JNTU Kakinada B-Tech 1-1 R161109 MATHEMATICS-II (MM) R16 May 2018 Question Paper

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