Download JNTUK (Jawaharlal Nehru Technological University Kakinada) B.Tech Regular 2014 Feb-March I Semester (1st Year 1st Sem) MATHEMATICS II Question Paper.

Subject Code: R13107/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-II (MATHEMATICAL METHODS)
(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Write the sufficient condition for the convergence of Newton-Raphson method?
(ii) Show that  


? 
?
(iii) Write the merits and demerits of Euler Modified method?
(iv) Write the Dirichlet?s conditions of f(x)?
(v) State Initial and Final value theorems of Z-transforms?
(vi) Write the statement of Fourier integral theorem?
[3+4+4+3+4+4]

PART- B
2.(a) Using Runge-Kutta method of fourth order solve

?
 , 1
 2   1.2    0.2.
(b) Find the Fourier transform of 



[8+8]
3. For the following data estimate f (1.720) using forward, f (2.68) using backward and
f (2.36) using central difference formula.

x 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
f(x) 0.0495 0.0605 0.0739 0.0903 0.1102 0.1346 0.1644 0.2009

4.(a) Solve the differential equation


  subject to 0
 1 by Picard?s method
and hence find 0.2
.
(b) Using Regula Falsi method find a real root of 
 2



 1  0 correct upto
two decimal places.
[8+8]
5.(a) Find the Fourier series for 
 2 !

" 0, 2
, hence show that



#
!


#


\$
#
!

%
#
 ? 
'
#


(b) Find the inverse Z transform of
\$(
#
)(
(
(

[8+8]

Page 1 of 2

Set No - 1

FirstRanker.com - FirstRanker's Choice
Subject Code: R13107/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-II (MATHEMATICAL METHODS)
(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Write the sufficient condition for the convergence of Newton-Raphson method?
(ii) Show that  


? 
?
(iii) Write the merits and demerits of Euler Modified method?
(iv) Write the Dirichlet?s conditions of f(x)?
(v) State Initial and Final value theorems of Z-transforms?
(vi) Write the statement of Fourier integral theorem?
[3+4+4+3+4+4]

PART- B
2.(a) Using Runge-Kutta method of fourth order solve

?
 , 1
 2   1.2    0.2.
(b) Find the Fourier transform of 



[8+8]
3. For the following data estimate f (1.720) using forward, f (2.68) using backward and
f (2.36) using central difference formula.

x 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
f(x) 0.0495 0.0605 0.0739 0.0903 0.1102 0.1346 0.1644 0.2009

4.(a) Solve the differential equation


  subject to 0
 1 by Picard?s method
and hence find 0.2
.
(b) Using Regula Falsi method find a real root of 
 2



 1  0 correct upto
two decimal places.
[8+8]
5.(a) Find the Fourier series for 
 2 !

" 0, 2
, hence show that



#
!


#


\$
#
!

%
#
 ? 
'
#


(b) Find the inverse Z transform of
\$(
#
)(
(
(

[8+8]

Page 1 of 2

Set No - 1
Subject Code: R13107/R13

6.(a) Find the Fourier transform of 
 *
1 !

, | | , 1
0 , | | - 1
.

(b) Find a real root of 
  log ! 2 using Newton-Raphson method.

[8+8]
7.(a) Find Z-transform of 
"

 2"  3 
sin 3"  5

(b) Find the half range Fourier sine series for 
 " 0, 9
?
[8+8]

Page 2 of 2
Set No - 1

FirstRanker.com - FirstRanker's Choice
Subject Code: R13107/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-II (MATHEMATICAL METHODS)
(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Write the sufficient condition for the convergence of Newton-Raphson method?
(ii) Show that  


? 
?
(iii) Write the merits and demerits of Euler Modified method?
(iv) Write the Dirichlet?s conditions of f(x)?
(v) State Initial and Final value theorems of Z-transforms?
(vi) Write the statement of Fourier integral theorem?
[3+4+4+3+4+4]

PART- B
2.(a) Using Runge-Kutta method of fourth order solve

?
 , 1
 2   1.2    0.2.
(b) Find the Fourier transform of 



[8+8]
3. For the following data estimate f (1.720) using forward, f (2.68) using backward and
f (2.36) using central difference formula.

x 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
f(x) 0.0495 0.0605 0.0739 0.0903 0.1102 0.1346 0.1644 0.2009

4.(a) Solve the differential equation


  subject to 0
 1 by Picard?s method
and hence find 0.2
.
(b) Using Regula Falsi method find a real root of 
 2



 1  0 correct upto
two decimal places.
[8+8]
5.(a) Find the Fourier series for 
 2 !

" 0, 2
, hence show that



#
!


#


\$
#
!

%
#
 ? 
'
#


(b) Find the inverse Z transform of
\$(
#
)(
(
(

[8+8]

Page 1 of 2

Set No - 1
Subject Code: R13107/R13

6.(a) Find the Fourier transform of 
 *
1 !

, | | , 1
0 , | | - 1
.

(b) Find a real root of 
  log ! 2 using Newton-Raphson method.

[8+8]
7.(a) Find Z-transform of 
"

 2"  3 
sin 3"  5

(b) Find the half range Fourier sine series for 
 " 0, 9
?
[8+8]

Page 2 of 2
Set No - 1
Subject Code: R13107/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-II (MATHEMATICAL METHODS)
(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) State Intermediate Value theorem?
(ii) Show that?:
;
log 2
?
(iii) Write the second order Runge-Kutta formula?
(iv) Give any one application of Fourer Series with example?
(v) State the convolution theorem of inverse Z-transforms?
(vi) Write the formulas Fourier cosine and sine transform?
[4+3+4+3+4+4]

PART- B
2.(a) Using modified Euler?s method to find the value of y at x = 0.2 with h = 0.1 where

?
 1 ! , 0
 0
(b) Find the Fourier transform of 
 *
0, | | , 
1, | | - 
.

[8+8]
3.(a) Prove the relation ? ?


=
> ?
=
! ?
?

=@?

(b) Use Lagrange?s interpolation formula to calculate f(3) from the following table.

x 0 1 2 4 5 6
f(x) 1 14 15 5 6 19
[4+12]
4.(a) Solve the differential equation


=x
2
y subject to y(0) =1 by Taylor series method
and hence find y(0.1), y(0.2).
(b) Using bisection method find a root of 
 ! cos  0.
[8+8]
5.(a) Obtain the Fourier series for 
 | | " B!9, 9C, hence show that



#


\$
#



#
 D 
'
#
E

(b) Solve F
)
 4F
)
 3F

 3

 F
?
 0; F

 1 using Z transforms
[8+8]

Page 1 of 2

Set No - 2

FirstRanker.com - FirstRanker's Choice
Subject Code: R13107/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-II (MATHEMATICAL METHODS)
(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Write the sufficient condition for the convergence of Newton-Raphson method?
(ii) Show that  


? 
?
(iii) Write the merits and demerits of Euler Modified method?
(iv) Write the Dirichlet?s conditions of f(x)?
(v) State Initial and Final value theorems of Z-transforms?
(vi) Write the statement of Fourier integral theorem?
[3+4+4+3+4+4]

PART- B
2.(a) Using Runge-Kutta method of fourth order solve

?
 , 1
 2   1.2    0.2.
(b) Find the Fourier transform of 



[8+8]
3. For the following data estimate f (1.720) using forward, f (2.68) using backward and
f (2.36) using central difference formula.

x 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
f(x) 0.0495 0.0605 0.0739 0.0903 0.1102 0.1346 0.1644 0.2009

4.(a) Solve the differential equation


  subject to 0
 1 by Picard?s method
and hence find 0.2
.
(b) Using Regula Falsi method find a real root of 
 2



 1  0 correct upto
two decimal places.
[8+8]
5.(a) Find the Fourier series for 
 2 !

" 0, 2
, hence show that



#
!


#


\$
#
!

%
#
 ? 
'
#


(b) Find the inverse Z transform of
\$(
#
)(
(
(

[8+8]

Page 1 of 2

Set No - 1
Subject Code: R13107/R13

6.(a) Find the Fourier transform of 
 *
1 !

, | | , 1
0 , | | - 1
.

(b) Find a real root of 
  log ! 2 using Newton-Raphson method.

[8+8]
7.(a) Find Z-transform of 
"

 2"  3 
sin 3"  5

(b) Find the half range Fourier sine series for 
 " 0, 9
?
[8+8]

Page 2 of 2
Set No - 1
Subject Code: R13107/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-II (MATHEMATICAL METHODS)
(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) State Intermediate Value theorem?
(ii) Show that?:
;
log 2
?
(iii) Write the second order Runge-Kutta formula?
(iv) Give any one application of Fourer Series with example?
(v) State the convolution theorem of inverse Z-transforms?
(vi) Write the formulas Fourier cosine and sine transform?
[4+3+4+3+4+4]

PART- B
2.(a) Using modified Euler?s method to find the value of y at x = 0.2 with h = 0.1 where

?
 1 ! , 0
 0
(b) Find the Fourier transform of 
 *
0, | | , 
1, | | - 
.

[8+8]
3.(a) Prove the relation ? ?


=
> ?
=
! ?
?

=@?

(b) Use Lagrange?s interpolation formula to calculate f(3) from the following table.

x 0 1 2 4 5 6
f(x) 1 14 15 5 6 19
[4+12]
4.(a) Solve the differential equation


=x
2
y subject to y(0) =1 by Taylor series method
and hence find y(0.1), y(0.2).
(b) Using bisection method find a root of 
 ! cos  0.
[8+8]
5.(a) Obtain the Fourier series for 
 | | " B!9, 9C, hence show that



#


\$
#



#
 D 
'
#
E

(b) Solve F
)
 4F
)
 3F

 3

 F
?
 0; F

 1 using Z transforms
[8+8]

Page 1 of 2

Set No - 2
Subject Code: R13107/R13

6.(a) Using Fourier integral, prove that :
;

;
'
I
JKL ;
;
#
)M
#
NO,  - 0, - 0
?
?

(b) Find a real root of 
 PQ
?
 1.2 using Newton-Raphson method.
[8+8]
7.(a) Find the Z transform of 
cos"  1
R 
sin 
'


(b) Obtain the Fourier series for spectrum of a periodic function with example?

[8+8]

Page 2 of 2

Set No - 2

FirstRanker.com - FirstRanker's Choice
Subject Code: R13107/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-II (MATHEMATICAL METHODS)
(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Write the sufficient condition for the convergence of Newton-Raphson method?
(ii) Show that  


? 
?
(iii) Write the merits and demerits of Euler Modified method?
(iv) Write the Dirichlet?s conditions of f(x)?
(v) State Initial and Final value theorems of Z-transforms?
(vi) Write the statement of Fourier integral theorem?
[3+4+4+3+4+4]

PART- B
2.(a) Using Runge-Kutta method of fourth order solve

?
 , 1
 2   1.2    0.2.
(b) Find the Fourier transform of 



[8+8]
3. For the following data estimate f (1.720) using forward, f (2.68) using backward and
f (2.36) using central difference formula.

x 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
f(x) 0.0495 0.0605 0.0739 0.0903 0.1102 0.1346 0.1644 0.2009

4.(a) Solve the differential equation


  subject to 0
 1 by Picard?s method
and hence find 0.2
.
(b) Using Regula Falsi method find a real root of 
 2



 1  0 correct upto
two decimal places.
[8+8]
5.(a) Find the Fourier series for 
 2 !

" 0, 2
, hence show that



#
!


#


\$
#
!

%
#
 ? 
'
#


(b) Find the inverse Z transform of
\$(
#
)(
(
(

[8+8]

Page 1 of 2

Set No - 1
Subject Code: R13107/R13

6.(a) Find the Fourier transform of 
 *
1 !

, | | , 1
0 , | | - 1
.

(b) Find a real root of 
  log ! 2 using Newton-Raphson method.

[8+8]
7.(a) Find Z-transform of 
"

 2"  3 
sin 3"  5

(b) Find the half range Fourier sine series for 
 " 0, 9
?
[8+8]

Page 2 of 2
Set No - 1
Subject Code: R13107/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-II (MATHEMATICAL METHODS)
(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) State Intermediate Value theorem?
(ii) Show that?:
;
log 2
?
(iii) Write the second order Runge-Kutta formula?
(iv) Give any one application of Fourer Series with example?
(v) State the convolution theorem of inverse Z-transforms?
(vi) Write the formulas Fourier cosine and sine transform?
[4+3+4+3+4+4]

PART- B
2.(a) Using modified Euler?s method to find the value of y at x = 0.2 with h = 0.1 where

?
 1 ! , 0
 0
(b) Find the Fourier transform of 
 *
0, | | , 
1, | | - 
.

[8+8]
3.(a) Prove the relation ? ?


=
> ?
=
! ?
?

=@?

(b) Use Lagrange?s interpolation formula to calculate f(3) from the following table.

x 0 1 2 4 5 6
f(x) 1 14 15 5 6 19
[4+12]
4.(a) Solve the differential equation


=x
2
y subject to y(0) =1 by Taylor series method
and hence find y(0.1), y(0.2).
(b) Using bisection method find a root of 
 ! cos  0.
[8+8]
5.(a) Obtain the Fourier series for 
 | | " B!9, 9C, hence show that



#


\$
#



#
 D 
'
#
E

(b) Solve F
)
 4F
)
 3F

 3

 F
?
 0; F

 1 using Z transforms
[8+8]

Page 1 of 2

Set No - 2
Subject Code: R13107/R13

6.(a) Using Fourier integral, prove that :
;

;
'
I
JKL ;
;
#
)M
#
NO,  - 0, - 0
?
?

(b) Find a real root of 
 PQ
?
 1.2 using Newton-Raphson method.
[8+8]
7.(a) Find the Z transform of 
cos"  1
R 
sin 
'


(b) Obtain the Fourier series for spectrum of a periodic function with example?

[8+8]

Page 2 of 2

Set No - 2
Subject Code: R13107/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-II (MATHEMATICAL METHODS)
(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Write the sufficient condition for the convergence of Newton-Raphson method?
(ii) Show that 


? 
?
(iv) Write the Fourier series when the given function f(x) is an even?
(v) Write the properties of multiplication by n and division by n of Z-transforms?
(vi) Write the complex form of Fourier integral theorem?
[3+3+4+4+4+4]

PART- B
2.(a) Using iteration method find a real root of 


! 3  1 correct upto three
decimal places starting with x=1.
(b) Solve F
)
! 2F
)
 F

 3"  5 using Z-Transforms?
[8+8]
3.(a) Evaluate ?:
;
log 2

(b) By using Lagrange?s interpolation formula, fit a polynomial data

x 0 1 3 4
f(x) -12 0 6 12
[4+12]
4.(a) Using modified Euler method solve numerically the equation


= 2 +S with
y(1) = 1 to find y(1.2)
(b) Find f(x) if its Fourier sine transform is
2
1 s
s
+

[8+8]
5.(a) Obtain the Fourier series for 
 9 !


" 0 , , 29 , hence deduce that



#



#


\$
#
 D 
'
#
T

(b) Using convolution theorem, evaluate U

B
(
#
(
#
%()\$
C
[8+8]

Page 1 of 2
Set No - 3

FirstRanker.com - FirstRanker's Choice
Subject Code: R13107/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-II (MATHEMATICAL METHODS)
(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Write the sufficient condition for the convergence of Newton-Raphson method?
(ii) Show that  


? 
?
(iii) Write the merits and demerits of Euler Modified method?
(iv) Write the Dirichlet?s conditions of f(x)?
(v) State Initial and Final value theorems of Z-transforms?
(vi) Write the statement of Fourier integral theorem?
[3+4+4+3+4+4]

PART- B
2.(a) Using Runge-Kutta method of fourth order solve

?
 , 1
 2   1.2    0.2.
(b) Find the Fourier transform of 



[8+8]
3. For the following data estimate f (1.720) using forward, f (2.68) using backward and
f (2.36) using central difference formula.

x 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
f(x) 0.0495 0.0605 0.0739 0.0903 0.1102 0.1346 0.1644 0.2009

4.(a) Solve the differential equation


  subject to 0
 1 by Picard?s method
and hence find 0.2
.
(b) Using Regula Falsi method find a real root of 
 2



 1  0 correct upto
two decimal places.
[8+8]
5.(a) Find the Fourier series for 
 2 !

" 0, 2
, hence show that



#
!


#


\$
#
!

%
#
 ? 
'
#


(b) Find the inverse Z transform of
\$(
#
)(
(
(

[8+8]

Page 1 of 2

Set No - 1
Subject Code: R13107/R13

6.(a) Find the Fourier transform of 
 *
1 !

, | | , 1
0 , | | - 1
.

(b) Find a real root of 
  log ! 2 using Newton-Raphson method.

[8+8]
7.(a) Find Z-transform of 
"

 2"  3 
sin 3"  5

(b) Find the half range Fourier sine series for 
 " 0, 9
?
[8+8]

Page 2 of 2
Set No - 1
Subject Code: R13107/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-II (MATHEMATICAL METHODS)
(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) State Intermediate Value theorem?
(ii) Show that?:
;
log 2
?
(iii) Write the second order Runge-Kutta formula?
(iv) Give any one application of Fourer Series with example?
(v) State the convolution theorem of inverse Z-transforms?
(vi) Write the formulas Fourier cosine and sine transform?
[4+3+4+3+4+4]

PART- B
2.(a) Using modified Euler?s method to find the value of y at x = 0.2 with h = 0.1 where

?
 1 ! , 0
 0
(b) Find the Fourier transform of 
 *
0, | | , 
1, | | - 
.

[8+8]
3.(a) Prove the relation ? ?


=
> ?
=
! ?
?

=@?

(b) Use Lagrange?s interpolation formula to calculate f(3) from the following table.

x 0 1 2 4 5 6
f(x) 1 14 15 5 6 19
[4+12]
4.(a) Solve the differential equation


=x
2
y subject to y(0) =1 by Taylor series method
and hence find y(0.1), y(0.2).
(b) Using bisection method find a root of 
 ! cos  0.
[8+8]
5.(a) Obtain the Fourier series for 
 | | " B!9, 9C, hence show that



#


\$
#



#
 D 
'
#
E

(b) Solve F
)
 4F
)
 3F

 3

 F
?
 0; F

 1 using Z transforms
[8+8]

Page 1 of 2

Set No - 2
Subject Code: R13107/R13

6.(a) Using Fourier integral, prove that :
;

;
'
I
JKL ;
;
#
)M
#
NO,  - 0, - 0
?
?

(b) Find a real root of 
 PQ
?
 1.2 using Newton-Raphson method.
[8+8]
7.(a) Find the Z transform of 
cos"  1
R 
sin 
'


(b) Obtain the Fourier series for spectrum of a periodic function with example?

[8+8]

Page 2 of 2

Set No - 2
Subject Code: R13107/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-II (MATHEMATICAL METHODS)
(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Write the sufficient condition for the convergence of Newton-Raphson method?
(ii) Show that 


? 
?
(iv) Write the Fourier series when the given function f(x) is an even?
(v) Write the properties of multiplication by n and division by n of Z-transforms?
(vi) Write the complex form of Fourier integral theorem?
[3+3+4+4+4+4]

PART- B
2.(a) Using iteration method find a real root of 


! 3  1 correct upto three
decimal places starting with x=1.
(b) Solve F
)
! 2F
)
 F

 3"  5 using Z-Transforms?
[8+8]
3.(a) Evaluate ?:
;
log 2

(b) By using Lagrange?s interpolation formula, fit a polynomial data

x 0 1 3 4
f(x) -12 0 6 12
[4+12]
4.(a) Using modified Euler method solve numerically the equation


= 2 +S with
y(1) = 1 to find y(1.2)
(b) Find f(x) if its Fourier sine transform is
2
1 s
s
+

[8+8]
5.(a) Obtain the Fourier series for 
 9 !


" 0 , , 29 , hence deduce that



#



#


\$
#
 D 
'
#
T

(b) Using convolution theorem, evaluate U

B
(
#
(
#
%()\$
C
[8+8]

Page 1 of 2
Set No - 3
Subject Code: R13107/R13

6.(a) Using Parseval?s identities, prove that
) ( 2 ) )( (
2 2 2 2
0
b a ab t b t a
dt
+
=
+ +
?
?
?

(b) Using Runge-Kutta method of third order, find the values of

PV  0.1, 0.2 where
?
 ! 2 , 0
 1.

[8+8]
7.(a) Find the half range sine series for 
 9 !
" 0, 9

(b) Find a real root of 

\$
! 19 correct upto three decimal places using Newton-
Raphson method
[8+8]

Page 2 of 2
Set No - 3

FirstRanker.com - FirstRanker's Choice
Subject Code: R13107/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-II (MATHEMATICAL METHODS)
(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Write the sufficient condition for the convergence of Newton-Raphson method?
(ii) Show that  


? 
?
(iii) Write the merits and demerits of Euler Modified method?
(iv) Write the Dirichlet?s conditions of f(x)?
(v) State Initial and Final value theorems of Z-transforms?
(vi) Write the statement of Fourier integral theorem?
[3+4+4+3+4+4]

PART- B
2.(a) Using Runge-Kutta method of fourth order solve

?
 , 1
 2   1.2    0.2.
(b) Find the Fourier transform of 



[8+8]
3. For the following data estimate f (1.720) using forward, f (2.68) using backward and
f (2.36) using central difference formula.

x 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
f(x) 0.0495 0.0605 0.0739 0.0903 0.1102 0.1346 0.1644 0.2009

4.(a) Solve the differential equation


  subject to 0
 1 by Picard?s method
and hence find 0.2
.
(b) Using Regula Falsi method find a real root of 
 2



 1  0 correct upto
two decimal places.
[8+8]
5.(a) Find the Fourier series for 
 2 !

" 0, 2
, hence show that



#
!


#


\$
#
!

%
#
 ? 
'
#


(b) Find the inverse Z transform of
\$(
#
)(
(
(

[8+8]

Page 1 of 2

Set No - 1
Subject Code: R13107/R13

6.(a) Find the Fourier transform of 
 *
1 !

, | | , 1
0 , | | - 1
.

(b) Find a real root of 
  log ! 2 using Newton-Raphson method.

[8+8]
7.(a) Find Z-transform of 
"

 2"  3 
sin 3"  5

(b) Find the half range Fourier sine series for 
 " 0, 9
?
[8+8]

Page 2 of 2
Set No - 1
Subject Code: R13107/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-II (MATHEMATICAL METHODS)
(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) State Intermediate Value theorem?
(ii) Show that?:
;
log 2
?
(iii) Write the second order Runge-Kutta formula?
(iv) Give any one application of Fourer Series with example?
(v) State the convolution theorem of inverse Z-transforms?
(vi) Write the formulas Fourier cosine and sine transform?
[4+3+4+3+4+4]

PART- B
2.(a) Using modified Euler?s method to find the value of y at x = 0.2 with h = 0.1 where

?
 1 ! , 0
 0
(b) Find the Fourier transform of 
 *
0, | | , 
1, | | - 
.

[8+8]
3.(a) Prove the relation ? ?


=
> ?
=
! ?
?

=@?

(b) Use Lagrange?s interpolation formula to calculate f(3) from the following table.

x 0 1 2 4 5 6
f(x) 1 14 15 5 6 19
[4+12]
4.(a) Solve the differential equation


=x
2
y subject to y(0) =1 by Taylor series method
and hence find y(0.1), y(0.2).
(b) Using bisection method find a root of 
 ! cos  0.
[8+8]
5.(a) Obtain the Fourier series for 
 | | " B!9, 9C, hence show that



#


\$
#



#
 D 
'
#
E

(b) Solve F
)
 4F
)
 3F

 3

 F
?
 0; F

 1 using Z transforms
[8+8]

Page 1 of 2

Set No - 2
Subject Code: R13107/R13

6.(a) Using Fourier integral, prove that :
;

;
'
I
JKL ;
;
#
)M
#
NO,  - 0, - 0
?
?

(b) Find a real root of 
 PQ
?
 1.2 using Newton-Raphson method.
[8+8]
7.(a) Find the Z transform of 
cos"  1
R 
sin 
'


(b) Obtain the Fourier series for spectrum of a periodic function with example?

[8+8]

Page 2 of 2

Set No - 2
Subject Code: R13107/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-II (MATHEMATICAL METHODS)
(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Write the sufficient condition for the convergence of Newton-Raphson method?
(ii) Show that 


? 
?
(iv) Write the Fourier series when the given function f(x) is an even?
(v) Write the properties of multiplication by n and division by n of Z-transforms?
(vi) Write the complex form of Fourier integral theorem?
[3+3+4+4+4+4]

PART- B
2.(a) Using iteration method find a real root of 


! 3  1 correct upto three
decimal places starting with x=1.
(b) Solve F
)
! 2F
)
 F

 3"  5 using Z-Transforms?
[8+8]
3.(a) Evaluate ?:
;
log 2

(b) By using Lagrange?s interpolation formula, fit a polynomial data

x 0 1 3 4
f(x) -12 0 6 12
[4+12]
4.(a) Using modified Euler method solve numerically the equation


= 2 +S with
y(1) = 1 to find y(1.2)
(b) Find f(x) if its Fourier sine transform is
2
1 s
s
+

[8+8]
5.(a) Obtain the Fourier series for 
 9 !


" 0 , , 29 , hence deduce that



#



#


\$
#
 D 
'
#
T

(b) Using convolution theorem, evaluate U

B
(
#
(
#
%()\$
C
[8+8]

Page 1 of 2
Set No - 3
Subject Code: R13107/R13

6.(a) Using Parseval?s identities, prove that
) ( 2 ) )( (
2 2 2 2
0
b a ab t b t a
dt
+
=
+ +
?
?
?

(b) Using Runge-Kutta method of third order, find the values of

PV  0.1, 0.2 where
?
 ! 2 , 0
 1.

[8+8]
7.(a) Find the half range sine series for 
 9 !
" 0, 9

(b) Find a real root of 

\$
! 19 correct upto three decimal places using Newton-
Raphson method
[8+8]

Page 2 of 2
Set No - 3
Subject Code: R13107/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-II (MATHEMATICAL METHODS)
(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Show that  


? 
?
(ii) Write the merits and demerits of Iteration method?
(iii) Write the merits and demerits of Euler Modified method?
(iv) Write the Dirichlet?s conditions of f(x)?
(v) State convolution theorem of Z-transforms?
(vi) Write the statement of Fourier integral theorem?
[3+4+4+3+4+4]

PART- B
2.(a) Find the Fourier sine and cosine transforms of ). . 5 . 2 (
2 5 x x
e e
? ?
+
(b) Given
?
?
?
? ? +
? ? ? ?
=
?
?
x x
x x
x f
0 , 1
0 , 1
) (
Is the function even or odd? Find the Fourier series for f(x).
[8+8]
3.(a) Prove the relation between E and D?
(b) For the following data estimate K (0.25) using backward difference formula.

m 0.20 0.22 0.24 0.26 0.28 0.30
K(m) 1.659624 1.669850 1.680373 1.691208 1.702374 1.713889
[4+12]
4.(a) Solve the differential equation


= 1+ xy subject to y(0) = 1 by Taylor series method
and hence find y(0.2).
(b) Solve the difference equation y
n+2
+3y
n+1
+2y
n
= 0, y
0
= 1, y
1
= 2 by z ? transform.
[8+8]
5.(a) Find the Fourier series of ? ? < < ? + = x x x x f , ) (
2
and hence deduce the series
12
. . . . . . .
3
1
2
1
1
1
2
2 2 2
?
= ? + ?
(b) Apply Runge - Kutta Method to find y(0.1) and y(0.2) where


= x
2
- y and y(0) = 1.
[8+8]

Page 1 of 2
Set No - 4

FirstRanker.com - FirstRanker's Choice
Subject Code: R13107/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-II (MATHEMATICAL METHODS)
(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Write the sufficient condition for the convergence of Newton-Raphson method?
(ii) Show that  


? 
?
(iii) Write the merits and demerits of Euler Modified method?
(iv) Write the Dirichlet?s conditions of f(x)?
(v) State Initial and Final value theorems of Z-transforms?
(vi) Write the statement of Fourier integral theorem?
[3+4+4+3+4+4]

PART- B
2.(a) Using Runge-Kutta method of fourth order solve

?
 , 1
 2   1.2    0.2.
(b) Find the Fourier transform of 



[8+8]
3. For the following data estimate f (1.720) using forward, f (2.68) using backward and
f (2.36) using central difference formula.

x 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
f(x) 0.0495 0.0605 0.0739 0.0903 0.1102 0.1346 0.1644 0.2009

4.(a) Solve the differential equation


  subject to 0
 1 by Picard?s method
and hence find 0.2
.
(b) Using Regula Falsi method find a real root of 
 2



 1  0 correct upto
two decimal places.
[8+8]
5.(a) Find the Fourier series for 
 2 !

" 0, 2
, hence show that



#
!


#


\$
#
!

%
#
 ? 
'
#


(b) Find the inverse Z transform of
\$(
#
)(
(
(

[8+8]

Page 1 of 2

Set No - 1
Subject Code: R13107/R13

6.(a) Find the Fourier transform of 
 *
1 !

, | | , 1
0 , | | - 1
.

(b) Find a real root of 
  log ! 2 using Newton-Raphson method.

[8+8]
7.(a) Find Z-transform of 
"

 2"  3 
sin 3"  5

(b) Find the half range Fourier sine series for 
 " 0, 9
?
[8+8]

Page 2 of 2
Set No - 1
Subject Code: R13107/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-II (MATHEMATICAL METHODS)
(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) State Intermediate Value theorem?
(ii) Show that?:
;
log 2
?
(iii) Write the second order Runge-Kutta formula?
(iv) Give any one application of Fourer Series with example?
(v) State the convolution theorem of inverse Z-transforms?
(vi) Write the formulas Fourier cosine and sine transform?
[4+3+4+3+4+4]

PART- B
2.(a) Using modified Euler?s method to find the value of y at x = 0.2 with h = 0.1 where

?
 1 ! , 0
 0
(b) Find the Fourier transform of 
 *
0, | | , 
1, | | - 
.

[8+8]
3.(a) Prove the relation ? ?


=
> ?
=
! ?
?

=@?

(b) Use Lagrange?s interpolation formula to calculate f(3) from the following table.

x 0 1 2 4 5 6
f(x) 1 14 15 5 6 19
[4+12]
4.(a) Solve the differential equation


=x
2
y subject to y(0) =1 by Taylor series method
and hence find y(0.1), y(0.2).
(b) Using bisection method find a root of 
 ! cos  0.
[8+8]
5.(a) Obtain the Fourier series for 
 | | " B!9, 9C, hence show that



#


\$
#



#
 D 
'
#
E

(b) Solve F
)
 4F
)
 3F

 3

 F
?
 0; F

 1 using Z transforms
[8+8]

Page 1 of 2

Set No - 2
Subject Code: R13107/R13

6.(a) Using Fourier integral, prove that :
;

;
'
I
JKL ;
;
#
)M
#
NO,  - 0, - 0
?
?

(b) Find a real root of 
 PQ
?
 1.2 using Newton-Raphson method.
[8+8]
7.(a) Find the Z transform of 
cos"  1
R 
sin 
'


(b) Obtain the Fourier series for spectrum of a periodic function with example?

[8+8]

Page 2 of 2

Set No - 2
Subject Code: R13107/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-II (MATHEMATICAL METHODS)
(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Write the sufficient condition for the convergence of Newton-Raphson method?
(ii) Show that 


? 
?
(iv) Write the Fourier series when the given function f(x) is an even?
(v) Write the properties of multiplication by n and division by n of Z-transforms?
(vi) Write the complex form of Fourier integral theorem?
[3+3+4+4+4+4]

PART- B
2.(a) Using iteration method find a real root of 


! 3  1 correct upto three
decimal places starting with x=1.
(b) Solve F
)
! 2F
)
 F

 3"  5 using Z-Transforms?
[8+8]
3.(a) Evaluate ?:
;
log 2

(b) By using Lagrange?s interpolation formula, fit a polynomial data

x 0 1 3 4
f(x) -12 0 6 12
[4+12]
4.(a) Using modified Euler method solve numerically the equation


= 2 +S with
y(1) = 1 to find y(1.2)
(b) Find f(x) if its Fourier sine transform is
2
1 s
s
+

[8+8]
5.(a) Obtain the Fourier series for 
 9 !


" 0 , , 29 , hence deduce that



#



#


\$
#
 D 
'
#
T

(b) Using convolution theorem, evaluate U

B
(
#
(
#
%()\$
C
[8+8]

Page 1 of 2
Set No - 3
Subject Code: R13107/R13

6.(a) Using Parseval?s identities, prove that
) ( 2 ) )( (
2 2 2 2
0
b a ab t b t a
dt
+
=
+ +
?
?
?

(b) Using Runge-Kutta method of third order, find the values of

PV  0.1, 0.2 where
?
 ! 2 , 0
 1.

[8+8]
7.(a) Find the half range sine series for 
 9 !
" 0, 9

(b) Find a real root of 

\$
! 19 correct upto three decimal places using Newton-
Raphson method
[8+8]

Page 2 of 2
Set No - 3
Subject Code: R13107/R13
I B. Tech I Semester Regular Examinations Feb./Mar. - 2014
MATHEMATICS-II (MATHEMATICAL METHODS)
(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)
Time: 3 hours Max. Marks: 70
Question Paper Consists of Part-A and Part-B
Answering the question in Part-A is Compulsory,
Three Questions should be answered from Part-B
*****
PART-A
1.(i) Show that  


? 
?
(ii) Write the merits and demerits of Iteration method?
(iii) Write the merits and demerits of Euler Modified method?
(iv) Write the Dirichlet?s conditions of f(x)?
(v) State convolution theorem of Z-transforms?
(vi) Write the statement of Fourier integral theorem?
[3+4+4+3+4+4]

PART- B
2.(a) Find the Fourier sine and cosine transforms of ). . 5 . 2 (
2 5 x x
e e
? ?
+
(b) Given
?
?
?
? ? +
? ? ? ?
=
?
?
x x
x x
x f
0 , 1
0 , 1
) (
Is the function even or odd? Find the Fourier series for f(x).
[8+8]
3.(a) Prove the relation between E and D?
(b) For the following data estimate K (0.25) using backward difference formula.

m 0.20 0.22 0.24 0.26 0.28 0.30
K(m) 1.659624 1.669850 1.680373 1.691208 1.702374 1.713889
[4+12]
4.(a) Solve the differential equation


= 1+ xy subject to y(0) = 1 by Taylor series method
and hence find y(0.2).
(b) Solve the difference equation y
n+2
+3y
n+1
+2y
n
= 0, y
0
= 1, y
1
= 2 by z ? transform.
[8+8]
5.(a) Find the Fourier series of ? ? < < ? + = x x x x f , ) (
2
and hence deduce the series
12
. . . . . . .
3
1
2
1
1
1
2
2 2 2
?
= ? + ?
(b) Apply Runge - Kutta Method to find y(0.1) and y(0.2) where


= x
2
- y and y(0) = 1.
[8+8]

Page 1 of 2
Set No - 4

Subject Code: R13107/R13

6.(a) Find the Fourier transform of
x
e
?

(b) Using Regula Falsi method find a real root of 
 2



 1  0 correct upto
two decimal places.
[8+8]
7.(a) Find )
! n
1
( z and hence evaluate
?
?
?
?
?
?
?
?
+
?
?
?
?
?
?
?
?
+ )! 2 n (
1
z and
)! 1 n (
1
z
(b) Find a real root of 
  log ! 2 using Newton-Raphson method.
[8+8]

Page 2 of 2
Set No - 4

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