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. 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

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

2 and 3

None of these

0 and 1

1 and 2

3. The number of significant figures in 48.710000

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

degree 3 or less

degree 4

degree 5

degree 6

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

1.60

1.16154

1.50

1.70

6. 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

7. The symbol used for shift operator

∇

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

0.265

0.242

0.234

0.246

9. Newton-Raphson method to solve equation having formula

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

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

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

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

10. 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

2.273

2.242

2.241

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

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

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

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

None

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

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

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

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

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

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

0.788

None of these

0.781

0.785

14. 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

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

2.740

2.729

2.735

2.730

16. Newton Raphson Formula is derived from

Roll’s Theorem

Bisection Formula

Binomial Theorem

Taylor’s Theorem

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

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

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

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

None

18. 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

3.5

2.75

4.0

19. Gauss- Serial iterative method is used to solve

system of linear equations

differential equation

system of non-linear equations

partial differential Equation

20. Relaxation method is known as

algebraic method

Direct method

Iterative method

simple method

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

1/81

1/22

1/3

1/9

22. 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

2.241

None of these

2.242

2.273

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

transcendental equation

polynomial equation

All of above

algebraic equation

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

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

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

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

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

25. The symbol used for forward diffefence operator is

∇

26. Relative error = ?

None

Error/ True value

Approximate error

Truncation error

27. 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

LU decomposition method

Crout’s method

28.

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

0.0003

0.0004

0.003

0.004

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

None of these

-0.00048

-0.000048

0.000046

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

333.5

334.8

334.5

335

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

1/60

1/80

1/70

1/20

32. The fixed iterative method has ________ converges

cubic

linear

quadratic

None of these

33. The order of convergence of iteration method is

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

3.465

3.461

3.412

None of these

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

Guass Seidal method

Crout’s method

Guass Jordan Method

Guass Jocobi method

36. 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

10.1995

10.0995

37. 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

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

transcendental equation

polynomial equation

algebraic equation

cubic equation

39. The symbol used for average operator

40. The number of significant figures in 0.021444 is

41. The number of significant digits in 8.00312

42. Newton’s method has ____________ convergence

None of these

cubic

linear

quadratic

43. The rate of convergence of secant method is

2.00

2.67

1.00

1.67

44. Bisection method is also known as

bolzano and Interval Halving method

Interval halving method

Bolzano method

successive method

45. 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

16.673

16.672

16.671

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

Guass-Elimination

None

Guass Seidal method

Guass-Jarden method

47. The rate of convergence of bisection method is

1.00

2.2

2.00

1.67

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

Euler’s modified method

Euler’s method

None of these

Ranga Kutta Method

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

Guass Jordan Method

Guass Elimination method

Guass Jocobi method

none

50. The Regula False method is somewhat similar to

iteration method

secant method

bisection method

none

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

Bisection method

Newton Method

None

tri-section

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

transcendental equation

algebraic equation

polynomial equation

none

53. 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

0.7410

0.7319

0.7306

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

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

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

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

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

55. Which of the following is iterative method

Guass-Elimination method

Guass Seidal method

Crout’s method

Guass Jardan method

56. The method of successive approximation is known as

convergent method

None

iteration method

secant method

57. The error in Trapezoidal rule is of order of

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

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

$\dpi{120} \small h$

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

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

0.15

0.10

0.20

0.25

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

f'(x)=0

f'(x)=

f(x)=0

f”(x)=0

60. 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

1.7265

1.857

1.7315

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

-7

-1/2

62. 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

Weddle’s rule

Trapezoidal rule

Simpson’s 1/3 rule

Newton-Cote’s Quadrature formula

63. The method of false position is also known as

secant method

Iteration method

Regula False method

bisection method

64. which method is known as Regula-Falsi method

secant method

Bisection method

Method of iteration

Method of interpolation

65. Method of factorization is also known as

Choleski method

triangularization method

LU-decomposition method

All of above

66. 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 $\dpi{120} \small x=0,\frac{1}{3},\frac{2}{3}, 0$