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. Gauss- Serial iterative method is used to solve

system of non-linear equations

partial differential Equation

differential equation

system of linear equations

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

Guass-Elimination

Guass-Jarden method

None

Guass Seidal method

3. 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

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

LU decomposition method

Crout’s method

All of these

Choleski method

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

-1/2

-7

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

4.0

3.5

2.75

2.2

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

f'(x)=

f(x)=0

f”(x)=0

f'(x)=0

8. 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

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

9. Relative error = ?

Truncation error

Approximate error

None

Error/ True value

10. 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

both of above

Simpson’s rule

Trapezoidal rule

11. 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

12. 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

3.136

None of these

3.236

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

0.234

0.265

0.242

0.246

14. The symbol used for average operator

15.

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

0.0004

0.004

0.003

0.0003

16. The Regula False method is somewhat similar to

bisection method

iteration method

none

secant method

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

None

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

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

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

18. 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

2.242

2.241

2.273

19. The symbol used for backward difference operator

∇

$\dpi{120} \small \Delta$

20. The order of convergence of iteration method is

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

Guass Jordan Method

Guass Seidal method

Crout’s method

Guass Jocobi method

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

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

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

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

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

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

1.16154

1.50

1.70

1.60

24. Newton-Raphson method to solve equation having formula

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

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

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

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

25. 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

26. The number of significant figures in 48.710000

27. The symbol used for shift operator

∇

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

tri-section

Bisection method

None

Newton Method

29. which method is known as Regula-Falsi method

Bisection method

Method of interpolation

Method of iteration

secant method

30. 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

10.0995

10.1995

10.2225

31. The number of significant figures in 0.021444 is

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

0.20

0.15

0.25

0.10

33. The method of false position is also known as

Regula False method

Iteration method

secant method

bisection method

34. 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

35. 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

2.241

2.273

2.242

36. The method of successive approximation is known as

secant method

iteration method

convergent method

None

37. Newton Raphson Formula is derived from

Binomial Theorem

Taylor’s Theorem

Bisection Formula

Roll’s Theorem

38. 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

0.7316

0.7319

0.7410

39. Newton’s method has ____________ convergence

quadratic

cubic

None of these

linear

40. The symbol used for forward diffefence operator is

∇

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

Ranga Kutta Method

None of these

Euler’s modified method

Euler’s method

42. The rate of convergence of secant method is

2.00

1.67

2.67

1.00

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

polynomial equation

algebraic equation

All of above

transcendental equation

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

None of these

0.785

0.781

0.788

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

None of these

circle

Hyperbola

parabola

46. 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

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

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

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

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

47. The rate of convergence of bisection method is

2.00

1.67

1.00

2.2

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

1/70

1/20

1/60

1/80

49. The fixed iterative method has ________ converges

cubic

None of these

linear

quadratic

50. Which of the following is iterative method

Guass Seidal method

Guass Jardan method

Guass-Elimination method

Crout’s method

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

transcendental equation

algebraic equation

polynomial equation

cubic equation

52. 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

1.7421

1.7315

1.7265

53. 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

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

333.5

335

334.8

334.5

55. 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

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

Guass Elimination method

Guass Jordan Method

Guass Jocobi method

none

57. The error in Trapezoidal rule is of order of

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

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

$\dpi{120} \small h$

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

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

2.735

2.740

2.730

2.729

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

degree 4

degree 5

degree 6

degree 3 or less

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

polynomial equation

none

transcendental equation

algebraic equation

61. Relaxation method is known as

simple method

Iterative method

algebraic method

Direct method

62. Bisection method is also known as

bolzano and Interval Halving method

Interval halving method

successive method

Bolzano method

63. The number of significant digits in 8.00312

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

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

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

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

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

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

None of these

2 and 3

0 and 1

1 and 2

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

| g'(x)| > 1

| g'(x)| = 1

| g'(x)| < 1

| g'(x)| = 0

67. Method of factorization is also known as

LU-decomposition method

triangularization method

Choleski method

All of above

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

3.461

None of these

3.465

3.412

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Numerical Analysis Multiple Choice Questions Answers

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