

Crout’s method

Guass Seidal method

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

None of these

3.465

3.461

3.412

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

0.785

0.788

None of these

0.781

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

1.60

1.70

1.16154

1.50

5. Newton-Raphson method to solve equation having formula

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

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

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

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

6. The symbol used for backward difference operator

$\dpi{120} \small \Delta$

∇

7. 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

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

f'(x)=

f(x)=0

f”(x)=0

f'(x)=0

9. 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

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

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

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

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

10. The method of false position is also known as

Regula False method

bisection method

Iteration method

secant method

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

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

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

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

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

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

0.234

0.246

0.265

0.242

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

-1/2

-7

14. The error in Trapezoidal rule is of order of

$\dpi{120} \small h$

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

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

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

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

algebraic equation

none

transcendental equation

polynomial equation

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

1 and 2

2 and 3

0 and 1

None of these

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

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

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

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

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

18. 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

19. 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

10.1995

10.2995

20. The symbol used for average operator

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

0.000046

None of these

-0.000048

-0.00048

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

2.729

2.730

2.735

2.740

23.

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

0.003

0.0003

0.0004

0.004

24. 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

4.0

3.5

25. The order of convergence of iteration method is

26. 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

0.7410

0.7306

0.7319

0.7316

27. The number of significant digits in 8.00312

28. Gauss- Serial iterative method is used to solve

system of non-linear equations

system of linear equations

differential equation

partial differential Equation

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

Ranga Kutta Method

Euler’s modified method

Euler’s method

None of these

30. The symbol used for forward diffefence operator is

∇

31. which method is known as Regula-Falsi method

secant method

Method of interpolation

Method of iteration

Bisection method

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

polynomial equation

All of above

transcendental equation

algebraic equation

33. The number of significant figures in 0.021444 is

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

Guass Jocobi method

Guass Seidal method

Guass Jordan Method

Crout’s method

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

Newton Method

None

tri-section

Bisection method

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

16.671

16.672

16.670

16.673

37. The method of successive approximation is known as

None

iteration method

convergent method

secant method

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

Weddle’s rule

Trapezoidal rule

Newton-Cote’s Quadrature formula

Simpson’s 1/3 rule

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

Guass-Elimination

Guass-Jarden method

None

Guass Seidal method

40. Bisection method is also known as

bolzano and Interval Halving method

Bolzano method

successive method

Interval halving method

41. Newton’s method has ____________ convergence

None of these

cubic

quadratic

linear

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

333.5

334.8

334.5

335

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

Crout’s method

All of these

Choleski method

LU decomposition method

44. Relaxation method is known as

simple method

Direct method

algebraic method

Iterative method

45. The rate of convergence of bisection method is

2.2

1.00

2.00

1.67

46. The Regula False method is somewhat similar to

iteration method

bisection method

none

secant method

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 $\dpi{120} \small x=0,\frac{1}{3},\frac{2}{3}, 0$

Simpson’s rule

Trapezoidal rule

None

both of above

48. The fixed point iteration method defined as $\dpi{120} \small x_{n+1}=g(x_n)$ converges if

| g'(x)| = 0

| g'(x)| < 1

| g'(x)| > 1

| g'(x)| = 1

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

degree 4

degree 5

degree 6

degree 3 or less

50. 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

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

1/9

1/81

1/3

1/22

52. Newton Raphson Formula is derived from

Bisection Formula

Roll’s Theorem

Binomial Theorem

Taylor’s Theorem

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

0.10

0.20

0.25

0.15

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

transcendental equation

algebraic equation

polynomial equation

cubic equation

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

Guass Jocobi method

Guass Elimination method

Guass Jordan Method

none

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

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

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

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

None

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

parabola

Hyperbola

None of these

circle

58. 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

2.273

None of these

2.242

59. Method of factorization is also known as

All of above

Choleski method

LU-decomposition method

triangularization method

60. The rate of convergence of secant method is

1.00

2.67

2.00

1.67

61. The fixed iterative method has ________ converges

None of these

linear

cubic

quadratic

62. Relative error = ?

None

Error/ True value

Truncation error

Approximate error

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

1/60

1/80

1/20

1/70

64. 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

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

65. 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

2.242

2.241

2.273

66. The number of significant figures in 48.710000

67. 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

1.7265

1.7315

68. The symbol used for shift operator

∇

Vector and tensor analysis mcqs with answers

Numerical Analysis Multiple Choice Questions Answers

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