Categories: First Year First Semester (1-1)

JNTU Kakinada (JNTUK) B-Tech First Year First Semester (1-1) MATHEMATICS-II MM Common to to CSE, IT, Agri E R16 Regulation May 2018 Question Paper

Code No: R161109

I B. Tech I Semester Supplementary Examinations, May – 2018

MATHEMATICS-II (MM) (Com. to CSE, IT, Agri E)Time: 3 hours Max. Marks: 70

Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the questions in Part-A

3. Answer any FOUR Questions from Part-B

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PART ?A

1. a) Write the working rule to find the root of f(x) = 0 by Newton Raphson method. (2M)

b) Prove that E = e

hD (2M)

c) Find y(0.2) by RK method of second order given that

2

, (0) 1

dy

x xy y

dx

= – = (2M)

d)Find half range sine series of () =

in [0,2] (2M)

e)Find the inverse Fourier finite sine transform of f(x) if ( ) 2 1( ) (0, )

3

S

n

F n in

n

p

p

–

= (2M)

f)Find the Fourier transform of

1 0 1( )

0 1 2

if x

f x

if x

=

?

?

(2M)

g) What are the initial conditions in one dimension wave equation? (2M)

PART -B

2. a) Find the root of the equation x

3

-x-11=0 using False position method. (7M)

b) Find the root of the equation x

4

-x-10=0 using Iteration method. (7M)

3. a) Find the Lagrange? s polynomial for the following data.

x 0 1 2 5

y 2 3 12 14

(7M)

b) Using Newton?s Forward difference formula find y(2) from the following table.

X 0 5 10 15 20 25

Y 7 11 14 18 24 32 (7M)

4.

a)Evaluate ( )

2

2

1

1

1

dx

x +

?

by (i) Simpson?s 1/3

rd

rule (iii) Simpson?s 3/8

th

Rule. (7M)

b)Solve

2

dy x y

dx

+

= using Taylor?s method for x=1.1 given y (1)=1

(7M)

SET – 1

R16

1 of 2

Code No: R161109

I B. Tech I Semester Supplementary Examinations, May – 2018

MATHEMATICS-II (MM) (Com. to CSE, IT, Agri E)Time: 3 hours Max. Marks: 70

Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the questions in Part-A

3. Answer any FOUR Questions from Part-B

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PART ?A

1. a) Write the working rule to find the root of f(x) = 0 by Newton Raphson method. (2M)

b) Prove that E = e

hD (2M)

c) Find y(0.2) by RK method of second order given that

2

, (0) 1

dy

x xy y

dx

= – = (2M)

d)Find half range sine series of () =

in [0,2] (2M)

e)Find the inverse Fourier finite sine transform of f(x) if ( ) 2 1( ) (0, )

3

S

n

F n in

n

p

p

–

= (2M)

f)Find the Fourier transform of

1 0 1( )

0 1 2

if x

f x

if x

=

?

?

(2M)

g) What are the initial conditions in one dimension wave equation? (2M)

PART -B

2. a) Find the root of the equation x

3

-x-11=0 using False position method. (7M)

b) Find the root of the equation x

4

-x-10=0 using Iteration method. (7M)

3. a) Find the Lagrange? s polynomial for the following data.

x 0 1 2 5

y 2 3 12 14

(7M)

b) Using Newton?s Forward difference formula find y(2) from the following table.

X 0 5 10 15 20 25

Y 7 11 14 18 24 32 (7M)

4.

a)Evaluate ( )

2

2

1

1

1

dx

x +

?

by (i) Simpson?s 1/3

rd

rule (iii) Simpson?s 3/8

th

Rule. (7M)

b)Solve

2

dy x y

dx

+

= using Taylor?s method for x=1.1 given y (1)=1

(7M)

SET – 1

R16

1 of 2

Code No: R161109

5.

a)Find the Fourier series of () =

0,-
1, 0

Hence deduce that 1-

+

+…=

p

(7M)

b)Obtain the half range cosine series of

2( ) 2 0 2 f x x x = – = =

(7M)

6. a)Find inverse Fourier cosine transform of

(7M)

b)Find the Fourier sine transform of cos

ax

e ax

–

(7M)

7. a) Solve 4 3

u u

u

x y

? ?

+ =

? ?

given that

5(0, ) 3

y y

u y e e

– –

= – (7M)

b)Solve

2 2

2 2

0

u u

x y

? ?

+ =

? ?

subject to ( ) ( ,0) 0( ) ( , ) 0( ) ( , ) 0,0( ) (0, ) ,0

i u x for all x

ii u x l for all x

iii u y y l

iv u y y y l

=

=

8 = = =

= = =

(7M)

2 of 2

SET -1

R16

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