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 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

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

transcendental equation

polynomial equation

cubic equation

algebraic equation

3. 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

2.2

2.75

4.0

4. The number of significant digits in 8.00312

5. The symbol used for backward difference operator

$\dpi{120} \small \Delta$

∇

6. Relative error = ?

None

Error/ True value

Truncation error

Approximate error

7. Newton Raphson Formula is derived from

Bisection Formula

Taylor’s Theorem

Roll’s Theorem

Binomial Theorem

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

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

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

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

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

9. The symbol used for shift operator

∇

10. Relaxation method is known as

Direct method

simple method

algebraic method

Iterative method

11. 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

LU decomposition method

Choleski method

12. The rate of convergence of bisection method is

1.67

2.2

1.00

2.00

13. The order of convergence of iteration method is

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

degree 4

degree 6

degree 5

degree 3 or less

15. 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

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

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

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

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

16. Which of the following is iterative method

Guass-Elimination method

Guass Jardan method

Guass Seidal method

Crout’s method

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

f'(x)=0

f'(x)=

f(x)=0

f”(x)=0

18. The number of significant figures in 0.021444 is

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

Euler’s modified method

Euler’s method

Ranga Kutta Method

None of these

20. 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

21. 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

Trapezoidal rule

None

Simpson’s rule

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

algebraic equation

transcendental equation

none

polynomial equation

23. 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

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

0.781

0.785

0.788

None of these

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

1/9

1/3

1/81

1/22

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

1.70

1.50

1.16154

1.60

27. 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

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

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

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

0.10

0.25

0.20

0.15

29. The symbol used for average operator

30. The method of successive approximation is known as

secant method

convergent method

iteration method

None

31. 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

0.7410

0.7316

0.7306

32. The rate of convergence of secant method is

2.00

2.67

1.67

1.00

33. The fixed iterative method has ________ converges

quadratic

linear

None of these

cubic

34. 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

35. 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

None of these

3.139

3.136

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

2.729

2.740

2.735

2.730

37. Bisection method is also known as

Interval halving method

bolzano and Interval Halving method

successive method

Bolzano method

38. 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

39. Method of factorization is also known as

triangularization method

Choleski method

All of above

LU-decomposition method

40. 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

10.2995

10.0995

10.1995

41. 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

2.242

2.241

None of these

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

tri-section

None

Bisection method

Newton Method

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

1 and 2

2 and 3

None of these

0 and 1

44. which method is known as Regula-Falsi method

secant method

Bisection method

Method of iteration

Method of interpolation

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

-7

-1/2

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

Guass Jordan Method

Guass Seidal method

Crout’s method

Guass Jocobi method

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

none

Guass Jordan Method

Guass Elimination method

Guass Jocobi method

48.

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

0.0004

0.0003

0.003

0.004

49. Gauss- Serial iterative method is used to solve

differential equation

system of linear equations

system of non-linear equations

partial differential Equation

50. The number of significant figures in 48.710000

51. The symbol used for forward diffefence operator is

∇

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

circle

None of these

Hyperbola

parabola

53. 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

16.672

16.670

54. 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

11/5

19/5

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

0.242

0.265

0.246

0.234

56. Newton’s method has ____________ convergence

quadratic

linear

cubic

None of these

57. Newton-Raphson method to solve equation having formula

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

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

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

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

58. The method of false position is also known as

Regula False method

secant method

Iteration method

bisection method

59. The Regula False method is somewhat similar to

bisection method

none

secant method

iteration method

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

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

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

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

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

61. 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

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

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

3.465

None of these

3.412

3.461

63. 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

2.273

2.241

64. 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

1.7315

1.857

1.7265

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

333.5

335

334.8

334.5

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

All of above

algebraic equation

transcendental equation

polynomial equation

67. The error in Trapezoidal rule is of order of

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

$\dpi{120} \small h$

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

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

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

None

Guass Seidal method

Guass-Jarden method

Guass-Elimination

Vector and tensor analysis mcqs with answers

Numerical Analysis Multiple Choice Questions Answers

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