Model Question Paper

Subject Code: BC0043

Subject Name: Computer Oriented Numerical Methods

Credits: 4 Marks: 140

Part A (One mark questions)

1. .. is an approach for solving complex mathematical problems using only simple

basic arithmetic operations

A) Numerical computing

B) Binary computing

C) Arithmetical computing

D) Factorial computing

2. Consider the two points P(a, f(a)) and Q(b, f(b)) are two points on the curve, slope of the line

joining the points P and Q is .

A) ba

bfaf

)()(

B) ab

afbf

)()(

C) ba

bfaf

)()(

D) ab

afbf

)()(

3. The remainder term Rn(x) of a taylor series is given by

A) )(!

)()( 4 f

n

axxR

n

n

, where a < < x

B) )(!

)()( 3 f

n

axxR

n

n

, where a < < x

C) )(!

)()( n

n

n fn

axxR

, where a < < x

D) )(!

)()( 2 f

n

axxR

n

n

, where a < < x

4. The expansion .......)0(!

....)0(!2

)0()0()(2

nn

fn

xf

xfxfxf is known as

A) Taylors series

B) Bernards series

C) Newtons series

D) Maclaurins series

5. Every algebraic equation of nth degree, where n is a positive integer, has only

A) n 1 roots

B) n + 1 roots

C) 2n roots

D) n roots

6. If a + ib is a root of f(x) = 0 then the other root is .

A) a ib

B) a

C) b

D) ib

7. If x = a is a root of f(x) = 0, then the factor of f(x) is .

A) x + a

B) a

C) x a

D) x

8. The equation 0543 23 xxx has ..

A) 3 negative roots

B) 1 positive root

C) 3 positive roots

D) 2 positive roots

9. The order of the matrix

2

4

2

is ..

A) 3 1

B) 1 3

C) 2 3

D) 3 3

10. The matrix

300

030

003

is called as a .

A) row matrix

B) scalar matrix

C) column matrix

D) null matrix

11. If

32

12A and

22

11B then A + B =

A)

10

01

B)

10

01

C)

10

01

D)

10

01

12. The matrix

cfg

fbh

gha

A is a

A) symmetric matrix

B) non-symmetric matrix

C) reducible matrix

D) irreducible matrix

13) Gauss-Jacobis method is a .. method

A) Non-iteration

B) Iteration

C) infinite

D) algebraic

14. A sufficient condition for the iterative solution to have exact solution is ..

A) niaan

ijj

ijij .....,,2,1,1

B) niaan

ijj

ijij .....,,2,1,1

C) niaan

ijj

ijij .....,,2,1,1

D) niaan

ijj

ijij .....,,2,1,1

15. Jacobis method is also called as ..

A) displacement method

B) simultaneous displacement method

C) simultaneous method

D) diagnol method

16. Convergence in the Gauss-Seidal method is as fast as Gauss-Jacobis method.

A) thrice

B) same

C) twice

D) five times

17. In the method of group of averages, the residual e1 is defined as

A) 2

111 )( cmxye

B) )( 111 cmxye

C) )( 111 cmxye

D) )( 111 cmxye

18. The method of group averages states that the sum of all the residuals is

A) e

B)

C) 100

D) 0

19. The method of finding a specific relation y = f(x) for the data to satisfy as accurately as

possible is called the

A) curve of least fit

B) curve of best fit

C) fitting curves

D) curve of equation

20. when curve fitting is done for the straight line y = a + bx by the method of least squares, it

has .. normal equations

A) 3

B) 4

C) 2

D) 1

21. Process of estimating the value of dependent variable at an intermediate value is

called

A) Interpolation

B) Extrapolation

C) Estimation

D) Dependency

22. The value of the independent variable x is called the ..

A) Entry

B) Argument

C) Depositary

D) Amplitude

23. The relationship between E and is

A) E = 1 + 2

B) E = 1

C) E = 1

D) E = 1 +

24. The polynomial y = f(x) satisfying the data is called ..

A) Dividing polynomial

B) Interpolating polynomial

C) Extrapolating polynomial

D) Polynomial

25. A .. is a relation between the differences of an unknown function at one or

more general values of the argument.

A) Differential equation

B) Partial differential equation

C) Difference equation

D) linear equation

26. . of difference equation is an expression for y(n) which satisfies the given

difference equation.

A) Function

B) Order

C) Solution

D) Degree

27. A difference equation is that in which yn+1, yn+2 etc. occur to the first degree only

and are not multiplied together.

A) Linear

B) Quadratic

C) Cubic

D) Quartic

28. A . solution is that solution which is obtained from the general solution by giving

particular values to the constants.

A) Accurate

B) Recurring

C) Particular

D) Integer

29. The error in the trapezoidal rule is of order ..

A) h2

B) h3

C) h4

D) h5

30. Simpsons 3

1rd rule is obtained by taking n = .. in the general quadrature formula

A) 1

B) 2

C) 3

D) 4

31. Error in Simpsons three eighth rule is .. compared to Simpsons one third rule.

A) Small

B) Negligible

C) Zero

D) Large

32. To apply Simpsons one third rule, the given interval must be divided into an

number of equal intervals.

A) Odd

B) Even

C) Countable

D) Uncountable

33. The .. of a differential equation is the order of the highest derivative appearing in it.

A) Value

B) Degree

C) Dimension

D) Order

34. The equation xxydx

dysin

3

is a .. order differential equation.

A) First

B) Second

C) Third

D) Fourth

35. A differential equation together with the initial condition is called ..

A) Initial value

B) Initial value problem

C) Problem

D) Conditioned problem

36. )(!4!3!2

5

0

4

0

3

0

2

001 hOyh

yh

yh

yhyy iv is a Taylor series method of order

..

A) Four

B) Three

C) Two

D) One

37. In . we approximate the curve of solution by the tangent in each interval.

A) Picards method

B) Eulers method

C) Newtons method

D) Runge Kutta method

38. The convergence in modified Eulers method is than that of Eulers method

A) Slower

B) compatible

C) Faster

D) one time more

39. The equation 2

22

dx

udc

dt

du is .

A) Hyperbolic

B) Parabolic

C) Elliptic

D) A wave

40. The equation 02

2

2

2

dy

ud

dx

udis a

A) One dimensional Laplace equation

B) Laplace equation

C) Two dimensional Laplace equation

D) Three dimensional Laplace equation

Part B (Two mark questions)

41. The truncation error in the result of the following function for 5

1x when we use first three

terms is

A) 2105402755.0

B) 2106402755.0

C) 2107402755.0

D)2101402755.0

42. If the number X = 0.51 and is correct to two decimal places, then X =

A) 0.006

B) 0.007

C) 0.005

D) 0.008

43. The percentage error if 625.483 is approximated to 3 significant digits is ..

A) 0.0662

B) 0.0772

C) 0.0552

D) 0.0882

44. The real root of the equation 53)( 3 xxxf lies between.

A) 1 and 3

B) 2 and 3

C) 3 and 4

D)1 and 2

45. Rewriting the equation 1xxe , in the form of )(xx we get .

A)xex

B) xex 2

C) xex 1

D) 6 xex

46. If

21

53A and

31

52B then the value of AB =

A)

11

11

B)

10

11

C)

10

01

D)

11

01

47. On expanding 0 IA , we get a nth degree equation in , called the

of the matrix A.

A) normal equation

B) ideal equation

C) characteristic equation

D) non-characteristic equation

48. In the characteristic equation 0672 , the value of the determinant is

A) 7

B) 6

C) 6

D) 2

49. In the method of moments the second moment is given by .

A) dxxfx )(2

B) dxxfx )(2

C) dxxfx )(

D) dxxfx )(

50. From the following given values

x 0 1 2 3 4

y = f(x) 1 2 4 5 9

the value of 03y is

A) 2

B) 2

C) 1

D) 4

51. If E is the shift operator then f(xnh) =

A) E-nf(2x)

B) E-nf(x2)

C) E-nf(x)

D) E-nf(3x)

52. In Newtons forward difference interpolation formula an =

A) nh

yn

n0

B) !

0

nh

yn

n

C) !

0

nh

yn

D) !

0

hn

yn

53. Consider the following data

x 2 4 5 6 8 10

y 10 96 196 350 868 1746

Here the value of )7(f is

A) 87

B) 68

C) 58

D) 78

54. The eigen values of the matrix

342

476

268

A is ..

A) 0, 3, 15

B) 1, 2, 14

C) 0, 3, 14

D) 1, 2, 15

55. The characterstic equation of the matrix

113

321

210

A is

A) 015 23

B) 015 23

C) 015 23

D) 015 23

56. Consider the following data

x 0 1 2 3 4

y 1 5 10 22 38

The straight line of best fit for this data is

A) y = 9.1 x + 3

B) y = 9.1 x 3

C) y = 7.1 x 3

D) y = 9.1 x 3

57. State whether true(T) or false(F)

The higher order forward differences are

(i) 00 )1( yEykk

(ii) 0)1( yyk

k

A) (i) T (ii) T

B) (i) T (ii) F

C) (i) F (ii) F

D) (i) F (ii) T

58. The value of ))()(( xbgxaf where a, b are constants is equal to

A) )]([)]([ xgbxfa

B) )]([)]([ xgaxfb

C) )]([)]([ xgbxfa

D) )]([)]([ xgaxfb

59. Consider the data

x 0 1 2 3 4 5

y 4 8 15 7 6 2

the value of y(0) =

A) 37.9

B) 27.9

C) 47.9

D) 17.9

60. The error in Simpsons one-third rule is

A) )(180

)( 4 ivyhah

B) )(180

)( 4 ivyhah

C) )(18

)( 4 ivyhah

D) )(180

)( 3 ivyhah

Part C (Four mark questions)

61. If 3

2 is approximated by 0.667, then the relative error is .

A) 410

2

1

B) 210

2

1

C)310

2

1

D) 3103

1

62. The real root of the equation 1xxe correct to four decimal places is ..

A) 0.8671

B) 0.6671

C) 0.5671

D) 0.7761

63. The real root of the equation 013cos xx correct to four decimal places by the

method of iteration is

A) 0.8071

B) 0.6071

C) 0.7071

D) 0.9071

64. The value of the determinant

0111

1011

1101

1110

is

A) 3

B) 3

C) 4

D) 4

65. The solution of the equations 2x + y + 4z = 12

4x + 11y z = 33

8x 3y + 2z = 20 is

A) x = 1, y = 2, z = 1

B) x = 1, y = 2, z = 1

C) x = 3, y = 2, z = 1

D) x = 1, y = 2, z = 1

66. The inverse of the matrix

211

323

111

A is

A)

111

013

111

B)

101

013

111

C)

101

012

111

D)

101

013

121

67. The equation of the best fitting straight line for the data given below is

x 1 3 4 6 8 9 11 14

y 1 2 4 4 5 7 8 9

A) y = 0.52 0.64x

B) y = 0.62 + 0.64x

C) y = 0.52 + 0.64x

D) y = 0.52 + 0.74x

68. Using the method of least squares, the relation of the form baxy , that fits the data given

below is

x 2 3 4 5

y 27.8 62.1 110 161

A) y = 7.375 x1.9311

B) y = 6.375 x1.9311

C) y = 5.375 x1.9311

D) y = 7.375 x2.9311

69. The value of f(15) from the following table of values is

A) 46.8672

B) 76.8672

C) 66.8672

D) 56.8672

70. The value of dx

dy and

2

2

dx

yd at x = 1 for the following data is

x 0 2 4 6 8

y 7 13 43 145 367

A) 2, 0

B) 2, 3

C) 4, 2

D) 3, 2

71. Consider nn

n BAy )3(2 , the differential equation we get by eliminating the constants

is

A) 0712 nnn yyy

B) 0612 nnn yyy

C) 062 12 nnn yyy

D) 0612 nnn yyy

x 10 20 30 40 50

y = f(x) 46 66 81 93 101

72. Using Simpsons one-third rule the value of

6.0

0

2

dxe x by taking 6 sub-intervals

is..

A) 0.5551

B) 0.5351

C) 0.6361

D) 0.7861

73. Using Taylor series method the initial value problem for 22 yx

dx

dy with y(0) = 1 for x =

0.25 is

A) 1.3333

B) 1.5555

C) 1.5454

D) 1.6754

74. If xydy

dx1 , y(0) = 2 then the value of y(0.3) by modified Eulers method is

A) 3.5019

B) 2.4019

C) 2.8765

D) 3.4089

75. If 21 y

dx

dy where y(0) = 0 then the value of y(0.6) is

A) 0.6841

B) 0.7853

C) 0.9873

D) 0.7658

Answer Keys

Part - A Part - B Part - C

Q. No. Ans. Key Q. No. Ans. Key Q. No. Ans. Key Q. No. Ans. Key

1 A 21 A 41 D 61 C

2 B 22 B 42 C 62 C

3 C 23 D 43 B 63 B

4 D 24 B 44 B 64 A

5 D 25 C 45 A 65 C

6 A 26 C 46 C 66 B

7 C 27 A 47 C 67 C

8 C 28 C 48 B 68 A

9 A 29 A 49 C 69 D

10 B 30 C 50 A 70 A

11 C 31 D 51 C 71 D

12 A 32 B 52 B 72 B

13 B 33 D 53 D 73 A

14 A 34 A 54 A 74 B

15 B 35 B 55 C 75 A

16 C 36 A 56 B

17 D 37 B 57 B

18 D 38 C 58 C

19 B 39 B 59 B

20 C 40 C 60 A