Download JNTUK (Jawaharlal Nehru Technological University Kakinada) B.Tech Supplementary 2013 Oct-Nov R10 I Semester (1st Year 1st Sem) MATHEMATICAL METHODS Question Paper.
I B.Tech I Semester Supplementary Examinations, Oct/Nov 2013
MATHEMATICAL METHODS
( Common to Civil Engineering, Electrical & Electronics Engineering,
Computer Science & Engineering, Electronics & Instrumentation
Engineering, Aeronautical Engineering, Bio-Technology and Automobile
Engineering)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?????
1. (a) Find rank of matrix using Echelon form A =
2
4
1 2 4
2 1 3
8 1 9
5
6
7
3
5
(b) Solve the equations using Gauss Jordan method
x+5y+z=9 , 2x+y+3z=12, 3x+y+4z=16 [7+8]
2. Using Cayley { Hamilton theorem nd A
8
if A =
1 2
2 1
[15]
3. Reduce the quadratic form 6x
2
1
+ 3x
2
2
+ 3x
2
3
4x
1
x
2
+ 4x
1
x
3
2x
2
x
3
to the sum of
squares form by diagonalization and nd the corresponding linear transformation.
Also nd the index and signature. [15]
4. (a) Find a real root of the equation x sinx +cosx=0, using Newton-Raphson's
method
(b) Evaluate
p
12 and
1
p
12
using xed point iteration method. [8+7]
5. (a) If the interval of di erencing is unity, prove the following:4
n
1
f(x)
o
=
4f(x)
f(x)f(x+1)
(b) Given that sin 45
o
= 0.7071, sin 50
o
= 0.8192, sin 60
o
= 0.8660, nd sin 48
o
.
[8+7]
6. (a) Computef
0
(1)using the given data:
X 1.0 1.5 2.0 2.5 3.0
f(x) 27 106.75 324 783.75 1621
(b) Using Simpson's 3/8
th
rule evaluate
R
6
0
dx
1+x
2
by dividing the range into 6 equal
parts [8+7]
7. (a) Solve y
1
=-xy
2
, y(o)=2 by modi ed Euler's method and hence nd y(o.1),
y(o.2)
(b) Solve
dy
dx
=
y
2
x
2
y
2
+x
2
, y(o)=1 by fourth order R-K method and hence nd y(o.2),
y(o.4) [8+7]
8. (a) Fit a least square parabola y= a+bx+cx
2
to the data (-1,2),(0,1),(1,4)
FirstRanker.com - FirstRanker's Choice
Code No: R10107/R10 Set No. 1
I B.Tech I Semester Supplementary Examinations, Oct/Nov 2013
MATHEMATICAL METHODS
( Common to Civil Engineering, Electrical & Electronics Engineering,
Computer Science & Engineering, Electronics & Instrumentation
Engineering, Aeronautical Engineering, Bio-Technology and Automobile
Engineering)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?????
1. (a) Find rank of matrix using Echelon form A =
2
4
1 2 4
2 1 3
8 1 9
5
6
7
3
5
(b) Solve the equations using Gauss Jordan method
x+5y+z=9 , 2x+y+3z=12, 3x+y+4z=16 [7+8]
2. Using Cayley { Hamilton theorem nd A
8
if A =
1 2
2 1
[15]
3. Reduce the quadratic form 6x
2
1
+ 3x
2
2
+ 3x
2
3
4x
1
x
2
+ 4x
1
x
3
2x
2
x
3
to the sum of
squares form by diagonalization and nd the corresponding linear transformation.
Also nd the index and signature. [15]
4. (a) Find a real root of the equation x sinx +cosx=0, using Newton-Raphson's
method
(b) Evaluate
p
12 and
1
p
12
using xed point iteration method. [8+7]
5. (a) If the interval of di erencing is unity, prove the following:4
n
1
f(x)
o
=
4f(x)
f(x)f(x+1)
(b) Given that sin 45
o
= 0.7071, sin 50
o
= 0.8192, sin 60
o
= 0.8660, nd sin 48
o
.
[8+7]
6. (a) Computef
0
(1)using the given data:
X 1.0 1.5 2.0 2.5 3.0
f(x) 27 106.75 324 783.75 1621
(b) Using Simpson's 3/8
th
rule evaluate
R
6
0
dx
1+x
2
by dividing the range into 6 equal
parts [8+7]
7. (a) Solve y
1
=-xy
2
, y(o)=2 by modi ed Euler's method and hence nd y(o.1),
y(o.2)
(b) Solve
dy
dx
=
y
2
x
2
y
2
+x
2
, y(o)=1 by fourth order R-K method and hence nd y(o.2),
y(o.4) [8+7]
8. (a) Fit a least square parabola y= a+bx+cx
2
to the data (-1,2),(0,1),(1,4)
Code No: R10107/R10 Set No. 1
(b) By the method of least squares t a straight line to the following data
x 5 10 15 15 20
y 15 19 23 26 30
[8+7]
?????
FirstRanker.com - FirstRanker's Choice
Code No: R10107/R10 Set No. 1
I B.Tech I Semester Supplementary Examinations, Oct/Nov 2013
MATHEMATICAL METHODS
( Common to Civil Engineering, Electrical & Electronics Engineering,
Computer Science & Engineering, Electronics & Instrumentation
Engineering, Aeronautical Engineering, Bio-Technology and Automobile
Engineering)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?????
1. (a) Find rank of matrix using Echelon form A =
2
4
1 2 4
2 1 3
8 1 9
5
6
7
3
5
(b) Solve the equations using Gauss Jordan method
x+5y+z=9 , 2x+y+3z=12, 3x+y+4z=16 [7+8]
2. Using Cayley { Hamilton theorem nd A
8
if A =
1 2
2 1
[15]
3. Reduce the quadratic form 6x
2
1
+ 3x
2
2
+ 3x
2
3
4x
1
x
2
+ 4x
1
x
3
2x
2
x
3
to the sum of
squares form by diagonalization and nd the corresponding linear transformation.
Also nd the index and signature. [15]
4. (a) Find a real root of the equation x sinx +cosx=0, using Newton-Raphson's
method
(b) Evaluate
p
12 and
1
p
12
using xed point iteration method. [8+7]
5. (a) If the interval of di erencing is unity, prove the following:4
n
1
f(x)
o
=
4f(x)
f(x)f(x+1)
(b) Given that sin 45
o
= 0.7071, sin 50
o
= 0.8192, sin 60
o
= 0.8660, nd sin 48
o
.
[8+7]
6. (a) Computef
0
(1)using the given data:
X 1.0 1.5 2.0 2.5 3.0
f(x) 27 106.75 324 783.75 1621
(b) Using Simpson's 3/8
th
rule evaluate
R
6
0
dx
1+x
2
by dividing the range into 6 equal
parts [8+7]
7. (a) Solve y
1
=-xy
2
, y(o)=2 by modi ed Euler's method and hence nd y(o.1),
y(o.2)
(b) Solve
dy
dx
=
y
2
x
2
y
2
+x
2
, y(o)=1 by fourth order R-K method and hence nd y(o.2),
y(o.4) [8+7]
8. (a) Fit a least square parabola y= a+bx+cx
2
to the data (-1,2),(0,1),(1,4)
Code No: R10107/R10 Set No. 1
(b) By the method of least squares t a straight line to the following data
x 5 10 15 15 20
y 15 19 23 26 30
[8+7]
?????
Code No: R10107/R10 Set No. 2
I B.Tech I Semester Supplementary Examinations, Oct/Nov 2013
MATHEMATICAL METHODS
( Common to Civil Engineering, Electrical & Electronics Engineering,
Computer Science & Engineering, Electronics & Instrumentation
Engineering, Aeronautical Engineering, Bio-Technology and Automobile
Engineering)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?????
1. (a) Find rank of matrix using Echelon form A =
2
4
1 1 1
2 3 4
3 2 3
3
5
(b) Solve the equations using Gauss Jordan method
x
1
+x
2
+x
3
=8 , 2x
1
+3x
2
+2x
3
=19 , 4x
1
+2x
2
+3x
3
=23 [7+8]
2. Verify Cayley { Hamilton theorem and nd A
1
if A =
2
4
1 0 3
2 1 1
1 1 1
3
5
[15]
3. (a) Find the nature of the quadratic form5x
2
+ 5y
2
+ 14z
2
+ 2xy 16yz 8zx
(b) If A=
1 0
0 3
then nd A
50
[8+7]
4. (a) Apply Newton-Raphson's formula to nd the cube root of 5 correct up to three
decimal places starting from x
0
=1.
(b) Find a real root of f(x)=x
2
3x + 1 = 0 correct up to three decimal places
starting with x=1 by Iterative method. [8+7]
5. The following table gives the population of a town during the last six censuses.
Estimate, using Newton's interpolation formula, the increase in the population
during the period 1986 to 1988.
year 1911 1921 1931 1941 1951 1961
Population
(in thousands)
12 15 20 27 39 52
[15]
6. (a) Given the following data of X and Y
X 1.0 1.2 1.4 1.6 1.8 2.0
Y 2.72 3.32 4.06 4.96 6.05 7.39
Find the rst and second derivatives at x = 1.0
(b) The table below shows the temperature f(t) as a function of time
t 1 2 3 4 5 6 7
f(t) 81 75 80 83 78 70 60
Use Simpson's 1/3 method to estimate
R
7
1
f (t)dt: [8+7]
FirstRanker.com - FirstRanker's Choice
Code No: R10107/R10 Set No. 1
I B.Tech I Semester Supplementary Examinations, Oct/Nov 2013
MATHEMATICAL METHODS
( Common to Civil Engineering, Electrical & Electronics Engineering,
Computer Science & Engineering, Electronics & Instrumentation
Engineering, Aeronautical Engineering, Bio-Technology and Automobile
Engineering)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?????
1. (a) Find rank of matrix using Echelon form A =
2
4
1 2 4
2 1 3
8 1 9
5
6
7
3
5
(b) Solve the equations using Gauss Jordan method
x+5y+z=9 , 2x+y+3z=12, 3x+y+4z=16 [7+8]
2. Using Cayley { Hamilton theorem nd A
8
if A =
1 2
2 1
[15]
3. Reduce the quadratic form 6x
2
1
+ 3x
2
2
+ 3x
2
3
4x
1
x
2
+ 4x
1
x
3
2x
2
x
3
to the sum of
squares form by diagonalization and nd the corresponding linear transformation.
Also nd the index and signature. [15]
4. (a) Find a real root of the equation x sinx +cosx=0, using Newton-Raphson's
method
(b) Evaluate
p
12 and
1
p
12
using xed point iteration method. [8+7]
5. (a) If the interval of di erencing is unity, prove the following:4
n
1
f(x)
o
=
4f(x)
f(x)f(x+1)
(b) Given that sin 45
o
= 0.7071, sin 50
o
= 0.8192, sin 60
o
= 0.8660, nd sin 48
o
.
[8+7]
6. (a) Computef
0
(1)using the given data:
X 1.0 1.5 2.0 2.5 3.0
f(x) 27 106.75 324 783.75 1621
(b) Using Simpson's 3/8
th
rule evaluate
R
6
0
dx
1+x
2
by dividing the range into 6 equal
parts [8+7]
7. (a) Solve y
1
=-xy
2
, y(o)=2 by modi ed Euler's method and hence nd y(o.1),
y(o.2)
(b) Solve
dy
dx
=
y
2
x
2
y
2
+x
2
, y(o)=1 by fourth order R-K method and hence nd y(o.2),
y(o.4) [8+7]
8. (a) Fit a least square parabola y= a+bx+cx
2
to the data (-1,2),(0,1),(1,4)
Code No: R10107/R10 Set No. 1
(b) By the method of least squares t a straight line to the following data
x 5 10 15 15 20
y 15 19 23 26 30
[8+7]
?????
Code No: R10107/R10 Set No. 2
I B.Tech I Semester Supplementary Examinations, Oct/Nov 2013
MATHEMATICAL METHODS
( Common to Civil Engineering, Electrical & Electronics Engineering,
Computer Science & Engineering, Electronics & Instrumentation
Engineering, Aeronautical Engineering, Bio-Technology and Automobile
Engineering)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?????
1. (a) Find rank of matrix using Echelon form A =
2
4
1 1 1
2 3 4
3 2 3
3
5
(b) Solve the equations using Gauss Jordan method
x
1
+x
2
+x
3
=8 , 2x
1
+3x
2
+2x
3
=19 , 4x
1
+2x
2
+3x
3
=23 [7+8]
2. Verify Cayley { Hamilton theorem and nd A
1
if A =
2
4
1 0 3
2 1 1
1 1 1
3
5
[15]
3. (a) Find the nature of the quadratic form5x
2
+ 5y
2
+ 14z
2
+ 2xy 16yz 8zx
(b) If A=
1 0
0 3
then nd A
50
[8+7]
4. (a) Apply Newton-Raphson's formula to nd the cube root of 5 correct up to three
decimal places starting from x
0
=1.
(b) Find a real root of f(x)=x
2
3x + 1 = 0 correct up to three decimal places
starting with x=1 by Iterative method. [8+7]
5. The following table gives the population of a town during the last six censuses.
Estimate, using Newton's interpolation formula, the increase in the population
during the period 1986 to 1988.
year 1911 1921 1931 1941 1951 1961
Population
(in thousands)
12 15 20 27 39 52
[15]
6. (a) Given the following data of X and Y
X 1.0 1.2 1.4 1.6 1.8 2.0
Y 2.72 3.32 4.06 4.96 6.05 7.39
Find the rst and second derivatives at x = 1.0
(b) The table below shows the temperature f(t) as a function of time
t 1 2 3 4 5 6 7
f(t) 81 75 80 83 78 70 60
Use Simpson's 1/3 method to estimate
R
7
1
f (t)dt: [8+7]
Code No: R10107/R10 Set No. 2
7. (a) Solve y
1
=3x
2
+1 by Euler's method and nd y at x=2 by taking h=0.5
(b) Solve by fourth order R-K method y
1
=x-y, y(1)=0.4 and hence nd y(1.2)
[8+7]
8. (a) Fit a curve of the type y= a+bx+cx
2
to the following data
x 10 15 20 25 30 35
y 35.3 32.4 29.2 26.1 23.2 20.5
(b) Fit a curve of the type y=ab
x
to the following data by the method of least
squares
x 1 2 5 10 20 30 40 50
Y 98.2 91.7 81.3 64 36.4 32.6 7.1 11.3 [7+8]
?????
FirstRanker.com - FirstRanker's Choice
Code No: R10107/R10 Set No. 1
I B.Tech I Semester Supplementary Examinations, Oct/Nov 2013
MATHEMATICAL METHODS
( Common to Civil Engineering, Electrical & Electronics Engineering,
Computer Science & Engineering, Electronics & Instrumentation
Engineering, Aeronautical Engineering, Bio-Technology and Automobile
Engineering)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?????
1. (a) Find rank of matrix using Echelon form A =
2
4
1 2 4
2 1 3
8 1 9
5
6
7
3
5
(b) Solve the equations using Gauss Jordan method
x+5y+z=9 , 2x+y+3z=12, 3x+y+4z=16 [7+8]
2. Using Cayley { Hamilton theorem nd A
8
if A =
1 2
2 1
[15]
3. Reduce the quadratic form 6x
2
1
+ 3x
2
2
+ 3x
2
3
4x
1
x
2
+ 4x
1
x
3
2x
2
x
3
to the sum of
squares form by diagonalization and nd the corresponding linear transformation.
Also nd the index and signature. [15]
4. (a) Find a real root of the equation x sinx +cosx=0, using Newton-Raphson's
method
(b) Evaluate
p
12 and
1
p
12
using xed point iteration method. [8+7]
5. (a) If the interval of di erencing is unity, prove the following:4
n
1
f(x)
o
=
4f(x)
f(x)f(x+1)
(b) Given that sin 45
o
= 0.7071, sin 50
o
= 0.8192, sin 60
o
= 0.8660, nd sin 48
o
.
[8+7]
6. (a) Computef
0
(1)using the given data:
X 1.0 1.5 2.0 2.5 3.0
f(x) 27 106.75 324 783.75 1621
(b) Using Simpson's 3/8
th
rule evaluate
R
6
0
dx
1+x
2
by dividing the range into 6 equal
parts [8+7]
7. (a) Solve y
1
=-xy
2
, y(o)=2 by modi ed Euler's method and hence nd y(o.1),
y(o.2)
(b) Solve
dy
dx
=
y
2
x
2
y
2
+x
2
, y(o)=1 by fourth order R-K method and hence nd y(o.2),
y(o.4) [8+7]
8. (a) Fit a least square parabola y= a+bx+cx
2
to the data (-1,2),(0,1),(1,4)
Code No: R10107/R10 Set No. 1
(b) By the method of least squares t a straight line to the following data
x 5 10 15 15 20
y 15 19 23 26 30
[8+7]
?????
Code No: R10107/R10 Set No. 2
I B.Tech I Semester Supplementary Examinations, Oct/Nov 2013
MATHEMATICAL METHODS
( Common to Civil Engineering, Electrical & Electronics Engineering,
Computer Science & Engineering, Electronics & Instrumentation
Engineering, Aeronautical Engineering, Bio-Technology and Automobile
Engineering)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?????
1. (a) Find rank of matrix using Echelon form A =
2
4
1 1 1
2 3 4
3 2 3
3
5
(b) Solve the equations using Gauss Jordan method
x
1
+x
2
+x
3
=8 , 2x
1
+3x
2
+2x
3
=19 , 4x
1
+2x
2
+3x
3
=23 [7+8]
2. Verify Cayley { Hamilton theorem and nd A
1
if A =
2
4
1 0 3
2 1 1
1 1 1
3
5
[15]
3. (a) Find the nature of the quadratic form5x
2
+ 5y
2
+ 14z
2
+ 2xy 16yz 8zx
(b) If A=
1 0
0 3
then nd A
50
[8+7]
4. (a) Apply Newton-Raphson's formula to nd the cube root of 5 correct up to three
decimal places starting from x
0
=1.
(b) Find a real root of f(x)=x
2
3x + 1 = 0 correct up to three decimal places
starting with x=1 by Iterative method. [8+7]
5. The following table gives the population of a town during the last six censuses.
Estimate, using Newton's interpolation formula, the increase in the population
during the period 1986 to 1988.
year 1911 1921 1931 1941 1951 1961
Population
(in thousands)
12 15 20 27 39 52
[15]
6. (a) Given the following data of X and Y
X 1.0 1.2 1.4 1.6 1.8 2.0
Y 2.72 3.32 4.06 4.96 6.05 7.39
Find the rst and second derivatives at x = 1.0
(b) The table below shows the temperature f(t) as a function of time
t 1 2 3 4 5 6 7
f(t) 81 75 80 83 78 70 60
Use Simpson's 1/3 method to estimate
R
7
1
f (t)dt: [8+7]
Code No: R10107/R10 Set No. 2
7. (a) Solve y
1
=3x
2
+1 by Euler's method and nd y at x=2 by taking h=0.5
(b) Solve by fourth order R-K method y
1
=x-y, y(1)=0.4 and hence nd y(1.2)
[8+7]
8. (a) Fit a curve of the type y= a+bx+cx
2
to the following data
x 10 15 20 25 30 35
y 35.3 32.4 29.2 26.1 23.2 20.5
(b) Fit a curve of the type y=ab
x
to the following data by the method of least
squares
x 1 2 5 10 20 30 40 50
Y 98.2 91.7 81.3 64 36.4 32.6 7.1 11.3 [7+8]
?????
Code No: R10107/R10 Set No. 3
I B.Tech I Semester Supplementary Examinations, Oct/Nov 2013
MATHEMATICAL METHODS
( Common to Civil Engineering, Electrical & Electronics Engineering,
Computer Science & Engineering, Electronics & Instrumentation
Engineering, Aeronautical Engineering, Bio-Technology and Automobile
Engineering)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?????
1. (a) De ne rank and nd the rank of matrix A =
2
4
1 3 6
1 4 5
1 5 4
1
1
3
3
5
using
Echelon form
(b) Find values of x,y and z using Gauss Jordon method 2x+y-z=1; x-y+z=2 ;
5x+5y-4z=3 [7+8]
2. Find Eigen Vectors of A =
2
4
5 2 0
2 6 2
0 2 7
3
5
[15]
3. (a) By Lagrange's reduction reduce the quadratic form X
T
AX to sum of squares
form for A=
2
4
1 2 4
2 6 2
4 2 18
3
5
.
(b) Find the values of a, b, c if
2
4
0 2b c
a b c
a b c
3
5
is an orthogonal matrix [8+7]
4. (a) Find a real root of the equation using Newton-Raphson's method Cos
2
x-x=0
(b) Find a root of the equation x
3
e
x
- x-1=0 by Bisection method. [8+7]
5. (a) (i) Solve (e
ax
logbx ) (ii) Prove thatr
6
y
8
=
6
y
2
.
(b) From the following table for nd f(3.3) using gauss forward interpolation for-
mula.
x 1 2 3 4 5
Y =
f(x)
15.30 15.10 15.00 14.50 14.00 [8+7]
6. (a) A curve is expressed by the following values of x and y. Find the slope at the
point x = 0.5.
X 0.4 0.5 0.6 0.7 0.8
y 1.58 1.80 2.04 2.33 2.65
Calculate the angular velocity and the angular acceleration of the rod when t
= 0.3 seconds.
FirstRanker.com - FirstRanker's Choice
Code No: R10107/R10 Set No. 1
I B.Tech I Semester Supplementary Examinations, Oct/Nov 2013
MATHEMATICAL METHODS
( Common to Civil Engineering, Electrical & Electronics Engineering,
Computer Science & Engineering, Electronics & Instrumentation
Engineering, Aeronautical Engineering, Bio-Technology and Automobile
Engineering)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?????
1. (a) Find rank of matrix using Echelon form A =
2
4
1 2 4
2 1 3
8 1 9
5
6
7
3
5
(b) Solve the equations using Gauss Jordan method
x+5y+z=9 , 2x+y+3z=12, 3x+y+4z=16 [7+8]
2. Using Cayley { Hamilton theorem nd A
8
if A =
1 2
2 1
[15]
3. Reduce the quadratic form 6x
2
1
+ 3x
2
2
+ 3x
2
3
4x
1
x
2
+ 4x
1
x
3
2x
2
x
3
to the sum of
squares form by diagonalization and nd the corresponding linear transformation.
Also nd the index and signature. [15]
4. (a) Find a real root of the equation x sinx +cosx=0, using Newton-Raphson's
method
(b) Evaluate
p
12 and
1
p
12
using xed point iteration method. [8+7]
5. (a) If the interval of di erencing is unity, prove the following:4
n
1
f(x)
o
=
4f(x)
f(x)f(x+1)
(b) Given that sin 45
o
= 0.7071, sin 50
o
= 0.8192, sin 60
o
= 0.8660, nd sin 48
o
.
[8+7]
6. (a) Computef
0
(1)using the given data:
X 1.0 1.5 2.0 2.5 3.0
f(x) 27 106.75 324 783.75 1621
(b) Using Simpson's 3/8
th
rule evaluate
R
6
0
dx
1+x
2
by dividing the range into 6 equal
parts [8+7]
7. (a) Solve y
1
=-xy
2
, y(o)=2 by modi ed Euler's method and hence nd y(o.1),
y(o.2)
(b) Solve
dy
dx
=
y
2
x
2
y
2
+x
2
, y(o)=1 by fourth order R-K method and hence nd y(o.2),
y(o.4) [8+7]
8. (a) Fit a least square parabola y= a+bx+cx
2
to the data (-1,2),(0,1),(1,4)
Code No: R10107/R10 Set No. 1
(b) By the method of least squares t a straight line to the following data
x 5 10 15 15 20
y 15 19 23 26 30
[8+7]
?????
Code No: R10107/R10 Set No. 2
I B.Tech I Semester Supplementary Examinations, Oct/Nov 2013
MATHEMATICAL METHODS
( Common to Civil Engineering, Electrical & Electronics Engineering,
Computer Science & Engineering, Electronics & Instrumentation
Engineering, Aeronautical Engineering, Bio-Technology and Automobile
Engineering)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?????
1. (a) Find rank of matrix using Echelon form A =
2
4
1 1 1
2 3 4
3 2 3
3
5
(b) Solve the equations using Gauss Jordan method
x
1
+x
2
+x
3
=8 , 2x
1
+3x
2
+2x
3
=19 , 4x
1
+2x
2
+3x
3
=23 [7+8]
2. Verify Cayley { Hamilton theorem and nd A
1
if A =
2
4
1 0 3
2 1 1
1 1 1
3
5
[15]
3. (a) Find the nature of the quadratic form5x
2
+ 5y
2
+ 14z
2
+ 2xy 16yz 8zx
(b) If A=
1 0
0 3
then nd A
50
[8+7]
4. (a) Apply Newton-Raphson's formula to nd the cube root of 5 correct up to three
decimal places starting from x
0
=1.
(b) Find a real root of f(x)=x
2
3x + 1 = 0 correct up to three decimal places
starting with x=1 by Iterative method. [8+7]
5. The following table gives the population of a town during the last six censuses.
Estimate, using Newton's interpolation formula, the increase in the population
during the period 1986 to 1988.
year 1911 1921 1931 1941 1951 1961
Population
(in thousands)
12 15 20 27 39 52
[15]
6. (a) Given the following data of X and Y
X 1.0 1.2 1.4 1.6 1.8 2.0
Y 2.72 3.32 4.06 4.96 6.05 7.39
Find the rst and second derivatives at x = 1.0
(b) The table below shows the temperature f(t) as a function of time
t 1 2 3 4 5 6 7
f(t) 81 75 80 83 78 70 60
Use Simpson's 1/3 method to estimate
R
7
1
f (t)dt: [8+7]
Code No: R10107/R10 Set No. 2
7. (a) Solve y
1
=3x
2
+1 by Euler's method and nd y at x=2 by taking h=0.5
(b) Solve by fourth order R-K method y
1
=x-y, y(1)=0.4 and hence nd y(1.2)
[8+7]
8. (a) Fit a curve of the type y= a+bx+cx
2
to the following data
x 10 15 20 25 30 35
y 35.3 32.4 29.2 26.1 23.2 20.5
(b) Fit a curve of the type y=ab
x
to the following data by the method of least
squares
x 1 2 5 10 20 30 40 50
Y 98.2 91.7 81.3 64 36.4 32.6 7.1 11.3 [7+8]
?????
Code No: R10107/R10 Set No. 3
I B.Tech I Semester Supplementary Examinations, Oct/Nov 2013
MATHEMATICAL METHODS
( Common to Civil Engineering, Electrical & Electronics Engineering,
Computer Science & Engineering, Electronics & Instrumentation
Engineering, Aeronautical Engineering, Bio-Technology and Automobile
Engineering)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?????
1. (a) De ne rank and nd the rank of matrix A =
2
4
1 3 6
1 4 5
1 5 4
1
1
3
3
5
using
Echelon form
(b) Find values of x,y and z using Gauss Jordon method 2x+y-z=1; x-y+z=2 ;
5x+5y-4z=3 [7+8]
2. Find Eigen Vectors of A =
2
4
5 2 0
2 6 2
0 2 7
3
5
[15]
3. (a) By Lagrange's reduction reduce the quadratic form X
T
AX to sum of squares
form for A=
2
4
1 2 4
2 6 2
4 2 18
3
5
.
(b) Find the values of a, b, c if
2
4
0 2b c
a b c
a b c
3
5
is an orthogonal matrix [8+7]
4. (a) Find a real root of the equation using Newton-Raphson's method Cos
2
x-x=0
(b) Find a root of the equation x
3
e
x
- x-1=0 by Bisection method. [8+7]
5. (a) (i) Solve (e
ax
logbx ) (ii) Prove thatr
6
y
8
=
6
y
2
.
(b) From the following table for nd f(3.3) using gauss forward interpolation for-
mula.
x 1 2 3 4 5
Y =
f(x)
15.30 15.10 15.00 14.50 14.00 [8+7]
6. (a) A curve is expressed by the following values of x and y. Find the slope at the
point x = 0.5.
X 0.4 0.5 0.6 0.7 0.8
y 1.58 1.80 2.04 2.33 2.65
Calculate the angular velocity and the angular acceleration of the rod when t
= 0.3 seconds.
Code No: R10107/R10 Set No. 3
(b) Evaluate
R
1
0
1
1+x
dx, by Trapezoidal rule and Simpson's
1
3
rule. [8+7]
7. Solve y
1
=x-y , y(0)=1 ,h=0.1 by Milne`s predictor corrector method to nd y(0.4).Use
Euler's modi ed method to evaluate y(0.1), y(0.2) ,y(0.3) [15]
8. (a) Fit a power curve y=ax
b
to the following data
X 1 2 3 4 5
Y 7.1 27.8 62.1 110 161
(b) Fit a least square parabola y= a+bx+cx
2
to the following data
x 0 1 2 3 4
y 1 5 10 22 38
[7+8]
?????
FirstRanker.com - FirstRanker's Choice
Code No: R10107/R10 Set No. 1
I B.Tech I Semester Supplementary Examinations, Oct/Nov 2013
MATHEMATICAL METHODS
( Common to Civil Engineering, Electrical & Electronics Engineering,
Computer Science & Engineering, Electronics & Instrumentation
Engineering, Aeronautical Engineering, Bio-Technology and Automobile
Engineering)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?????
1. (a) Find rank of matrix using Echelon form A =
2
4
1 2 4
2 1 3
8 1 9
5
6
7
3
5
(b) Solve the equations using Gauss Jordan method
x+5y+z=9 , 2x+y+3z=12, 3x+y+4z=16 [7+8]
2. Using Cayley { Hamilton theorem nd A
8
if A =
1 2
2 1
[15]
3. Reduce the quadratic form 6x
2
1
+ 3x
2
2
+ 3x
2
3
4x
1
x
2
+ 4x
1
x
3
2x
2
x
3
to the sum of
squares form by diagonalization and nd the corresponding linear transformation.
Also nd the index and signature. [15]
4. (a) Find a real root of the equation x sinx +cosx=0, using Newton-Raphson's
method
(b) Evaluate
p
12 and
1
p
12
using xed point iteration method. [8+7]
5. (a) If the interval of di erencing is unity, prove the following:4
n
1
f(x)
o
=
4f(x)
f(x)f(x+1)
(b) Given that sin 45
o
= 0.7071, sin 50
o
= 0.8192, sin 60
o
= 0.8660, nd sin 48
o
.
[8+7]
6. (a) Computef
0
(1)using the given data:
X 1.0 1.5 2.0 2.5 3.0
f(x) 27 106.75 324 783.75 1621
(b) Using Simpson's 3/8
th
rule evaluate
R
6
0
dx
1+x
2
by dividing the range into 6 equal
parts [8+7]
7. (a) Solve y
1
=-xy
2
, y(o)=2 by modi ed Euler's method and hence nd y(o.1),
y(o.2)
(b) Solve
dy
dx
=
y
2
x
2
y
2
+x
2
, y(o)=1 by fourth order R-K method and hence nd y(o.2),
y(o.4) [8+7]
8. (a) Fit a least square parabola y= a+bx+cx
2
to the data (-1,2),(0,1),(1,4)
Code No: R10107/R10 Set No. 1
(b) By the method of least squares t a straight line to the following data
x 5 10 15 15 20
y 15 19 23 26 30
[8+7]
?????
Code No: R10107/R10 Set No. 2
I B.Tech I Semester Supplementary Examinations, Oct/Nov 2013
MATHEMATICAL METHODS
( Common to Civil Engineering, Electrical & Electronics Engineering,
Computer Science & Engineering, Electronics & Instrumentation
Engineering, Aeronautical Engineering, Bio-Technology and Automobile
Engineering)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?????
1. (a) Find rank of matrix using Echelon form A =
2
4
1 1 1
2 3 4
3 2 3
3
5
(b) Solve the equations using Gauss Jordan method
x
1
+x
2
+x
3
=8 , 2x
1
+3x
2
+2x
3
=19 , 4x
1
+2x
2
+3x
3
=23 [7+8]
2. Verify Cayley { Hamilton theorem and nd A
1
if A =
2
4
1 0 3
2 1 1
1 1 1
3
5
[15]
3. (a) Find the nature of the quadratic form5x
2
+ 5y
2
+ 14z
2
+ 2xy 16yz 8zx
(b) If A=
1 0
0 3
then nd A
50
[8+7]
4. (a) Apply Newton-Raphson's formula to nd the cube root of 5 correct up to three
decimal places starting from x
0
=1.
(b) Find a real root of f(x)=x
2
3x + 1 = 0 correct up to three decimal places
starting with x=1 by Iterative method. [8+7]
5. The following table gives the population of a town during the last six censuses.
Estimate, using Newton's interpolation formula, the increase in the population
during the period 1986 to 1988.
year 1911 1921 1931 1941 1951 1961
Population
(in thousands)
12 15 20 27 39 52
[15]
6. (a) Given the following data of X and Y
X 1.0 1.2 1.4 1.6 1.8 2.0
Y 2.72 3.32 4.06 4.96 6.05 7.39
Find the rst and second derivatives at x = 1.0
(b) The table below shows the temperature f(t) as a function of time
t 1 2 3 4 5 6 7
f(t) 81 75 80 83 78 70 60
Use Simpson's 1/3 method to estimate
R
7
1
f (t)dt: [8+7]
Code No: R10107/R10 Set No. 2
7. (a) Solve y
1
=3x
2
+1 by Euler's method and nd y at x=2 by taking h=0.5
(b) Solve by fourth order R-K method y
1
=x-y, y(1)=0.4 and hence nd y(1.2)
[8+7]
8. (a) Fit a curve of the type y= a+bx+cx
2
to the following data
x 10 15 20 25 30 35
y 35.3 32.4 29.2 26.1 23.2 20.5
(b) Fit a curve of the type y=ab
x
to the following data by the method of least
squares
x 1 2 5 10 20 30 40 50
Y 98.2 91.7 81.3 64 36.4 32.6 7.1 11.3 [7+8]
?????
Code No: R10107/R10 Set No. 3
I B.Tech I Semester Supplementary Examinations, Oct/Nov 2013
MATHEMATICAL METHODS
( Common to Civil Engineering, Electrical & Electronics Engineering,
Computer Science & Engineering, Electronics & Instrumentation
Engineering, Aeronautical Engineering, Bio-Technology and Automobile
Engineering)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?????
1. (a) De ne rank and nd the rank of matrix A =
2
4
1 3 6
1 4 5
1 5 4
1
1
3
3
5
using
Echelon form
(b) Find values of x,y and z using Gauss Jordon method 2x+y-z=1; x-y+z=2 ;
5x+5y-4z=3 [7+8]
2. Find Eigen Vectors of A =
2
4
5 2 0
2 6 2
0 2 7
3
5
[15]
3. (a) By Lagrange's reduction reduce the quadratic form X
T
AX to sum of squares
form for A=
2
4
1 2 4
2 6 2
4 2 18
3
5
.
(b) Find the values of a, b, c if
2
4
0 2b c
a b c
a b c
3
5
is an orthogonal matrix [8+7]
4. (a) Find a real root of the equation using Newton-Raphson's method Cos
2
x-x=0
(b) Find a root of the equation x
3
e
x
- x-1=0 by Bisection method. [8+7]
5. (a) (i) Solve (e
ax
logbx ) (ii) Prove thatr
6
y
8
=
6
y
2
.
(b) From the following table for nd f(3.3) using gauss forward interpolation for-
mula.
x 1 2 3 4 5
Y =
f(x)
15.30 15.10 15.00 14.50 14.00 [8+7]
6. (a) A curve is expressed by the following values of x and y. Find the slope at the
point x = 0.5.
X 0.4 0.5 0.6 0.7 0.8
y 1.58 1.80 2.04 2.33 2.65
Calculate the angular velocity and the angular acceleration of the rod when t
= 0.3 seconds.
Code No: R10107/R10 Set No. 3
(b) Evaluate
R
1
0
1
1+x
dx, by Trapezoidal rule and Simpson's
1
3
rule. [8+7]
7. Solve y
1
=x-y , y(0)=1 ,h=0.1 by Milne`s predictor corrector method to nd y(0.4).Use
Euler's modi ed method to evaluate y(0.1), y(0.2) ,y(0.3) [15]
8. (a) Fit a power curve y=ax
b
to the following data
X 1 2 3 4 5
Y 7.1 27.8 62.1 110 161
(b) Fit a least square parabola y= a+bx+cx
2
to the following data
x 0 1 2 3 4
y 1 5 10 22 38
[7+8]
?????
Code No: R10107/R10 Set No. 4
I B.Tech I Semester Supplementary Examinations, Oct/Nov 2013
MATHEMATICAL METHODS
( Common to Civil Engineering, Electrical & Electronics Engineering,
Computer Science & Engineering, Electronics & Instrumentation
Engineering, Aeronautical Engineering, Bio-Technology and Automobile
Engineering)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?????
1. (a) Find rank of matrix A =
2
6
6
4
1 2 3
2 2 0
3
2
1
3
4
1
3
7
7
5
using Normal form.
(b) Solve system of equations, if consistent x+y+2z=4 , 2x-y+3z=9, 3x-y-z=2
[7+8]
2. Show that matrix A =
2
4
0 c b
c 0 a
b a 0
3
5
satis es Cayley { Hamilton theorem
[15]
3. Find the rank, signature and index of the quadratic form 2x
2
1
+x
2
2
3x
2
3
+ 12x
1
x
2
4x
1
x
3
8x
2
x
3
by reducing it to normal form .Also write the linear transformation
which brings about the normal reduction [15]
4. (a) Find a real root of the equation x sinx +cosx=0, using Newton-Raphson's
method
(b) Evaluate
p
12 and
1
p
12
using xed point iteration method. [8+7]
5. (a) Evaluate the following, interval of di erencing being unity. 4 tan
1
ax (ii)
4 (e
2x
log 3x )
(b) Find y(25), given that y
20
= 24, y
24
= 32, y
28
= 35, y
32
= 40, Using Gauss
forward di erence Interpolation formula. [8+7]
6. (a) For the function y = f(x) given by the following Table, nd y
0
at x = 0.04
using the Bessel's formula.
x 0.01 0.02 0.03 0.04 0.05 0.06
y 0.1023 0.1047 0.1071 0.1096 0.1122 0.1148
(b) Evaluate
R
4
0
e
1=x
dx by using the Simpson's 3/8
th
rule, by dividing the interval
into 3 equal parts. [8+7]
7. (a) Solve y
1
=3x
2
+1 by Euler's method and nd y at x=2 by taking h=0.5
(b) Solve by fourth order R-K method y
1
=x-y, y(1)=0.4 and hence nd y(1.2)
[8+7]
FirstRanker.com - FirstRanker's Choice
Code No: R10107/R10 Set No. 1
I B.Tech I Semester Supplementary Examinations, Oct/Nov 2013
MATHEMATICAL METHODS
( Common to Civil Engineering, Electrical & Electronics Engineering,
Computer Science & Engineering, Electronics & Instrumentation
Engineering, Aeronautical Engineering, Bio-Technology and Automobile
Engineering)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?????
1. (a) Find rank of matrix using Echelon form A =
2
4
1 2 4
2 1 3
8 1 9
5
6
7
3
5
(b) Solve the equations using Gauss Jordan method
x+5y+z=9 , 2x+y+3z=12, 3x+y+4z=16 [7+8]
2. Using Cayley { Hamilton theorem nd A
8
if A =
1 2
2 1
[15]
3. Reduce the quadratic form 6x
2
1
+ 3x
2
2
+ 3x
2
3
4x
1
x
2
+ 4x
1
x
3
2x
2
x
3
to the sum of
squares form by diagonalization and nd the corresponding linear transformation.
Also nd the index and signature. [15]
4. (a) Find a real root of the equation x sinx +cosx=0, using Newton-Raphson's
method
(b) Evaluate
p
12 and
1
p
12
using xed point iteration method. [8+7]
5. (a) If the interval of di erencing is unity, prove the following:4
n
1
f(x)
o
=
4f(x)
f(x)f(x+1)
(b) Given that sin 45
o
= 0.7071, sin 50
o
= 0.8192, sin 60
o
= 0.8660, nd sin 48
o
.
[8+7]
6. (a) Computef
0
(1)using the given data:
X 1.0 1.5 2.0 2.5 3.0
f(x) 27 106.75 324 783.75 1621
(b) Using Simpson's 3/8
th
rule evaluate
R
6
0
dx
1+x
2
by dividing the range into 6 equal
parts [8+7]
7. (a) Solve y
1
=-xy
2
, y(o)=2 by modi ed Euler's method and hence nd y(o.1),
y(o.2)
(b) Solve
dy
dx
=
y
2
x
2
y
2
+x
2
, y(o)=1 by fourth order R-K method and hence nd y(o.2),
y(o.4) [8+7]
8. (a) Fit a least square parabola y= a+bx+cx
2
to the data (-1,2),(0,1),(1,4)
Code No: R10107/R10 Set No. 1
(b) By the method of least squares t a straight line to the following data
x 5 10 15 15 20
y 15 19 23 26 30
[8+7]
?????
Code No: R10107/R10 Set No. 2
I B.Tech I Semester Supplementary Examinations, Oct/Nov 2013
MATHEMATICAL METHODS
( Common to Civil Engineering, Electrical & Electronics Engineering,
Computer Science & Engineering, Electronics & Instrumentation
Engineering, Aeronautical Engineering, Bio-Technology and Automobile
Engineering)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?????
1. (a) Find rank of matrix using Echelon form A =
2
4
1 1 1
2 3 4
3 2 3
3
5
(b) Solve the equations using Gauss Jordan method
x
1
+x
2
+x
3
=8 , 2x
1
+3x
2
+2x
3
=19 , 4x
1
+2x
2
+3x
3
=23 [7+8]
2. Verify Cayley { Hamilton theorem and nd A
1
if A =
2
4
1 0 3
2 1 1
1 1 1
3
5
[15]
3. (a) Find the nature of the quadratic form5x
2
+ 5y
2
+ 14z
2
+ 2xy 16yz 8zx
(b) If A=
1 0
0 3
then nd A
50
[8+7]
4. (a) Apply Newton-Raphson's formula to nd the cube root of 5 correct up to three
decimal places starting from x
0
=1.
(b) Find a real root of f(x)=x
2
3x + 1 = 0 correct up to three decimal places
starting with x=1 by Iterative method. [8+7]
5. The following table gives the population of a town during the last six censuses.
Estimate, using Newton's interpolation formula, the increase in the population
during the period 1986 to 1988.
year 1911 1921 1931 1941 1951 1961
Population
(in thousands)
12 15 20 27 39 52
[15]
6. (a) Given the following data of X and Y
X 1.0 1.2 1.4 1.6 1.8 2.0
Y 2.72 3.32 4.06 4.96 6.05 7.39
Find the rst and second derivatives at x = 1.0
(b) The table below shows the temperature f(t) as a function of time
t 1 2 3 4 5 6 7
f(t) 81 75 80 83 78 70 60
Use Simpson's 1/3 method to estimate
R
7
1
f (t)dt: [8+7]
Code No: R10107/R10 Set No. 2
7. (a) Solve y
1
=3x
2
+1 by Euler's method and nd y at x=2 by taking h=0.5
(b) Solve by fourth order R-K method y
1
=x-y, y(1)=0.4 and hence nd y(1.2)
[8+7]
8. (a) Fit a curve of the type y= a+bx+cx
2
to the following data
x 10 15 20 25 30 35
y 35.3 32.4 29.2 26.1 23.2 20.5
(b) Fit a curve of the type y=ab
x
to the following data by the method of least
squares
x 1 2 5 10 20 30 40 50
Y 98.2 91.7 81.3 64 36.4 32.6 7.1 11.3 [7+8]
?????
Code No: R10107/R10 Set No. 3
I B.Tech I Semester Supplementary Examinations, Oct/Nov 2013
MATHEMATICAL METHODS
( Common to Civil Engineering, Electrical & Electronics Engineering,
Computer Science & Engineering, Electronics & Instrumentation
Engineering, Aeronautical Engineering, Bio-Technology and Automobile
Engineering)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?????
1. (a) De ne rank and nd the rank of matrix A =
2
4
1 3 6
1 4 5
1 5 4
1
1
3
3
5
using
Echelon form
(b) Find values of x,y and z using Gauss Jordon method 2x+y-z=1; x-y+z=2 ;
5x+5y-4z=3 [7+8]
2. Find Eigen Vectors of A =
2
4
5 2 0
2 6 2
0 2 7
3
5
[15]
3. (a) By Lagrange's reduction reduce the quadratic form X
T
AX to sum of squares
form for A=
2
4
1 2 4
2 6 2
4 2 18
3
5
.
(b) Find the values of a, b, c if
2
4
0 2b c
a b c
a b c
3
5
is an orthogonal matrix [8+7]
4. (a) Find a real root of the equation using Newton-Raphson's method Cos
2
x-x=0
(b) Find a root of the equation x
3
e
x
- x-1=0 by Bisection method. [8+7]
5. (a) (i) Solve (e
ax
logbx ) (ii) Prove thatr
6
y
8
=
6
y
2
.
(b) From the following table for nd f(3.3) using gauss forward interpolation for-
mula.
x 1 2 3 4 5
Y =
f(x)
15.30 15.10 15.00 14.50 14.00 [8+7]
6. (a) A curve is expressed by the following values of x and y. Find the slope at the
point x = 0.5.
X 0.4 0.5 0.6 0.7 0.8
y 1.58 1.80 2.04 2.33 2.65
Calculate the angular velocity and the angular acceleration of the rod when t
= 0.3 seconds.
Code No: R10107/R10 Set No. 3
(b) Evaluate
R
1
0
1
1+x
dx, by Trapezoidal rule and Simpson's
1
3
rule. [8+7]
7. Solve y
1
=x-y , y(0)=1 ,h=0.1 by Milne`s predictor corrector method to nd y(0.4).Use
Euler's modi ed method to evaluate y(0.1), y(0.2) ,y(0.3) [15]
8. (a) Fit a power curve y=ax
b
to the following data
X 1 2 3 4 5
Y 7.1 27.8 62.1 110 161
(b) Fit a least square parabola y= a+bx+cx
2
to the following data
x 0 1 2 3 4
y 1 5 10 22 38
[7+8]
?????
Code No: R10107/R10 Set No. 4
I B.Tech I Semester Supplementary Examinations, Oct/Nov 2013
MATHEMATICAL METHODS
( Common to Civil Engineering, Electrical & Electronics Engineering,
Computer Science & Engineering, Electronics & Instrumentation
Engineering, Aeronautical Engineering, Bio-Technology and Automobile
Engineering)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?????
1. (a) Find rank of matrix A =
2
6
6
4
1 2 3
2 2 0
3
2
1
3
4
1
3
7
7
5
using Normal form.
(b) Solve system of equations, if consistent x+y+2z=4 , 2x-y+3z=9, 3x-y-z=2
[7+8]
2. Show that matrix A =
2
4
0 c b
c 0 a
b a 0
3
5
satis es Cayley { Hamilton theorem
[15]
3. Find the rank, signature and index of the quadratic form 2x
2
1
+x
2
2
3x
2
3
+ 12x
1
x
2
4x
1
x
3
8x
2
x
3
by reducing it to normal form .Also write the linear transformation
which brings about the normal reduction [15]
4. (a) Find a real root of the equation x sinx +cosx=0, using Newton-Raphson's
method
(b) Evaluate
p
12 and
1
p
12
using xed point iteration method. [8+7]
5. (a) Evaluate the following, interval of di erencing being unity. 4 tan
1
ax (ii)
4 (e
2x
log 3x )
(b) Find y(25), given that y
20
= 24, y
24
= 32, y
28
= 35, y
32
= 40, Using Gauss
forward di erence Interpolation formula. [8+7]
6. (a) For the function y = f(x) given by the following Table, nd y
0
at x = 0.04
using the Bessel's formula.
x 0.01 0.02 0.03 0.04 0.05 0.06
y 0.1023 0.1047 0.1071 0.1096 0.1122 0.1148
(b) Evaluate
R
4
0
e
1=x
dx by using the Simpson's 3/8
th
rule, by dividing the interval
into 3 equal parts. [8+7]
7. (a) Solve y
1
=3x
2
+1 by Euler's method and nd y at x=2 by taking h=0.5
(b) Solve by fourth order R-K method y
1
=x-y, y(1)=0.4 and hence nd y(1.2)
[8+7]
Code No: R10107/R10 Set No. 4
8. (a) Fit a least square parabola y= a+bx+cx
2
to the following data
x 1 2 3 4 5
y 2 3 5 8 10
(b) Fit a straight line of the form y= a+bx to the following data
x -1 0 1 2 3 4 5 6
y 10 9 7 5 4 3 0 -1
[8+7]
?????
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This post was last modified on 03 December 2019