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.

This page consist of mcq on numerical methods with answers , mcq on bisection method, numerical methods objective, multiple choice questions on interpolation, mcq on mathematical methods of physics, multiple choice questions on , ,trapezoidal rule , computer oriented statistical methods mcq and mcqs of gaussian elimination method
We study Numerical Analysis for the preparation of mathematics for the purpose of M.Phil Math, P.hD math, EDUCATORS, LECTURER, SS, SSS, PPSC, FPSC tests. our team try ourselves best to touch every topic of Numerical Analysis to provide concept at all.

Note: You can also give valuable suggestions for the improvements of this subject.

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

0.15

0.25

0.20

0.10

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

parabola

circle

Hyperbola

None of these

3. 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

3.136

None of these

3.236

3.139

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

f”(x)=0

f(x)=0

f'(x)=

f'(x)=0

5. 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

1.7315

1.7265

1.7421

6. 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

7. 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

1/81

1/9

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

degree 5

degree 3 or less

degree 6

degree 4

9. The order of convergence of iteration method is

10. The symbol used for average operator

11. which method is known as Regula-Falsi method

Method of interpolation

Bisection method

Method of iteration

secant method

12. 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

13. The symbol used for shift operator

∇

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

Guass-Elimination

None

Guass-Jarden method

Guass Seidal method

15. The method of false position is also known as

secant method

Regula False method

bisection method

Iteration method

16. 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

10.2225

10.0995

10.1995

17. The rate of convergence of secant method is

2.00

1.00

2.67

1.67

18. The symbol used for backward difference operator

∇

$\dpi{120} \small \Delta$

19. 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

Simpson’s rule

None

20. Gauss- Serial iterative method is used to solve

system of linear equations

partial differential Equation

differential equation

system of non-linear equations

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

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

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

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

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

22. 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

23. 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

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

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

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

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

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

25. 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

Simpson’s 1/3 rule

Weddle’s rule

Trapezoidal rule

26.

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

0.0004

0.003

0.004

0.0003

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

Guass Elimination method

Guass Jocobi method

Guass Jordan Method

none

28. 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

29. Newton’s method has ____________ convergence

linear

cubic

None of these

quadratic

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

Guass Jordan Method

Guass Jocobi method

Crout’s method

Guass Seidal method

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

0.246

0.265

0.234

0.242

32. The Regula False method is somewhat similar to

secant method

iteration method

none

bisection method

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

None

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

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

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

34. 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

35. The symbol used for forward diffefence operator is

∇

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

0.781

0.788

0.785

None of these

37. The number of significant figures in 48.710000

38. Relative error = ?

Approximate error

Truncation error

Error/ True value

None

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

1.50

1.60

1.70

1.16154

40. The fixed iterative method has ________ converges

None of these

quadratic

linear

cubic

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

None

Newton Method

Bisection method

tri-section

42. Newton Raphson Formula is derived from

Bisection Formula

Taylor’s Theorem

Binomial Theorem

Roll’s Theorem

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

None of these

Ranga Kutta Method

Euler’s modified method

Euler’s method

44. 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

45. Bisection method is also known as

successive method

Bolzano method

Interval halving method

bolzano and Interval Halving method

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

2.730

2.729

2.740

2.735

47. 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

2.241

2.242

2.273

48. 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

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

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

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

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

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

334.8

334.5

335

333.5

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

None

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

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

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

51. Newton-Raphson method to solve equation having formula

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

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

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

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

52. The number of significant digits in 8.00312

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

16.672

16.670

16.671

54. The number of significant figures in 0.021444 is

55. Relaxation method is known as

algebraic method

Iterative method

Direct method

simple method

56. 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

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

transcendental equation

polynomial equation

cubic equation

algebraic equation

58. Which of the following is iterative method

Crout’s method

Guass Jardan method

Guass-Elimination method

Guass Seidal method

59. 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

60. Method of factorization is also known as

Choleski method

triangularization method

LU-decomposition method

All of above

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

All of above

algebraic equation

transcendental equation

polynomial equation

62. 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

63. The error in Trapezoidal rule is of order of

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

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

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

$\dpi{120} \small h$

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

-7

-1/2

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

-0.000048

-0.00048

0.000046

None of these

66. The rate of convergence of bisection method is

1.67

2.2

1.00

2.00

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

algebraic equation

none

polynomial equation

transcendental equation

68. The method of successive approximation is known as

convergent method

iteration method

None

secant method

Vector and tensor analysis mcqs with answers

Numerical Analysis Multiple Choice Questions Answers

Useful Links:

Leave a Comment Cancel Reply