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
L2 Understanding (8)
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.
L2 Understanding (8)
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.
L2 Understanding (8)
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
L2 Understanding (8)
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
L2 Understanding (8)
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
L2 Understanding (8)
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
L2 Understanding (8)
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
L2 Understanding (8)
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
L2 Understanding (8)
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.
L2 Understanding (8)
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.
L2 Understanding (8)
13.a-i Using Newton’s iterative method, find the root
between 0 and 1 of x3 = 6x -4 correct to two decimal
places.
L2 Understanding (8)
13.a-i Find the real positive root of 3x – cos x – 1 = 0 by
Newton’s method correct to 6 decimal places.
L2 Understanding (8)
13.a-ii Solve the system of equation 28x+4y-z=32; x+3y+10z=24;
2x+17y+4z=35 using Gauss elimination method.
L2 Understanding (8)
13.a-ii Using the Gauss –elimination method to solve the
following equations. 7513102;1210 zyxzyxzyx
L2 Understanding (8)
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
L2 Understanding (8)
13.a-ii Using the Gauss –Jordan method solve the
following equations. 7513102;1210 zyxzyxzyx
L2 Understanding (8)
13.a-ii Solve, x + 3y + 3z=16, x + 4y + 3z 18, x + 3y +
4z=19 , by Gauss-Jordan method.
L2 Understanding (8)
13.b-i Solve the following system of equations by Gauss-
seidel method. 722156;11054;85627 zyxzyxzyx
L2 Understanding (8)
13.b-i Solve the following equations by Gauss-Seidel
method 4 x + 2y + z = 14, x + 5y -z = 10, x + y + 8z = 20.
L2 Understanding (8)
13.b-i Solve the system of equations by Gauss-
elimination
10x -2y+3z =23, 2x +10y -5z = -33,3x-4y+10z =41.
L2 Understanding (8)
13.b-i Solve the system of equations by Gauss-
elimination
83x +11y-4z =95, 7x +52y +13z = 104,3x+8y+29z
=72.
L2 Understanding (8)
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
L2 Understanding (8)
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
L2 Understanding (8)
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
L2 Understanding (8)
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
L2 Understanding (8)
14.b-i
Weight in lbs 0-40 40-60 60-80 80-100 100-120
L2 Understanding (8)
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
L2 Understanding (8)
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
L2 Understanding (8)
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
L2 Understanding (8)
.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.
L2 Understanding (8)
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).
L2 Understanding (8)
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).
L2 Understanding (8)
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.
L2 Understanding (8)
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).
L2 Understanding (16)
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
L2 Understanding (16)
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.
L2 Understanding (16)
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).
L2 Understanding (16)
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
L2 Understanding (16)
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).
L2 Understanding (16)
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