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

None of these

3.412

3.461

3.465

2. Newton’s method has ____________ convergence

quadratic

cubic

linear

None of these

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

1.70

1.50

1.16154

1.60

4. The Regula False method is somewhat similar to

bisection method

none

secant method

iteration method

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

0.234

0.242

0.246

0.265

6. Relative error = ?

Error/ True value

Approximate error

Truncation error

None

7. 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

8. 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

16.670

16.672

16.673

16.671

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

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

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

None

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

10. The rate of convergence of secant method is

2.67

1.67

2.00

1.00

11. The error in Trapezoidal rule is of order of

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

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

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

$\dpi{120} \small h$

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

None of these

0.781

0.788

0.785

13. The order of convergence of iteration method is

14. 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

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

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

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

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

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

16. Which of the following is iterative method

Crout’s method

Guass-Elimination method

Guass Seidal method

Guass Jardan method

17. Method of factorization is also known as

triangularization method

Choleski method

All of above

LU-decomposition method

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

degree 4

degree 6

degree 3 or less

degree 5

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

algebraic equation

polynomial equation

cubic equation

transcendental equation

20. 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

2.273

2.241

2.240

2.242

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

Bisection method

None

tri-section

Newton Method

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

Guass Elimination method

Guass Jocobi method

none

Guass Jordan Method

23. The number of significant figures in 48.710000

24. 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

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

None

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

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

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

26. The symbol used for forward diffefence operator is

∇

27. 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

None of these

3.139

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

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

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

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

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

29. which method is known as Regula-Falsi method

Bisection method

Method of iteration

secant method

Method of interpolation

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

Choleski method

All of these

Crout’s method

LU decomposition method

31. The symbol used for backward difference operator

∇

$\dpi{120} \small \Delta$

32. Bisection method is also known as

Interval halving method

bolzano and Interval Halving method

Bolzano method

successive method

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

2.729

2.735

2.740

2.730

34. Newton Raphson Formula is derived from

Taylor’s Theorem

Binomial Theorem

Bisection Formula

Roll’s Theorem

35. The fixed iterative method has ________ converges

cubic

None of these

quadratic

linear

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

f'(x)=0

f”(x)=0

f(x)=0

f'(x)=

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

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

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

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

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

38. Gauss- Serial iterative method is used to solve

partial differential Equation

differential equation

system of linear equations

system of non-linear equations

39. 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

0.7410

0.7306

40. 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

2.273

2.241

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

algebraic equation

polynomial equation

transcendental equation

All of above

42. The symbol used for shift operator

∇

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

0.10

0.20

0.15

0.25

44. 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

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

Guass-Jarden method

Guass Seidal method

Guass-Elimination

None

46. The method of false position is also known as

Iteration method

Regula False method

bisection method

secant method

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

transcendental equation

algebraic equation

polynomial equation

none

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

1/20

1/60

1/80

1/70

49. 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

11/5

19/5

9/5

50. 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

10.1995

10.2995

10.0995

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

Hyperbola

parabola

None of these

circle

52. The symbol used for average operator

53.

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

0.0004

0.004

0.003

0.0003

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

335

333.5

334.5

334.8

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

2 and 3

1 and 2

None of these

0 and 1

56. The method of successive approximation is known as

secant method

iteration method

convergent method

None

57. 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

Simpson’s rule

Trapezoidal rule

None

58. Relaxation method is known as

Direct method

Iterative method

algebraic method

simple method

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

Crout’s method

Guass Seidal method

Guass Jocobi method

Guass Jordan Method

60. Newton-Raphson method to solve equation having formula

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

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

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

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

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

-7

-1/2

62. 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

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

Euler’s modified method

None of these

Euler’s method

Ranga Kutta Method

64. 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

2.2

3.5

2.75

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

1/22

1/3

1/9

1/81

66. The number of significant figures in 0.021444 is

67. The rate of convergence of bisection method is

2.00

1.00

2.2

1.67

68. The number of significant digits in 8.00312

Vector and tensor analysis mcqs with answers

Numerical Analysis Multiple Choice Questions Answers

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