Nadar Saraswathi College of Engineering and Technology ...

SEM- 4th Semester – B.E. / B.Tech

BR- Department of Mechanical Engineering

Sub:- MA6452 – Statistics and Numerical Methods

Part-A (10 x 2) = 20 Marks)

UNIT I TESTING OF HYPOTHESIS

No Question Level Competence Mark

1.1 Define Null hypothesis L1 Remembering 2

1.2 What is Type I, Type II error? L2 Understanding 2

1.3 Define test statistics L1 Remembering 2

1.4 Write the application of F-Test and χ2. L1 Remembering 2

1.5 Write two applications of 2 -Test. L3 Applying 2

1.6 Define a F – variance? L1 Remembering 2

1.7 Define Critical region. L1 Remembering 2

2.1 What is sampling distribution? L5 Evaluation 2

2.2 What are the parameters and statistics in sampling? L3 Application 2

2.3 Mention the various steps involved in testing of

hypothesis.

L3 Application 2

2.4 Define student’s t-test for difference of means of

two samples.

L5 Evaluation 2

2.5 Explain Null Hypothesis L1 Remembering 2

2.6 a b L2 Understanding 2

Nadar Saraswathi College of Engineering and Technology,

Vadapudupatti, Theni - 625 531

(Approved by AICTE, New Delhi and Affiliated to Anna University, Chennai)

Format No. NAC/TLP-

07a.12

Rev. No. 01

Date 14-11-2017

Total Pages 01

Question Bank for the Units – I to V

c d

What are the expected frequencies of 2x2

contingency table given above.

2.7 If two samples are taken from two population of

unequal variances can we apply t-test to test the

difference of mean

L3 Applying 2

UNIT-II DESIGN OF EXPERIMENTS

3.1 What is meant by Latin square? L1 Remembering 2

3.2 Compare one-way classification method with two-way

classification method.

L2 Understanding 2

3.3 Define Analysis of variance. L1 Remembering 2

3.4 What is the assumption in analysis of variance? L1 Remembering 2

3.5 What are the three essential steps to plan an

experiment?

L1 Remembering 2

3.6 What are the basic steps in ANOVA? L2 Understanding 2

3.7 State the formula to find SSC. L2 Understanding 2

4.1 Write the steps to find F- ratio. L4 Analyzing 2

4.2 Write down the ANOVA table for One-way

classification.

L1 Remembering 2

4.3 What are the advantages of completely randomized

block design?

L4 Analyzing 2

4.4 State the uses of ANOVA. L3 Applying 2

4.5 Write the ANOVA table for randomized block design. L1 Remembering 2

4.6 Define replication. L1 Remembering 2

4.7 Write the ANOVA table for Latin square. L1 Remembering 2

UNIT-III SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS

5.1 If g(x) is continuous in [a, b], then under what

condition the iterative method x=g(x) has a unique

solution in [a, b]?

L2 Understanding

2

5.2 Find an iterative formula to find ,N where N is

positive number.

L3 Applying 2

5.3 State the order of convergence and convergence

condition for Newton’s Raphson method.

L3 Applying 2

5.4 Derive the Newton-Raphson formula to find the cube

root of a positive number K.

L1 Remembering 2

5.5 Locate the negative root of ,0523 xx

approximately.

L2 Understanding 2

5.6 Evaluate 12 applying Newton formula. L2 Understanding 2

5.7 Establish an iteration formula to find the reciprocal of

a positive number N by Newton-Raphson method?

L4 Analyzing 2

6.1 Compare Gauss-Jacobi and Gauss-Seidal methods for

solving linear systems of the form AX = B.

L4 Analyzing 2

6.2 For solving a linear system, compare Gaussian

elimination method and Gauss-Jordan method.

L4 Analyzing 2

6.3 State the two differences between direct and

iterative methods for solving system of equations.

L4 Analyzing 2

6.4 Gauss-seidal method is better than Gauss-Jacobi

method. Why?

L4 Analyzing 2

6.5 What is the condition for convergence of Gauss-Jacobi

method of iteration?

L1 Remembering 2

6.6 Write the first iteration; values of x,y,z when the

equations

1105,722156,85627 zyxzyxzyx are

solved by Gauss-Seidal method.

L2 Understanding

2

6.7 Explain briefly Gauss-Jordan iteration to solve

simultaneous equation.

L1 Remembering 2

UNIT-IV INERPOLATIONL NUMERICAL DIFFERENTIATION AND NUMERICXAL

INTEGRATION

7.1 Construct a linear interpolating polynomial given the

points (xo, yo) and (x1,y1).

L1 Remembering 2

7.2 What is the Lagrange’s formula to find y if three sets

of values (xo,yo) and (x1,y1), (x2,y2).are given?

L1 Remembering 2

7.3 Find the second degree polynomial fitting the following

x 1 2 4

y 4 5 13

L2 Understanding

2

7.4 Give inverse Lagrange’s interpolation formula. L1 Remembering 2

7.5 State Lagrange’s interpolation formula L1 Remembering 2

7.6 Obtain the divided difference table for the following

data.

x -1 0 2 3

y -8 3 1 12

L2 Understanding

2

7.7 Give the Newton’s divided difference interpolation

formula.

L1 Remembering 2

8.1 Taking h to be the interval of differencing find )(2 xe . L2 Understanding 2

8.2 Form the divided difference table for the following

data

x 2 5 10

y 5 29 109

L2 Understanding

2

8.3 Find ( log x ) L2 Understanding 2

8.4 What are the errors in Trapezoidal rule of numerical

integration?

L1 Remembering 2

8.5 What is the order of error in Trapezoidal rule? L1 Remembering 2

8.6 What is the error’s in Simpson’s rules of numerical

integration?

L1 Remembering 2

8.7 Why Simpson’s one third rule is called a closed

formula?

L1 Remembering 2

UNIT-V NUMERICAL SOLUCLTION OF ORDINARY DIFFERENTIAL EQUATIONS

9.1 Compute Y (0,1) by Taylor’s series method to three

places of decimals given that .1)0(; yyxdx

dy

L2 Understanding 2

9.2 Write the merits and demerits of the Taylor method

of solution. .

L1 Remembering 2

9.3 Solve 0)0(;1 yy

dx

dy for x=0.1.by Euler’s method.

L2 Understanding 2

9.4 Solve 1)0(; yy

dx

dyto find y(0.01)using Euler’s

method.

L2 Understanding 2

9.5 Given

yx

xyy

' with initial condition y=1 at x=0 find y

L1 Remembering 2

for x-o.1 by Euler’s method.

9.6 .1)0(;2 yyx

dx

dyDetermine y(0.02) using Euler’s

modified method

L2 Understanding 2

9.7 What are the single step and multistep methods? Give

an example.

L2 Understanding 2

10.1 Compare Taylor series and Runge –Kutta method. L2 Understanding 2

10.2 What are the advantages of R-K method over Taylor’s

method?

L4 Analyzing 2

10.3 Write the Milne’s Predictor-Corrector formula. L2 Understanding 2

10.4 Write the Adams Bashforth Predictor – Corrector

formula

L2 Understanding 2

10.5 In the derivation of fourth order Range – Kutta

formula, why it is called fourth order?

L4 Analyzing 2

10.6 Write down the formula for 4th order Range-Kutta

formula.

L2 Understanding 2

10.7 Explain the meaning of explicit and implicit method in

numerical calculation.

L4 Analyzing 2

Part – B ( 5 x 16 = 80 Marks)

UNIT I TESTING OF HYPOTHESIS

11.a-i A sample of 900 members has a mean 3.4 cm and

standard deviation 2.61 cm.Is the sample from a

large population of mean 3.25 cms and standard

deviation of 2.61cms?(Test at 5% level of

significance.The value of z at 5% level is

z <1.96)

L2 Understanding (8)

11.a-i The mean life time of a sample of 100 light bulbs

produced by a company is computed to 1570 hours

with a standard deviation of 120 hours. If is

the mean life time of all the bulbs produced by

the company, test the hypothesis = 1600 hours,

against the alternative hypothesis ≠1600 hours

with =0.05 and 0.01


11.a-i Two horses A and B were tested according to the

time (in seconds) to run a particular rave with

the following results:

Horse A 25 30 32 33 33 29 34

Horse B 29 30 30 24 27 29

Test whether the horse A is running faster than B

at 5% level.


11.a-i A random sample of 10 boys had the following

L.Q’s: 70,120,110,101,88,83,95,98,107,100.Do

these data support the assumption of a population

mean I.Q 100? Find a reasonable rang in which

most of the mean I.Q. values of samples of 10boys

life.


11.a-i The table below gives the number of aircraft

accidents that occurred during the various days of

the week. Test whether the accidents are

uniformly distributed over the week.

Days: Mon Tue Wed Thur. Fri Sat

No. of accidents: 14 18 12 11 15 14


11.a-ii Out of 8000 graduates in a town 800 are females;

out of 1600 graduate employees 120 are females.

Use χ2.to determines if any distinction is made in

appointment on the basis of sex. Value of χ2.at

5% level for one degree of freedom is3.84

L3 Applying (8)

11.a-ii An automobile company gives the following information

about age groups and the liking for particular model of

car which it plans to introduce. On the basis of this

data can it be concluded that the model appeal is

independent of the age group (χ2 0.05(3) =

7.815)

Persons who: Below20 20-39 40-59 60 and

above

Liked the car: 140 80 40 20 Disliked the car: 60 50 30 80

L4 Analyzing (8)

11.a-ii Two sample polls of votes for two candidates A and B

for a public office are taken one from among residents

of rural areas. The results are given below Examine

whether the nature of the area is related to voting

preference in this election.

Area/Votes for A B Total

Rural 620 380 1000

L4 Analyzing (8)

Urban 650 450 1000

Total 1170 830 2000

11.a-ii The sales manager of a large company conducted a

sample survey in states A and B taking 400 samples in

each case. The results were in the following table.

Test whether the average sales in the same in the 2

states at 1% level.

State – A State-B

Average sales Rs. 2,500 Rs. 2,200

S.D Rs. 400 Rs. 550

L4 Analyzing (8)

11.a-ii A mathematics test was given to 50 girls and 75 boys.

The girls made an average grade of 82 with a SD of 2.

Test whether there is any significant difference

between the performance of boys and girls.

L3 Applying (8)

11.b-i Theory predicts that the proportion of beans in

four groups A,B,C,D should he 9:3:3:1. In an

experiment among 1600 beans, the numbers in the

four groups were 882,313,287 and 118.Does the

experiment support the theory?

L3 Applying (8)

11.b-i A group of 10 rats fed on diet A and another

group of 8 rats fed on diet B, recorded the

following increase in weight.

Diet A : 5 6 8 1 12 4 3 9 6 10

Diet B : 2 3 6 8 10 1 2 8

Find if the variances are significantly different.

L3 Applying (8))

11.b-i Two independent samples of sizes 9 and 7 from a

normal population had the following values of the

variables.

Sample I : 18 13 12 15 12 14 16 14 15

Sample II: 16 19 13 16 18 13 15

Do the estimates of the population variance differ

significantly at 5% level?

L3 Applying (8))

11.b-i Two random samples give the following results

Sample

Size

Mean

Sum of squares of

deviations from the

mean

I 10 15 90

II 12 14 108

Test whether the samples could have come from

the same normal population.

L4 Analyzing (8))

11.b-i Two researcher’s A and B adopted different

techniques while rating the students level. Can you

say that the techniques adopted by them are

significant?

Resear

cher’s

Below

avera

ge

Avera

ge

Above

average

Genius Total

A 40 33 25 2 100

B 86 60 44 10 200

Total 126 93 69 12 300

L4 Analyzing (8)

11.b-ii 1000 students at college level were graded

according to their I.Q. and their economic

conditions. What conclusion can you draw from

the following data:

Economic

Conditions

I.Q Level

High Low

Rich 460 140

Poor 240 160

L4 Analyzing (8)

11.b-ii Find if there is any association between

extravagance in fathers and extravagance in sons

from the following Data.

Extra average

Father

Miserly Father

Extra average

son

327 741

Miserly son 545 234

Determine the coefficient of association also.

L4 Analyzing (8)

11.b-ii The following is the distribution of the hourly

number of trucks arriving at a company’s

warehouse.

Trucks

arriving

per hour

0 1 2 3 4 5 6 7 8

Frequen

cy:

52 151 130 102 45 12 5 1 2

Find the mean of the distribution and using its

mean (rounded to one decimal ) as the parameter

fit a Poisson distribution. Test for goodness of

fit at the level of significance = 0.05.

L4 Analyzing (8)

11.b-ii Sandal powder is packed into packets by a L4 Analyzing (8)

machine. A random sample of 12 packets is drawn

and their weights are found to be (in kg )

0.49,0.48,0.47,0.48,0.49,0.50,0.51,0.49,0.48,0.50,

0.51,and 0.48 Test if the average weight of the

packing can be taken as 0.5 kg.

11.b-ii The following are the number of sales which a

sample of 9 salespeople of industrial chemicals in

Gujarat and a sample of 6 sales people of

industrial chemicals in Maharashtra made over a

certain fixed period of time:

Gujarat: 59 68 44 71 63 46 69 54

48

Maharashtra: 50 36 62 52 70 41

L4 Analyzing (8)

UNIT-II DESIGN OF EXPERIMENTS

12.a The following are the numbers of mistakes made in

5 successive days of 4 technicians working for a

photographic laboratory

Tech. I

(X1)

Tech. II

(X2)

Tech. III

(X3)

Tech. IV

(X4)

6 14 10 9

14 9 12 12

10 12 7 8

8 10 15 10

11 14 11 11

Test at the level of significance α = 0.01 where

the differences among the 4 sample means, can be

attributed to chance.

L3 Applying (16)

12.a The following table shows the lives in hours of

four brands of electric lamps.

Brand

A : 1610 1610 1650 1680 1700 1720 1800

B : 1580 1640 1640 1700 1750

C: 1460 1550 1600 1620 1640 1660 1740 1820

D: 1510 1520 1530 1570 1600 1680

Perform an analysis of variance test the

homogeneity of the mean lives of the four of

lamps.

L3 Applying (16)

12.a An experiment was designed to study the performance

of 4 different detergents for cleaning fuel injectors.

The following cleanliness readings were obtained with

L3 Applying (16)

rspecially designed equipment for 12 tanks of gas

distributed over 3 different models of engines.

Engine 1 Engine 2 Engine 3 Total

Detergent A 45 43 51 139

Detergent B 47 46 62 145

Detergent C 48 50 55 153

Detergent D 42 37 49 128

Total 182 176 207 565

Perform the ANOVA and test at 0.01 level of

significance, whether there are differences in the

detergents or in the engines.

12.a Analysis the following RBD and find your

conclusion.

Treatments

Blocks

T1 T2 T3 T 4

B1 12 14 20 22

B2 17 27 19 15

B3 15 14 17 12

B4 18 16 22 12

B5 19 15 20 14

L3 Applying (16)

12.a A tea company appoints four salesman A,B,C and D

and observes their sales in three-seasons-summer,

winter and monsoon. The figures (in lakhs) are given in

the following table.

Seasons Salesman Total

A B C D

Summer 36 36 21 35 128

Winter 28 29 31 32 120

Mansoon 26 28 29 29 112

Total 90 93 81 96 360

(i) Do the salesmen significantly differ in

performance?

(ii) Is there significant difference between the

seasons?

L3 Applying (16)

12.b In a Latin square experiment given below are the

yields in quintals per acre on the paddy crop

carried out for testing the effect of five

fertilizers A,B,C,D,E. Analyze the data for

variations.

B25 A18 E27 D30 C27

A19 D31 C29 E26 B23

C28 B22 D33 A18 E27


E28 C26 A20 B25 D33

D32 E25 B23 C28 A20

12.b The following is a Latin square of a design, when 4

varieties of seeds are being tested. Set up the

analysis of variance table and state your

conclusion. You may carry out suitable change of

origin and scale.

A105 B95 C125 D115

C115 D125 A105 B105

D115 C95 B105 A115

B95 A135 D95 C115


12.b The accompanying data resulted from an

experiment comparing the degree of soiling for

fabric co-polymerized with the three different

mixtures of methacrylic acid. Analysis is the given

classification.

Mixture 1 .56 1.12 .90 1.07 .94

Mixture 2 .72 .69 .87 .78 . 91

Mixture 3 .62 1.08 1.07 .99 .93


12.b Analyze the following of Latin square experiment.

1 2 3 3

1 A(12) D(20) C(16) B(10)

2 D(18) A(14) B(11) C(14)

3 B(12) C(15) D(19) A(13)

3 C(16) B(11) A(15) D(20)

The letters A,B,C,D denote the treatments and the

figures in brackets denote the observations


12.b Find out the main effects and interactions in the

following 22 –factorial experiment and write down the

Analysis of Variance table:

Block/F (1)

00

a

10

b

01

ab

11

I 64 25 30 06

II 75 14 50 33

III 76 12 41 17

IV 75 33 25 10


UNIT-III SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS

13.a-i Find a real root of the equation x3+x2-1=0 by fixed

point iteration method.


13.a-i Solve the iteration method 2x-log10x=7 L2 Understanding (8)

13.a-i Find a root of x log10x – 1.2 = 0 by N.R method

correct to three decimal places.


13.a-i Using Newton’s iterative method, find the root

between 0 and 1 of x3 = 6x -4 correct to two decimal

places.


13.a-i Find the real positive root of 3x – cos x – 1 = 0 by

Newton’s method correct to 6 decimal places.


13.a-ii Solve the system of equation 28x+4y-z=32; x+3y+10z=24;

2x+17y+4z=35 using Gauss elimination method.


13.a-ii Using the Gauss –elimination method to solve the

following equations. 7513102;1210 zyxzyxzyx


13.a-ii Solve the following system by Gauss – Jorden method p+q+r+4s=6’ p+7q+r+s=12; p+q+6r+s=-5; 5p+q+r+s=4


13.a-ii Using the Gauss –Jordan method solve the

following equations. 7513102;1210 zyxzyxzyx


13.a-ii Solve, x + 3y + 3z=16, x + 4y + 3z 18, x + 3y +

4z=19 , by Gauss-Jordan method.


13.b-i Solve the following system of equations by Gauss-

seidel method. 722156;11054;85627 zyxzyxzyx


13.b-i Solve the following equations by Gauss-Seidel

method 4 x + 2y + z = 14, x + 5y -z = 10, x + y + 8z = 20.


13.b-i Solve the system of equations by Gauss-

elimination

10x -2y+3z =23, 2x +10y -5z = -33,3x-4y+10z =41.


13.b-i Solve the system of equations by Gauss-

elimination

83x +11y-4z =95, 7x +52y +13z = 104,3x+8y+29z

=72.


13.b-i Using power method to find the dominant Eigen values L3 Applying (8)

and eigenvector of A =

210

421

012

13.b-ii Find the numerically largest Eigen value of

A =

536

144

231

by power method

L3 Applying (8)

13.b-ii Using power method, find all the Eigenvalues of

A =

501

020

105

by power method

L3 Applying (8)

13.b-ii Find the numerically largest Eigen value of

A =

402

031

2125

by power method

L3 Applying (8)

13.b-ii Find all the eigenvalues and eigenvectors of the matrix

A =

122

232

221

using Jacobi’s method.

L3 Applying (8)

13.b-ii Find all the eigenvalues and eigenvectors of he matrix A =

210

121

012

using Jacobi’s method.

L3 Applying (8)

UNIT-IV INERPOLATIONL NUMERICAL DIFFERENTIATION AND NUMERICXAL

INTEGRATION

14.a-i Find the polynomial f(x) by using Lagrange’s formula

and hence find f (3) for

x 0 1 2 5

f(x) 2 3 12 147

L3 Applying (8)

14.a-i Using Lagrange’s interpolation, calculate the profit in

the year 2000 from the following data:

Year 1997 1998 2001 2002

Profit in lakhs. 43 65 159 248

L3 Applying (8)

14.a-i Find the third-degree polynomial f(x) satisfying the

following data:

x 1 3 5 7

y 24 120 336 720

L3 Applying (8)

14.a-i Using Lagrange interpolation find Y(2) from the

following data.

x 0 1 3 4 5

y 0 1 81 256 625

L3 Applying (8)

14.a-i Using Lagrange's interpolation formula, find Y(10) given

that Y(5)=12, Y(6)=13,y(9) = 14, y(11)=16.

L3 Applying (8)

14.a-ii Using Newton's divided difference formula, find U(3)

given u(1) =-26, U(2) = 12, u(4) = 256, u(6) = 844.

L3 Applying (8)

14.a-ii Find f(x) as a polynomial in x for the following data by

Newton's divided difference formula

x -4 -1 0 2 5

f(x) 1245 33 5 9 1335

L3 Applying (8)

14.a-ii Find f(8) by Newton's divided difference formula for

the data

x 4 5 7 10 11 13

f(x) 48 100 294 900 1210 2028


14.a-ii Using Newton's divided difference formula , find f(x)

and f(6) from the following data.

x 1 2 7 8

f(x) 1 5 5 4


14.a-ii Using Newton's forward interpolation formula, find the

polynomial f(x) satisfying the following data .Hence ,

evaluate y at x = 5

x 4 6 8 10

y 1 3 8 10


14.b-i Using Newton's forwarded interpolation formula find

the cubic polynomial which takes place the following

values

x 0 1 2 3

f(x) 1 2 1 10


14.b-i

Weight in lbs 0-40 40-60 60-80 80-100 100-120


From the data given below, find the number of

students whose weight is between 60 to 70.

No.of stu. 250 120 100 70 50

14.b-i The following data are taken from the steam table:

Find the pressure at temperature t = 1420 and t = 1750

Tem 0c 140 150 160 170 180 Pressure kg/cm2 3.685 4.854 6.302 8.076 10.225


14.b-i Find the first, ssecond and third derivatives of f(x) at

x = 1.5 if

x 1.5 2.0 2.5 3 3.5 4

f(x) 3.375 7.000 13.625 24.000 38.875 59.000


14.b-i Using Trapezoidal rule, evaluate dx

x

1

1

21

1 taking 8

intervals.

L3 Applying (8)

14.b-ii Dividing the range into 10 equal parts, find the value of

2/

0

sin xdx by (i) Trapezoidal rule (ii) Simpson’s rule.

L3 Applying (8)

14.b-ii The velocity v of a particle at a distance S from a point

on its path is given by the table below.

S in met 0 10 20 30 40 50 60

V m/sec 47 58 64 65 61 52 38

Estimate the time taken to travel 60 metres by

Simpson’s 1/3rule.

L3 Applying (8)

14.b-ii Evaluate, numerically

2

1

2

1

dxdyyx

xywith h = k =0.25

Trapezoidal rule.

L3 Applying (8)

14.b-ii Evaluate, numerically

2

1

2

1

22 yx

dxdywith h =0.2 and k

=0.25 Trapezoidal rule.

L3 Applying (8)

14.b-ii Evaluate using Simpson’s 1/3 rule

1

0

1

01

1dxdy

yxtaking h=k=0.5.

L3 Applying (8)

UNIT-V NUMERICAL SOLUCLTION OF ORDINARY DIFFERENTIAL EQUATIONS

15.a-i By means of Taylor's series expansion, find y at x =

0.1,0.2 correct to three significant digits given


.0)0(,32 yeydx

dy x

15.a-i Using Euler's method find y(0.2) and y(0.4) from

,yxdx

dy y(0) = 1 with h = 0.2.


15.a-i Solve y' = 1-y, y(0) = 0 by modified Euler's method.

Find y(0.1), y(0.2) and y(0.3).


15.a-i Consider the initial value problem ,12 xy

dx

dyy(0) =

0.5 using the modified Euler's method, find y(0.2).


15.a-i Using R-K method of fourth order, solve

22

22

xy

xy

dx

dy

with y(0)=1 at x=0.2.

L3 Applying (8)

15.a-ii

Using R-K method of fourth order find y(0.1) and y(0.2)

for the initial value problem

L3 Applying (8)

15.a-ii Find y(0.7) and y(0.8) given that

7379.1)6.0(,2' yxyy by using Runge-Kutta method

of fourth order. Take h=0.1.

L3 Applying (8)

15.a-ii Using Milne's method find y(4.4) given 025 2' yxy

given y(4)=1,y(4.1)=1.0049,y(4.2)=1.0097 and

y(4.3)=1.0143.

L3 Applying (8)

15.a-ii Use Milne's predictor-corrector formula to find

y(0.4) given

12.1)2.0(,06.1)1.0(,1)0(,2

)1( 22

yyyyx

dx

dyand

y(0.3)=1.21

L3 Applying (8)

15.a-ii

Given

,1755.2)4.0(,0933.2)2.0(,2)0(,1'

yyyyx

y

Y(0.6)=2.2493,y(0.8) by Adam’s Bashforth

predictor corrector method.


15.b Solve 0)0(,10,2' yxyxy ,y(0.2)=0.02,y(0.4)=

0.0795, Y(0.6)=0.1762 by Milne's method to find

y(0.8) and y(1).


15.b Using R-K method of order 4,find y for x=0.1,0.2,0.3

given that 1)0(,2 yyxydx

dyand also find the


solution at x=0.4 using Milne's method.

15.b Solve for y(0.1) and z(0.1) from the simultaneous

differential equations

5.0)0(,0)0(;3;2 zyzydx

dzzy

dx

dyusing Runge-

Kutta method of the fourth order.


15.b Determine the value of y(0.4) using Milne's method

given 1)0(,2' yyxyy ; use Taylor series to get the

values of y(0.1),y(0.2)and y(0.3).


15.b Solve the initial value problem 2yx

dx

dy , y(0)=0

to find y(0.4) by Adam’s method. Starting solution

required to be obtained using Runge-Kutta method

of fourth order using step value h=0.1


15.b Using Adam’s method find y(0.4) given

2

xyy , y(0)=1

use Euler method to get the values of; y(0.1); y(0.2);

y(0.3).


L1: Remembering L2: Comprehension, L3: Application, L4: Analysis, L5: Evaluation,

QUESTION BANK SUMMARY

S.NO UNIT DETAILS L1 L2 L3 L4 L5 L6 TOTAL

1 Unit-1 PART-A 6 2 4 2 - 14

PART-B 5 5 10 - - 20

2 Unit-2 PART-A 7 4 3 - - - 14

PART-B - 5 5 - - - 10

3 Unit-3 PART-A 3 4 2 5 - - 14

PART-B - 15 5 - - - 20

4 Unit-4 PART-A 9 5 - - - - 14

PART-B - 7 13 - - - 20

5 Unit-5 PART-A 2 9 - 3 - - 14

PART-B - 15 - - - - 15

Total No of Questions

PART-A PART-B TOTAL

70 85 155

Prepared By:

Staff Name1: B. MALLAIYSAMY

Staff Name2: G. SOLAILAKSHMI

STAFF IN CHARGE HOD PRINCIPAL

Nadar Saraswathi College of Engineering and Technology ...

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