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. 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

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

f(x)=0

f'(x)=

f”(x)=0

f'(x)=0

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

degree 4

degree 3 or less

degree 6

degree 5

4. which method is known as Regula-Falsi method

Method of iteration

secant method

Method of interpolation

Bisection method

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

None of these

Ranga Kutta Method

Euler’s method

Euler’s modified method

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

-0.00048

None of these

0.000046

-0.000048

7. Relative error = ?

Truncation error

Error/ True value

Approximate error

None

8. The symbol used for backward difference operator

∇

$\dpi{120} \small \Delta$

9. 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

Choleski method

All of these

10. The method of false position is also known as

Regula False method

secant method

Iteration method

bisection method

11. The order of convergence of iteration method is

12. 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

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

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

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

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

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

None

Guass-Elimination

Guass Seidal method

Guass-Jarden method

14. 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

16.672

16.673

16.671

16.670

15. The symbol used for forward diffefence operator is

∇

16. 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

17. The method of successive approximation is known as

secant method

iteration method

convergent method

None

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

None

tri-section

Bisection method

Newton Method

19. 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

1/9

1/3

20.

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

0.004

0.003

0.0003

0.0004

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

Guass Elimination method

none

Guass Jordan Method

Guass Jocobi method

22. The number of significant figures in 0.021444 is

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

0.20

0.10

0.25

0.15

24. 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

2.241

2.273

2.240

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

None of these

1 and 2

2 and 3

0 and 1

26. The Regula False method is somewhat similar to

bisection method

iteration method

none

secant method

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

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

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

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

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

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

polynomial equation

All of above

transcendental equation

algebraic equation

29. 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

Trapezoidal rule

both of above

30. Newton’s method has ____________ convergence

quadratic

None of these

cubic

linear

31. The rate of convergence of secant method is

1.67

2.67

2.00

1.00

32. Which of the following is iterative method

Guass Jardan method

Guass-Elimination method

Crout’s method

Guass Seidal method

33. 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

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

Crout’s method

Guass Jordan Method

Guass Jocobi method

Guass Seidal method

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

None of these

0.788

0.785

0.781

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

-1/2

-7

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

0.246

0.265

0.242

0.234

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

1.70

1.60

1.16154

1.50

39. The symbol used for shift operator

∇

40. The error in Trapezoidal rule is of order of

$\dpi{120} \small h$

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

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

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

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

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

None

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

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

42. The number of significant digits in 8.00312

43. 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

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

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

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

Hyperbola

parabola

circle

None of these

45. The symbol used for average operator

46. 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

Newton-Cote’s Quadrature formula

Simpson’s 1/3 rule

Weddle’s rule

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

cubic equation

transcendental equation

algebraic equation

polynomial equation

48. Bisection method is also known as

successive method

Interval halving method

Bolzano method

bolzano and Interval Halving method

49. The number of significant figures in 48.710000

50. 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

51. 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

52. 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

0.7306

0.7319

0.7410

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

algebraic equation

transcendental equation

polynomial equation

none

54. 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

2.242

2.241

2.273

None of these

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

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

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

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

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

56. 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

57. 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

58. The fixed iterative method has ________ converges

None of these

quadratic

linear

cubic

59. 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

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

1/60

1/20

1/70

1/80

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

3.465

3.412

None of these

3.461

62. The rate of convergence of bisection method is

2.2

1.00

1.67

2.00

63. Relaxation method is known as

Iterative method

simple method

algebraic method

Direct method

64. Newton Raphson Formula is derived from

Roll’s Theorem

Binomial Theorem

Taylor’s Theorem

Bisection Formula

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

334.5

334.8

333.5

335

66. Newton-Raphson method to solve equation having formula

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

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

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

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

67. Method of factorization is also known as

All of above

LU-decomposition method

Choleski method

triangularization method

68. Gauss- Serial iterative method is used to solve

system of non-linear equations

system of linear equations

partial differential Equation

differential equation

Vector and tensor analysis mcqs with answers

Numerical Analysis Multiple Choice Questions Answers

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