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

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

[16]

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

[16]

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

[16]

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

[16]

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

[16]

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

?

?

(iii) Write the advantages & disadvantages of Taylor series method?

(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

[16]

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

?

?

(iii) Write the advantages & disadvantages of Taylor series method?

(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

[16]

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

?

?

(iii) Write the advantages & disadvantages of Taylor series method?

(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

[16]

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

?

?

(iii) Write the advantages & disadvantages of Taylor series method?

(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

FirstRanker.com - FirstRanker's Choice

This post was last modified on 03 December 2019