# JNTU Kakinada B-Tech 1-2 R161202 MATHEMATICS-II (MM) R16 May 2018 Question Paper

JNTU Kakinada (JNTUK) B-Tech First Year Second Semester (1-2) MATHEMATICS-II MM Com to CE,EEE,ME,AE,AME,Bio-Tech,Chem E,Metal E,Min E,PCE,PE R16 Regulation May 2018 Question Paper

Code No: R161202
I B. Tech II Semester Regular/Supplementary Examinations, April/May – 2018
MATHEMATICS-II (MM) (Com to CE,EEE,ME,AE,AME,Bio-Tech,Chem E,Metal E,Min E,PCE,PE)Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a)Write the iteration formula to find N using Newton Raphson method. (2M)
b) Prove that
[ ]
1
2
?d = ?+? (2M)
c) Write the formula for RK method of second order. (2M)
d) Write Simpson?s 1/3
rd
Rule. (2M)
e) Find the value of a
0
for
1 0
2( )
1
2
x
f x
x
p
p
p
?
?
?
=
?
?
– ?
?
(2M)
f) State Linear property in Fourier Transform. (2M)
g)Write the equation for the PDE 4 3
u u
u
x y
? ?
+ =
? ?
by variable separable method. (2M)
PART -B
2. a) Find the root of the equation x
3
-6x-4=0 using iteration method. (7M)
b) Find the root of the equation 2x-log
10
x=7 using False position method.
(7M)
3. a) Find the parabola passing through the points (0,1), (1,3) and (3,55) using
Lagrange?s interpolation formula. (7M)
b) Area A of circle and diameter d is given for the following values
d 80 85 90 95 100
A 5026 5674 6362 7088 7854
Calculate the area of circle of diameter 105.

(7M)
SET – 1
R16
1 of 2

Code No: R161202
I B. Tech II Semester Regular/Supplementary Examinations, April/May – 2018
MATHEMATICS-II (MM) (Com to CE,EEE,ME,AE,AME,Bio-Tech,Chem E,Metal E,Min E,PCE,PE)Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a)Write the iteration formula to find N using Newton Raphson method. (2M)
b) Prove that
[ ]
1
2
?d = ?+? (2M)
c) Write the formula for RK method of second order. (2M)
d) Write Simpson?s 1/3
rd
Rule. (2M)
e) Find the value of a
0
for
1 0
2( )
1
2
x
f x
x
p
p
p
?
?
?
=
?
?
– ?
?
(2M)
f) State Linear property in Fourier Transform. (2M)
g)Write the equation for the PDE 4 3
u u
u
x y
? ?
+ =
? ?
by variable separable method. (2M)
PART -B
2. a) Find the root of the equation x
3
-6x-4=0 using iteration method. (7M)
b) Find the root of the equation 2x-log
10
x=7 using False position method.
(7M)
3. a) Find the parabola passing through the points (0,1), (1,3) and (3,55) using
Lagrange?s interpolation formula. (7M)
b) Area A of circle and diameter d is given for the following values
d 80 85 90 95 100
A 5026 5674 6362 7088 7854
Calculate the area of circle of diameter 105.

(7M)
SET – 1
R16
1 of 2

Code No: R161202

4.
a)Evaluate y (0.1) using RK method of fourth order for
2
, (0) 1
dy x
y y
dx y
= – = (7M)
b)Evaluate y (0.1) ,y(0.2) using Picard?s method for , (0) 1
dy
x y y
dx
= + =
(7M)

5.

a)Find the Fourier series of
2
1 0( )
2
1 0
x
if x
f x
x
if x
p
p
p
p
?
+ – = ?
?
=
?
?
– = ?
?

Hence deduce that
2
2 2
1 1
1 ……
3 5 8
p
+ + + =
(7M)
b) Find the Half range sine series of f(x) = x
2
in [ 0,2]
(7M)
6.
a) Using Fourier integral, Show that
2
0
cos sin
0
1 0
0
x
x x
d
if x
if x
e
? ? ?
?
? p

8
?
+
=
? ?
+ >
?
(7M)

b)Find the Fourier cosine transform of
2
1
1 x +
and hence deduce Fourier sine
transform
2
1
x
x +
(7M)
7. a)Solve the PDE 4
u u
x y
? ?
=
? ?
where
3(0, ) 8
y
u x e

= (7M)
b) A tightly stretched string with fixed end points at x = 0 and x = 1 is initially in a
position given by
1
0
2( )
1
1 1
2
x x
f x
x x
?
?
?
=
?
?
– ?
?
If it is released from this position with velocity zero find the displacement u(x, t)at any point of x of the string at any time is t > 0. (7M)

2 of 2
SET – 1
R16

Code No: R161202
I B. Tech II Semester Regular/Supplementary Examinations, April/May – 2018
MATHEMATICS-II (MM) (Com to CE,EEE,ME,AE,AME,Bio-Tech,Chem E,Metal E,Min E,PCE,PE)Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a)Write the iteration formula to find N using Newton Raphson method. (2M)
b) Prove that
[ ]
1
2
?d = ?+? (2M)
c) Write the formula for RK method of second order. (2M)
d) Write Simpson?s 1/3
rd
Rule. (2M)
e) Find the value of a
0
for
1 0
2( )
1
2
x
f x
x
p
p
p
?
?
?
=
?
?
– ?
?
(2M)
f) State Linear property in Fourier Transform. (2M)
g)Write the equation for the PDE 4 3
u u
u
x y
? ?
+ =
? ?
by variable separable method. (2M)
PART -B
2. a) Find the root of the equation x
3
-6x-4=0 using iteration method. (7M)
b) Find the root of the equation 2x-log
10
x=7 using False position method.
(7M)
3. a) Find the parabola passing through the points (0,1), (1,3) and (3,55) using
Lagrange?s interpolation formula. (7M)
b) Area A of circle and diameter d is given for the following values
d 80 85 90 95 100
A 5026 5674 6362 7088 7854
Calculate the area of circle of diameter 105.

(7M)
SET – 1
R16
1 of 2

Code No: R161202

4.
a)Evaluate y (0.1) using RK method of fourth order for
2
, (0) 1
dy x
y y
dx y
= – = (7M)
b)Evaluate y (0.1) ,y(0.2) using Picard?s method for , (0) 1
dy
x y y
dx
= + =
(7M)

5.

a)Find the Fourier series of
2
1 0( )
2
1 0
x
if x
f x
x
if x
p
p
p
p
?
+ – = ?
?
=
?
?
– = ?
?

Hence deduce that
2
2 2
1 1
1 ……
3 5 8
p
+ + + =
(7M)
b) Find the Half range sine series of f(x) = x
2
in [ 0,2]
(7M)
6.
a) Using Fourier integral, Show that
2
0
cos sin
0
1 0
0
x
x x
d
if x
if x
e
? ? ?
?
? p

8
?
+
=
? ?
+ >
?
(7M)

b)Find the Fourier cosine transform of
2
1
1 x +
and hence deduce Fourier sine
transform
2
1
x
x +
(7M)
7. a)Solve the PDE 4
u u
x y
? ?
=
? ?
where
3(0, ) 8
y
u x e

= (7M)
b) A tightly stretched string with fixed end points at x = 0 and x = 1 is initially in a
position given by
1
0
2( )
1
1 1
2
x x
f x
x x
?
?
?
=
?
?
– ?
?
If it is released from this position with velocity zero find the displacement u(x, t)at any point of x of the string at any time is t > 0. (7M)

2 of 2
SET – 1
R16

Code No: R161202
I B. Tech II Semester Regular/Supplementary Examinations, April/May – 2018
MATHEMATICS-II (MM) (Com to CE,EEE,ME,AE,AME,Bio-Tech,Chem E,Metal E,Min E,PCE,PE) Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a) Find two iterations of x = cosx using bisection method. (2M)
b)Prove that ( )
log ( ) log 1( )
f x
f x
f x
? ? ?
? = +
? ?
? ?(2M)
c) Write Trapezoidal Rule. (2M)
d) Write the Dirichlet conditions for Fourier series. (2M)
e) Find the value of a
n
for
1
1 0
2( )
1
1 1
2
x
f x
x
?
?
?
=
?
?
– ?
?
(2M)
f) State modulation property in Fourier transforms. (2M)
g) Write two dimensional steady state equation. (2M)
PART -B
2. a) Find the root of the equation x e
x
= 2 using Newton Raphson method. (7M)
b) Find the root of the equation 3x = 1+cosx

using False position method. (7M)
3. a) Find the Lagrange?s polynomial for the following data, hence find y(15).
x -5 6 9 11
y 12 13 14 16 (7M)

b)Find y(23) for the following data using Gauss Forward interpolation formula.
x 10 20 30 40 50
y 9.21 17.54 31.82 55.32 92.51
(7M)
4.
a)Evaluate y (0.1) using RK method of fourth order for , (0) 1
x
dy
y xe y
dx
= + = (7M)

b)Evaluate y (0.1) using Taylor?s method for
2
, (0) 1
dy
x y y
dx
= + =

(7M)
SET – 2
R16
1 of 2

Code No: R161202
I B. Tech II Semester Regular/Supplementary Examinations, April/May – 2018
MATHEMATICS-II (MM) (Com to CE,EEE,ME,AE,AME,Bio-Tech,Chem E,Metal E,Min E,PCE,PE)Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a)Write the iteration formula to find N using Newton Raphson method. (2M)
b) Prove that
[ ]
1
2
?d = ?+? (2M)
c) Write the formula for RK method of second order. (2M)
d) Write Simpson?s 1/3
rd
Rule. (2M)
e) Find the value of a
0
for
1 0
2( )
1
2
x
f x
x
p
p
p
?
?
?
=
?
?
– ?
?
(2M)
f) State Linear property in Fourier Transform. (2M)
g)Write the equation for the PDE 4 3
u u
u
x y
? ?
+ =
? ?
by variable separable method. (2M)
PART -B
2. a) Find the root of the equation x
3
-6x-4=0 using iteration method. (7M)
b) Find the root of the equation 2x-log
10
x=7 using False position method.
(7M)
3. a) Find the parabola passing through the points (0,1), (1,3) and (3,55) using
Lagrange?s interpolation formula. (7M)
b) Area A of circle and diameter d is given for the following values
d 80 85 90 95 100
A 5026 5674 6362 7088 7854
Calculate the area of circle of diameter 105.

(7M)
SET – 1
R16
1 of 2

Code No: R161202

4.
a)Evaluate y (0.1) using RK method of fourth order for
2
, (0) 1
dy x
y y
dx y
= – = (7M)
b)Evaluate y (0.1) ,y(0.2) using Picard?s method for , (0) 1
dy
x y y
dx
= + =
(7M)

5.

a)Find the Fourier series of
2
1 0( )
2
1 0
x
if x
f x
x
if x
p
p
p
p
?
+ – = ?
?
=
?
?
– = ?
?

Hence deduce that
2
2 2
1 1
1 ……
3 5 8
p
+ + + =
(7M)
b) Find the Half range sine series of f(x) = x
2
in [ 0,2]
(7M)
6.
a) Using Fourier integral, Show that
2
0
cos sin
0
1 0
0
x
x x
d
if x
if x
e
? ? ?
?
? p

8
?
+
=
? ?
+ >
?
(7M)

b)Find the Fourier cosine transform of
2
1
1 x +
and hence deduce Fourier sine
transform
2
1
x
x +
(7M)
7. a)Solve the PDE 4
u u
x y
? ?
=
? ?
where
3(0, ) 8
y
u x e

= (7M)
b) A tightly stretched string with fixed end points at x = 0 and x = 1 is initially in a
position given by
1
0
2( )
1
1 1
2
x x
f x
x x
?
?
?
=
?
?
– ?
?
If it is released from this position with velocity zero find the displacement u(x, t)at any point of x of the string at any time is t > 0. (7M)

2 of 2
SET – 1
R16

Code No: R161202
I B. Tech II Semester Regular/Supplementary Examinations, April/May – 2018
MATHEMATICS-II (MM) (Com to CE,EEE,ME,AE,AME,Bio-Tech,Chem E,Metal E,Min E,PCE,PE) Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a) Find two iterations of x = cosx using bisection method. (2M)
b)Prove that ( )
log ( ) log 1( )
f x
f x
f x
? ? ?
? = +
? ?
? ?(2M)
c) Write Trapezoidal Rule. (2M)
d) Write the Dirichlet conditions for Fourier series. (2M)
e) Find the value of a
n
for
1
1 0
2( )
1
1 1
2
x
f x
x
?
?
?
=
?
?
– ?
?
(2M)
f) State modulation property in Fourier transforms. (2M)
g) Write two dimensional steady state equation. (2M)
PART -B
2. a) Find the root of the equation x e
x
= 2 using Newton Raphson method. (7M)
b) Find the root of the equation 3x = 1+cosx

using False position method. (7M)
3. a) Find the Lagrange?s polynomial for the following data, hence find y(15).
x -5 6 9 11
y 12 13 14 16 (7M)

b)Find y(23) for the following data using Gauss Forward interpolation formula.
x 10 20 30 40 50
y 9.21 17.54 31.82 55.32 92.51
(7M)
4.
a)Evaluate y (0.1) using RK method of fourth order for , (0) 1
x
dy
y xe y
dx
= + = (7M)

b)Evaluate y (0.1) using Taylor?s method for
2
, (0) 1
dy
x y y
dx
= + =

(7M)
SET – 2
R16
1 of 2

Code No: R161202

5. a) Find the Fourier series of f(x) = sinhax in ?p b) Find the half range sine series of
0
2( )
2
l
x x
f x
l
l x x l
?
?
?
=
?
?
– ?
?

(7M)
6.
a) Using Fourier cosine integral, show that
2
cos
2 1
0
x
x
e d
p ?
?
?
8

=
?
+
(7M)

b)Find the Fourier sine transform of the function f(x) = x in (0,8)

(7M)
7. a)Solve 4 3
z z
z
x y
? ?
– =
? ?
and
5(0, )
y
z y e

= (7M)
b) Find the temperature u(x, t) in a homogenous bar of heat conducting method of
length ?l? whose ends are kept at 0
0
c and whose initial temperature is ( )
2
ax
l x
l
– (7M)

2 of 2
SET – 2
R16

Code No: R161202
I B. Tech II Semester Regular/Supplementary Examinations, April/May – 2018
MATHEMATICS-II (MM) (Com to CE,EEE,ME,AE,AME,Bio-Tech,Chem E,Metal E,Min E,PCE,PE)Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a)Write the iteration formula to find N using Newton Raphson method. (2M)
b) Prove that
[ ]
1
2
?d = ?+? (2M)
c) Write the formula for RK method of second order. (2M)
d) Write Simpson?s 1/3
rd
Rule. (2M)
e) Find the value of a
0
for
1 0
2( )
1
2
x
f x
x
p
p
p
?
?
?
=
?
?
– ?
?
(2M)
f) State Linear property in Fourier Transform. (2M)
g)Write the equation for the PDE 4 3
u u
u
x y
? ?
+ =
? ?
by variable separable method. (2M)
PART -B
2. a) Find the root of the equation x
3
-6x-4=0 using iteration method. (7M)
b) Find the root of the equation 2x-log
10
x=7 using False position method.
(7M)
3. a) Find the parabola passing through the points (0,1), (1,3) and (3,55) using
Lagrange?s interpolation formula. (7M)
b) Area A of circle and diameter d is given for the following values
d 80 85 90 95 100
A 5026 5674 6362 7088 7854
Calculate the area of circle of diameter 105.

(7M)
SET – 1
R16
1 of 2

Code No: R161202

4.
a)Evaluate y (0.1) using RK method of fourth order for
2
, (0) 1
dy x
y y
dx y
= – = (7M)
b)Evaluate y (0.1) ,y(0.2) using Picard?s method for , (0) 1
dy
x y y
dx
= + =
(7M)

5.

a)Find the Fourier series of
2
1 0( )
2
1 0
x
if x
f x
x
if x
p
p
p
p
?
+ – = ?
?
=
?
?
– = ?
?

Hence deduce that
2
2 2
1 1
1 ……
3 5 8
p
+ + + =
(7M)
b) Find the Half range sine series of f(x) = x
2
in [ 0,2]
(7M)
6.
a) Using Fourier integral, Show that
2
0
cos sin
0
1 0
0
x
x x
d
if x
if x
e
? ? ?
?
? p

8
?
+
=
? ?
+ >
?
(7M)

b)Find the Fourier cosine transform of
2
1
1 x +
and hence deduce Fourier sine
transform
2
1
x
x +
(7M)
7. a)Solve the PDE 4
u u
x y
? ?
=
? ?
where
3(0, ) 8
y
u x e

= (7M)
b) A tightly stretched string with fixed end points at x = 0 and x = 1 is initially in a
position given by
1
0
2( )
1
1 1
2
x x
f x
x x
?
?
?
=
?
?
– ?
?
If it is released from this position with velocity zero find the displacement u(x, t)at any point of x of the string at any time is t > 0. (7M)

2 of 2
SET – 1
R16

Code No: R161202
I B. Tech II Semester Regular/Supplementary Examinations, April/May – 2018
MATHEMATICS-II (MM) (Com to CE,EEE,ME,AE,AME,Bio-Tech,Chem E,Metal E,Min E,PCE,PE) Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a) Find two iterations of x = cosx using bisection method. (2M)
b)Prove that ( )
log ( ) log 1( )
f x
f x
f x
? ? ?
? = +
? ?
? ?(2M)
c) Write Trapezoidal Rule. (2M)
d) Write the Dirichlet conditions for Fourier series. (2M)
e) Find the value of a
n
for
1
1 0
2( )
1
1 1
2
x
f x
x
?
?
?
=
?
?
– ?
?
(2M)
f) State modulation property in Fourier transforms. (2M)
g) Write two dimensional steady state equation. (2M)
PART -B
2. a) Find the root of the equation x e
x
= 2 using Newton Raphson method. (7M)
b) Find the root of the equation 3x = 1+cosx

using False position method. (7M)
3. a) Find the Lagrange?s polynomial for the following data, hence find y(15).
x -5 6 9 11
y 12 13 14 16 (7M)

b)Find y(23) for the following data using Gauss Forward interpolation formula.
x 10 20 30 40 50
y 9.21 17.54 31.82 55.32 92.51
(7M)
4.
a)Evaluate y (0.1) using RK method of fourth order for , (0) 1
x
dy
y xe y
dx
= + = (7M)

b)Evaluate y (0.1) using Taylor?s method for
2
, (0) 1
dy
x y y
dx
= + =

(7M)
SET – 2
R16
1 of 2

Code No: R161202

5. a) Find the Fourier series of f(x) = sinhax in ?p b) Find the half range sine series of
0
2( )
2
l
x x
f x
l
l x x l
?
?
?
=
?
?
– ?
?

(7M)
6.
a) Using Fourier cosine integral, show that
2
cos
2 1
0
x
x
e d
p ?
?
?
8

=
?
+
(7M)

b)Find the Fourier sine transform of the function f(x) = x in (0,8)

(7M)
7. a)Solve 4 3
z z
z
x y
? ?
– =
? ?
and
5(0, )
y
z y e

= (7M)
b) Find the temperature u(x, t) in a homogenous bar of heat conducting method of
length ?l? whose ends are kept at 0
0
c and whose initial temperature is ( )
2
ax
l x
l
– (7M)

2 of 2
SET – 2
R16

Code No: R161202
I B. Tech II Semester Regular/Supplementary Examinations, April/May – 2018
MATHEMATICS-II (MM) (Com to CE,EEE,ME,AE,AME,Bio-Tech,Chem E,Metal E,Min E,PCE,PE)Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a) Find two iterations of x e
x
= 2 using False position method. (2M)
b)Show that
1
1 E

?= – (2M)
c)Evaluate y (0.1) by Euler?s method for , (0) 1
dy x y
y
dx y x
+
= =

. (2M)
d) Write Simpson?s 3/8
th
Rule. (2M)

e)Find the value of b
n
for
1 0
2( )
1
2
x
f x
x
p
p
p
?
?
?
=
?
?
– ?
?
(2M)
f) Write shifting theorem in Fourier transforms. (2M)
g) Write one dimensional heat equation. (2M)
PART -B
2. a) Find the root of the equation x
4
– 10 = x using Bisection method. (7M)
b) Find the root of the equation xtanx+1=0

using Newton Raphson method.
(7M)
3. a) Find the Lagrange?s polynomial for the following data.

x 0 2 3 6
y 648 704 729 792 (7M)

b)Fit a y(0.5) the following data using Newton Forward interpolation formula.
x -1 0 1 2
y 10 5 8 10
(7M)
4.
a)Evaluate
2
0
1
1
dx
x +
?
by taking h = 0.1 by (i) Trapezoidal rule. (ii) Simpson?s 1/3
rd
rule
(7M)
b)Evaluate y (0.1) using Modified Euler?s method for
2 2
, (0) 1
dy
x y y
dx
= + =
(7M)
SET – 3
R16
1 of 2

Code No: R161202
I B. Tech II Semester Regular/Supplementary Examinations, April/May – 2018
MATHEMATICS-II (MM) (Com to CE,EEE,ME,AE,AME,Bio-Tech,Chem E,Metal E,Min E,PCE,PE)Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a)Write the iteration formula to find N using Newton Raphson method. (2M)
b) Prove that
[ ]
1
2
?d = ?+? (2M)
c) Write the formula for RK method of second order. (2M)
d) Write Simpson?s 1/3
rd
Rule. (2M)
e) Find the value of a
0
for
1 0
2( )
1
2
x
f x
x
p
p
p
?
?
?
=
?
?
– ?
?
(2M)
f) State Linear property in Fourier Transform. (2M)
g)Write the equation for the PDE 4 3
u u
u
x y
? ?
+ =
? ?
by variable separable method. (2M)
PART -B
2. a) Find the root of the equation x
3
-6x-4=0 using iteration method. (7M)
b) Find the root of the equation 2x-log
10
x=7 using False position method.
(7M)
3. a) Find the parabola passing through the points (0,1), (1,3) and (3,55) using
Lagrange?s interpolation formula. (7M)
b) Area A of circle and diameter d is given for the following values
d 80 85 90 95 100
A 5026 5674 6362 7088 7854
Calculate the area of circle of diameter 105.

(7M)
SET – 1
R16
1 of 2

Code No: R161202

4.
a)Evaluate y (0.1) using RK method of fourth order for
2
, (0) 1
dy x
y y
dx y
= – = (7M)
b)Evaluate y (0.1) ,y(0.2) using Picard?s method for , (0) 1
dy
x y y
dx
= + =
(7M)

5.

a)Find the Fourier series of
2
1 0( )
2
1 0
x
if x
f x
x
if x
p
p
p
p
?
+ – = ?
?
=
?
?
– = ?
?

Hence deduce that
2
2 2
1 1
1 ……
3 5 8
p
+ + + =
(7M)
b) Find the Half range sine series of f(x) = x
2
in [ 0,2]
(7M)
6.
a) Using Fourier integral, Show that
2
0
cos sin
0
1 0
0
x
x x
d
if x
if x
e
? ? ?
?
? p

8
?
+
=
? ?
+ >
?
(7M)

b)Find the Fourier cosine transform of
2
1
1 x +
and hence deduce Fourier sine
transform
2
1
x
x +
(7M)
7. a)Solve the PDE 4
u u
x y
? ?
=
? ?
where
3(0, ) 8
y
u x e

= (7M)
b) A tightly stretched string with fixed end points at x = 0 and x = 1 is initially in a
position given by
1
0
2( )
1
1 1
2
x x
f x
x x
?
?
?
=
?
?
– ?
?
If it is released from this position with velocity zero find the displacement u(x, t)at any point of x of the string at any time is t > 0. (7M)

2 of 2
SET – 1
R16

Code No: R161202
I B. Tech II Semester Regular/Supplementary Examinations, April/May – 2018
MATHEMATICS-II (MM) (Com to CE,EEE,ME,AE,AME,Bio-Tech,Chem E,Metal E,Min E,PCE,PE) Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a) Find two iterations of x = cosx using bisection method. (2M)
b)Prove that ( )
log ( ) log 1( )
f x
f x
f x
? ? ?
? = +
? ?
? ?(2M)
c) Write Trapezoidal Rule. (2M)
d) Write the Dirichlet conditions for Fourier series. (2M)
e) Find the value of a
n
for
1
1 0
2( )
1
1 1
2
x
f x
x
?
?
?
=
?
?
– ?
?
(2M)
f) State modulation property in Fourier transforms. (2M)
g) Write two dimensional steady state equation. (2M)
PART -B
2. a) Find the root of the equation x e
x
= 2 using Newton Raphson method. (7M)
b) Find the root of the equation 3x = 1+cosx

using False position method. (7M)
3. a) Find the Lagrange?s polynomial for the following data, hence find y(15).
x -5 6 9 11
y 12 13 14 16 (7M)

b)Find y(23) for the following data using Gauss Forward interpolation formula.
x 10 20 30 40 50
y 9.21 17.54 31.82 55.32 92.51
(7M)
4.
a)Evaluate y (0.1) using RK method of fourth order for , (0) 1
x
dy
y xe y
dx
= + = (7M)

b)Evaluate y (0.1) using Taylor?s method for
2
, (0) 1
dy
x y y
dx
= + =

(7M)
SET – 2
R16
1 of 2

Code No: R161202

5. a) Find the Fourier series of f(x) = sinhax in ?p b) Find the half range sine series of
0
2( )
2
l
x x
f x
l
l x x l
?
?
?
=
?
?
– ?
?

(7M)
6.
a) Using Fourier cosine integral, show that
2
cos
2 1
0
x
x
e d
p ?
?
?
8

=
?
+
(7M)

b)Find the Fourier sine transform of the function f(x) = x in (0,8)

(7M)
7. a)Solve 4 3
z z
z
x y
? ?
– =
? ?
and
5(0, )
y
z y e

= (7M)
b) Find the temperature u(x, t) in a homogenous bar of heat conducting method of
length ?l? whose ends are kept at 0
0
c and whose initial temperature is ( )
2
ax
l x
l
– (7M)

2 of 2
SET – 2
R16

Code No: R161202
I B. Tech II Semester Regular/Supplementary Examinations, April/May – 2018
MATHEMATICS-II (MM) (Com to CE,EEE,ME,AE,AME,Bio-Tech,Chem E,Metal E,Min E,PCE,PE)Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a) Find two iterations of x e
x
= 2 using False position method. (2M)
b)Show that
1
1 E

?= – (2M)
c)Evaluate y (0.1) by Euler?s method for , (0) 1
dy x y
y
dx y x
+
= =

. (2M)
d) Write Simpson?s 3/8
th
Rule. (2M)

e)Find the value of b
n
for
1 0
2( )
1
2
x
f x
x
p
p
p
?
?
?
=
?
?
– ?
?
(2M)
f) Write shifting theorem in Fourier transforms. (2M)
g) Write one dimensional heat equation. (2M)
PART -B
2. a) Find the root of the equation x
4
– 10 = x using Bisection method. (7M)
b) Find the root of the equation xtanx+1=0

using Newton Raphson method.
(7M)
3. a) Find the Lagrange?s polynomial for the following data.

x 0 2 3 6
y 648 704 729 792 (7M)

b)Fit a y(0.5) the following data using Newton Forward interpolation formula.
x -1 0 1 2
y 10 5 8 10
(7M)
4.
a)Evaluate
2
0
1
1
dx
x +
?
by taking h = 0.1 by (i) Trapezoidal rule. (ii) Simpson?s 1/3
rd
rule
(7M)
b)Evaluate y (0.1) using Modified Euler?s method for
2 2
, (0) 1
dy
x y y
dx
= + =
(7M)
SET – 3
R16
1 of 2

Code No: R161202

5.

a)Find the Half range cosine of
0
2( )( )
2
kx x
f x
k x x
p
p
p p
?
?
?
=
?
?
– ?
?

(7M)

b)Find the Fourier series of ( ) 0 2
2
x
f x in x
p –
= (7M)
6.
a) Express the ( ) f x defend by
1 1( )
0 1
if x
f x
if x
? ?
=
?
>
?
?
as a Fourier integral
Hence Evaluate
sin cos
0
x
d
? ?
?
?
8
?
(7M)

b)Find Fourier transform of
2( ) ,
x
f x e x

= -8 3
x
F e
? ?

? ?
? ?
? ?
? ?
? ?
(ii)2
4( 3) x
F e
? ? – –
? ?
? ?

(7M)
7.
a)Solve 4 3
u u
u
x y
? ?
+ =
? ?
given that
5(0, ) 3
y y
u y e e
– –
= –
(7M)
b) A rectangular plate with insulated surface is 8 cm wide. If the temperature along
one short edge y = 8 cm. is given by100sin
8
x p
, 0 edges x = 0 and x = 8 and other edge are kept 0
0
temperature at any point on the plane (7M)

2 of 2
SET – 3
R16

Code No: R161202
I B. Tech II Semester Regular/Supplementary Examinations, April/May – 2018
MATHEMATICS-II (MM) (Com to CE,EEE,ME,AE,AME,Bio-Tech,Chem E,Metal E,Min E,PCE,PE)Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a)Write the iteration formula to find N using Newton Raphson method. (2M)
b) Prove that
[ ]
1
2
?d = ?+? (2M)
c) Write the formula for RK method of second order. (2M)
d) Write Simpson?s 1/3
rd
Rule. (2M)
e) Find the value of a
0
for
1 0
2( )
1
2
x
f x
x
p
p
p
?
?
?
=
?
?
– ?
?
(2M)
f) State Linear property in Fourier Transform. (2M)
g)Write the equation for the PDE 4 3
u u
u
x y
? ?
+ =
? ?
by variable separable method. (2M)
PART -B
2. a) Find the root of the equation x
3
-6x-4=0 using iteration method. (7M)
b) Find the root of the equation 2x-log
10
x=7 using False position method.
(7M)
3. a) Find the parabola passing through the points (0,1), (1,3) and (3,55) using
Lagrange?s interpolation formula. (7M)
b) Area A of circle and diameter d is given for the following values
d 80 85 90 95 100
A 5026 5674 6362 7088 7854
Calculate the area of circle of diameter 105.

(7M)
SET – 1
R16
1 of 2

Code No: R161202

4.
a)Evaluate y (0.1) using RK method of fourth order for
2
, (0) 1
dy x
y y
dx y
= – = (7M)
b)Evaluate y (0.1) ,y(0.2) using Picard?s method for , (0) 1
dy
x y y
dx
= + =
(7M)

5.

a)Find the Fourier series of
2
1 0( )
2
1 0
x
if x
f x
x
if x
p
p
p
p
?
+ – = ?
?
=
?
?
– = ?
?

Hence deduce that
2
2 2
1 1
1 ……
3 5 8
p
+ + + =
(7M)
b) Find the Half range sine series of f(x) = x
2
in [ 0,2]
(7M)
6.
a) Using Fourier integral, Show that
2
0
cos sin
0
1 0
0
x
x x
d
if x
if x
e
? ? ?
?
? p

8
?
+
=
? ?
+ >
?
(7M)

b)Find the Fourier cosine transform of
2
1
1 x +
and hence deduce Fourier sine
transform
2
1
x
x +
(7M)
7. a)Solve the PDE 4
u u
x y
? ?
=
? ?
where
3(0, ) 8
y
u x e

= (7M)
b) A tightly stretched string with fixed end points at x = 0 and x = 1 is initially in a
position given by
1
0
2( )
1
1 1
2
x x
f x
x x
?
?
?
=
?
?
– ?
?
If it is released from this position with velocity zero find the displacement u(x, t)at any point of x of the string at any time is t > 0. (7M)

2 of 2
SET – 1
R16

Code No: R161202
I B. Tech II Semester Regular/Supplementary Examinations, April/May – 2018
MATHEMATICS-II (MM) (Com to CE,EEE,ME,AE,AME,Bio-Tech,Chem E,Metal E,Min E,PCE,PE) Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a) Find two iterations of x = cosx using bisection method. (2M)
b)Prove that ( )
log ( ) log 1( )
f x
f x
f x
? ? ?
? = +
? ?
? ?(2M)
c) Write Trapezoidal Rule. (2M)
d) Write the Dirichlet conditions for Fourier series. (2M)
e) Find the value of a
n
for
1
1 0
2( )
1
1 1
2
x
f x
x
?
?
?
=
?
?
– ?
?
(2M)
f) State modulation property in Fourier transforms. (2M)
g) Write two dimensional steady state equation. (2M)
PART -B
2. a) Find the root of the equation x e
x
= 2 using Newton Raphson method. (7M)
b) Find the root of the equation 3x = 1+cosx

using False position method. (7M)
3. a) Find the Lagrange?s polynomial for the following data, hence find y(15).
x -5 6 9 11
y 12 13 14 16 (7M)

b)Find y(23) for the following data using Gauss Forward interpolation formula.
x 10 20 30 40 50
y 9.21 17.54 31.82 55.32 92.51
(7M)
4.
a)Evaluate y (0.1) using RK method of fourth order for , (0) 1
x
dy
y xe y
dx
= + = (7M)

b)Evaluate y (0.1) using Taylor?s method for
2
, (0) 1
dy
x y y
dx
= + =

(7M)
SET – 2
R16
1 of 2

Code No: R161202

5. a) Find the Fourier series of f(x) = sinhax in ?p b) Find the half range sine series of
0
2( )
2
l
x x
f x
l
l x x l
?
?
?
=
?
?
– ?
?

(7M)
6.
a) Using Fourier cosine integral, show that
2
cos
2 1
0
x
x
e d
p ?
?
?
8

=
?
+
(7M)

b)Find the Fourier sine transform of the function f(x) = x in (0,8)

(7M)
7. a)Solve 4 3
z z
z
x y
? ?
– =
? ?
and
5(0, )
y
z y e

= (7M)
b) Find the temperature u(x, t) in a homogenous bar of heat conducting method of
length ?l? whose ends are kept at 0
0
c and whose initial temperature is ( )
2
ax
l x
l
– (7M)

2 of 2
SET – 2
R16

Code No: R161202
I B. Tech II Semester Regular/Supplementary Examinations, April/May – 2018
MATHEMATICS-II (MM) (Com to CE,EEE,ME,AE,AME,Bio-Tech,Chem E,Metal E,Min E,PCE,PE)Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a) Find two iterations of x e
x
= 2 using False position method. (2M)
b)Show that
1
1 E

?= – (2M)
c)Evaluate y (0.1) by Euler?s method for , (0) 1
dy x y
y
dx y x
+
= =

. (2M)
d) Write Simpson?s 3/8
th
Rule. (2M)

e)Find the value of b
n
for
1 0
2( )
1
2
x
f x
x
p
p
p
?
?
?
=
?
?
– ?
?
(2M)
f) Write shifting theorem in Fourier transforms. (2M)
g) Write one dimensional heat equation. (2M)
PART -B
2. a) Find the root of the equation x
4
– 10 = x using Bisection method. (7M)
b) Find the root of the equation xtanx+1=0

using Newton Raphson method.
(7M)
3. a) Find the Lagrange?s polynomial for the following data.

x 0 2 3 6
y 648 704 729 792 (7M)

b)Fit a y(0.5) the following data using Newton Forward interpolation formula.
x -1 0 1 2
y 10 5 8 10
(7M)
4.
a)Evaluate
2
0
1
1
dx
x +
?
by taking h = 0.1 by (i) Trapezoidal rule. (ii) Simpson?s 1/3
rd
rule
(7M)
b)Evaluate y (0.1) using Modified Euler?s method for
2 2
, (0) 1
dy
x y y
dx
= + =
(7M)
SET – 3
R16
1 of 2

Code No: R161202

5.

a)Find the Half range cosine of
0
2( )( )
2
kx x
f x
k x x
p
p
p p
?
?
?
=
?
?
– ?
?

(7M)

b)Find the Fourier series of ( ) 0 2
2
x
f x in x
p –
= (7M)
6.
a) Express the ( ) f x defend by
1 1( )
0 1
if x
f x
if x
? ?
=
?
>
?
?
as a Fourier integral
Hence Evaluate
sin cos
0
x
d
? ?
?
?
8
?
(7M)

b)Find Fourier transform of
2( ) ,
x
f x e x

= -8 3
x
F e
? ?

? ?
? ?
? ?
? ?
? ?
(ii)2
4( 3) x
F e
? ? – –
? ?
? ?

(7M)
7.
a)Solve 4 3
u u
u
x y
? ?
+ =
? ?
given that
5(0, ) 3
y y
u y e e
– –
= –
(7M)
b) A rectangular plate with insulated surface is 8 cm wide. If the temperature along
one short edge y = 8 cm. is given by100sin
8
x p
, 0 edges x = 0 and x = 8 and other edge are kept 0
0
temperature at any point on the plane (7M)

2 of 2
SET – 3
R16

Code No: R161202
I B. Tech II Semester Regular/Supplementary Examinations, April/May – 2018
MATHEMATICS-II (MM) (Com to CE,EEE,ME,AE,AME,Bio-Tech,Chem E,Metal E,Min E,PCE,PE) Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a) Find two iterations of x = sinx using iteration method. (2M)
b) Find
1
1
tan
n
n

– ? ? ? ?
?
? ? ? ?
? ? ? ?
by taking h=1 (2M)

c)Evaluate y (0.1) by Euler?s method for , (0) 1
dy
x y y
dx
= + = .
(2M)
d) Write half range sine series for f(x) = 1 in [0,2] (2M)

e)Find the value of a
n
for
1
1 0
2( )
1
1 1
2
x
f x
x
?
?
?
=
?
?
– ?
?
(2M)
f) Write Finite Fourier cosine transform for f(x) (2M)
g) Write one dimensional wave equation. (2M)
PART -B
2. a) Find the root of the equation x
3
-8x- 4 = 0 using Newton raphson method. (7M)
b) Find the root of the equation 4sinx = e
x

using False position method. (7M)
3. a) Find y(10) for the data
y(3)=2.7,y(4)=6.4,y(5)=12.5,y(6)=21.6,y(7)=34.3,y(8)=51.2,y(9) = 72.9 (7M)
b) Evaluate y(2) from the following table.
X 1 3 5 6 8
Y 2 1.5 2.4 4 5.6 (7M)
4. a)Evaluate
1
4
0
1 x dx +
?
by taking h = 0.125 by (i) Simpson?s 1/3
rd
rule (ii) Simpson?s 3/8
th
rule (7M)
b)Evaluate y (0.1) using Taylor?s for
2 2
, (0) 1
dy
x y y
dx
= – =
(7M)
SET – 4
R16
1 of 2

Code No: R161202
I B. Tech II Semester Regular/Supplementary Examinations, April/May – 2018
MATHEMATICS-II (MM) (Com to CE,EEE,ME,AE,AME,Bio-Tech,Chem E,Metal E,Min E,PCE,PE)Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a)Write the iteration formula to find N using Newton Raphson method. (2M)
b) Prove that
[ ]
1
2
?d = ?+? (2M)
c) Write the formula for RK method of second order. (2M)
d) Write Simpson?s 1/3
rd
Rule. (2M)
e) Find the value of a
0
for
1 0
2( )
1
2
x
f x
x
p
p
p
?
?
?
=
?
?
– ?
?
(2M)
f) State Linear property in Fourier Transform. (2M)
g)Write the equation for the PDE 4 3
u u
u
x y
? ?
+ =
? ?
by variable separable method. (2M)
PART -B
2. a) Find the root of the equation x
3
-6x-4=0 using iteration method. (7M)
b) Find the root of the equation 2x-log
10
x=7 using False position method.
(7M)
3. a) Find the parabola passing through the points (0,1), (1,3) and (3,55) using
Lagrange?s interpolation formula. (7M)
b) Area A of circle and diameter d is given for the following values
d 80 85 90 95 100
A 5026 5674 6362 7088 7854
Calculate the area of circle of diameter 105.

(7M)
SET – 1
R16
1 of 2

Code No: R161202

4.
a)Evaluate y (0.1) using RK method of fourth order for
2
, (0) 1
dy x
y y
dx y
= – = (7M)
b)Evaluate y (0.1) ,y(0.2) using Picard?s method for , (0) 1
dy
x y y
dx
= + =
(7M)

5.

a)Find the Fourier series of
2
1 0( )
2
1 0
x
if x
f x
x
if x
p
p
p
p
?
+ – = ?
?
=
?
?
– = ?
?

Hence deduce that
2
2 2
1 1
1 ……
3 5 8
p
+ + + =
(7M)
b) Find the Half range sine series of f(x) = x
2
in [ 0,2]
(7M)
6.
a) Using Fourier integral, Show that
2
0
cos sin
0
1 0
0
x
x x
d
if x
if x
e
? ? ?
?
? p

8
?
+
=
? ?
+ >
?
(7M)

b)Find the Fourier cosine transform of
2
1
1 x +
and hence deduce Fourier sine
transform
2
1
x
x +
(7M)
7. a)Solve the PDE 4
u u
x y
? ?
=
? ?
where
3(0, ) 8
y
u x e

= (7M)
b) A tightly stretched string with fixed end points at x = 0 and x = 1 is initially in a
position given by
1
0
2( )
1
1 1
2
x x
f x
x x
?
?
?
=
?
?
– ?
?
If it is released from this position with velocity zero find the displacement u(x, t)at any point of x of the string at any time is t > 0. (7M)

2 of 2
SET – 1
R16

Code No: R161202
I B. Tech II Semester Regular/Supplementary Examinations, April/May – 2018
MATHEMATICS-II (MM) (Com to CE,EEE,ME,AE,AME,Bio-Tech,Chem E,Metal E,Min E,PCE,PE) Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a) Find two iterations of x = cosx using bisection method. (2M)
b)Prove that ( )
log ( ) log 1( )
f x
f x
f x
? ? ?
? = +
? ?
? ?(2M)
c) Write Trapezoidal Rule. (2M)
d) Write the Dirichlet conditions for Fourier series. (2M)
e) Find the value of a
n
for
1
1 0
2( )
1
1 1
2
x
f x
x
?
?
?
=
?
?
– ?
?
(2M)
f) State modulation property in Fourier transforms. (2M)
g) Write two dimensional steady state equation. (2M)
PART -B
2. a) Find the root of the equation x e
x
= 2 using Newton Raphson method. (7M)
b) Find the root of the equation 3x = 1+cosx

using False position method. (7M)
3. a) Find the Lagrange?s polynomial for the following data, hence find y(15).
x -5 6 9 11
y 12 13 14 16 (7M)

b)Find y(23) for the following data using Gauss Forward interpolation formula.
x 10 20 30 40 50
y 9.21 17.54 31.82 55.32 92.51
(7M)
4.
a)Evaluate y (0.1) using RK method of fourth order for , (0) 1
x
dy
y xe y
dx
= + = (7M)

b)Evaluate y (0.1) using Taylor?s method for
2
, (0) 1
dy
x y y
dx
= + =

(7M)
SET – 2
R16
1 of 2

Code No: R161202

5. a) Find the Fourier series of f(x) = sinhax in ?p b) Find the half range sine series of
0
2( )
2
l
x x
f x
l
l x x l
?
?
?
=
?
?
– ?
?

(7M)
6.
a) Using Fourier cosine integral, show that
2
cos
2 1
0
x
x
e d
p ?
?
?
8

=
?
+
(7M)

b)Find the Fourier sine transform of the function f(x) = x in (0,8)

(7M)
7. a)Solve 4 3
z z
z
x y
? ?
– =
? ?
and
5(0, )
y
z y e

= (7M)
b) Find the temperature u(x, t) in a homogenous bar of heat conducting method of
length ?l? whose ends are kept at 0
0
c and whose initial temperature is ( )
2
ax
l x
l
– (7M)

2 of 2
SET – 2
R16

Code No: R161202
I B. Tech II Semester Regular/Supplementary Examinations, April/May – 2018
MATHEMATICS-II (MM) (Com to CE,EEE,ME,AE,AME,Bio-Tech,Chem E,Metal E,Min E,PCE,PE)Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a) Find two iterations of x e
x
= 2 using False position method. (2M)
b)Show that
1
1 E

?= – (2M)
c)Evaluate y (0.1) by Euler?s method for , (0) 1
dy x y
y
dx y x
+
= =

. (2M)
d) Write Simpson?s 3/8
th
Rule. (2M)

e)Find the value of b
n
for
1 0
2( )
1
2
x
f x
x
p
p
p
?
?
?
=
?
?
– ?
?
(2M)
f) Write shifting theorem in Fourier transforms. (2M)
g) Write one dimensional heat equation. (2M)
PART -B
2. a) Find the root of the equation x
4
– 10 = x using Bisection method. (7M)
b) Find the root of the equation xtanx+1=0

using Newton Raphson method.
(7M)
3. a) Find the Lagrange?s polynomial for the following data.

x 0 2 3 6
y 648 704 729 792 (7M)

b)Fit a y(0.5) the following data using Newton Forward interpolation formula.
x -1 0 1 2
y 10 5 8 10
(7M)
4.
a)Evaluate
2
0
1
1
dx
x +
?
by taking h = 0.1 by (i) Trapezoidal rule. (ii) Simpson?s 1/3
rd
rule
(7M)
b)Evaluate y (0.1) using Modified Euler?s method for
2 2
, (0) 1
dy
x y y
dx
= + =
(7M)
SET – 3
R16
1 of 2

Code No: R161202

5.

a)Find the Half range cosine of
0
2( )( )
2
kx x
f x
k x x
p
p
p p
?
?
?
=
?
?
– ?
?

(7M)

b)Find the Fourier series of ( ) 0 2
2
x
f x in x
p –
= (7M)
6.
a) Express the ( ) f x defend by
1 1( )
0 1
if x
f x
if x
? ?
=
?
>
?
?
as a Fourier integral
Hence Evaluate
sin cos
0
x
d
? ?
?
?
8
?
(7M)

b)Find Fourier transform of
2( ) ,
x
f x e x

= -8 3
x
F e
? ?

? ?
? ?
? ?
? ?
? ?
(ii)2
4( 3) x
F e
? ? – –
? ?
? ?

(7M)
7.
a)Solve 4 3
u u
u
x y
? ?
+ =
? ?
given that
5(0, ) 3
y y
u y e e
– –
= –
(7M)
b) A rectangular plate with insulated surface is 8 cm wide. If the temperature along
one short edge y = 8 cm. is given by100sin
8
x p
, 0 edges x = 0 and x = 8 and other edge are kept 0
0
temperature at any point on the plane (7M)

2 of 2
SET – 3
R16

Code No: R161202
I B. Tech II Semester Regular/Supplementary Examinations, April/May – 2018
MATHEMATICS-II (MM) (Com to CE,EEE,ME,AE,AME,Bio-Tech,Chem E,Metal E,Min E,PCE,PE) Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a) Find two iterations of x = sinx using iteration method. (2M)
b) Find
1
1
tan
n
n

– ? ? ? ?
?
? ? ? ?
? ? ? ?
by taking h=1 (2M)

c)Evaluate y (0.1) by Euler?s method for , (0) 1
dy
x y y
dx
= + = .
(2M)
d) Write half range sine series for f(x) = 1 in [0,2] (2M)

e)Find the value of a
n
for
1
1 0
2( )
1
1 1
2
x
f x
x
?
?
?
=
?
?
– ?
?
(2M)
f) Write Finite Fourier cosine transform for f(x) (2M)
g) Write one dimensional wave equation. (2M)
PART -B
2. a) Find the root of the equation x
3
-8x- 4 = 0 using Newton raphson method. (7M)
b) Find the root of the equation 4sinx = e
x

using False position method. (7M)
3. a) Find y(10) for the data
y(3)=2.7,y(4)=6.4,y(5)=12.5,y(6)=21.6,y(7)=34.3,y(8)=51.2,y(9) = 72.9 (7M)
b) Evaluate y(2) from the following table.
X 1 3 5 6 8
Y 2 1.5 2.4 4 5.6 (7M)
4. a)Evaluate
1
4
0
1 x dx +
?
by taking h = 0.125 by (i) Simpson?s 1/3
rd
rule (ii) Simpson?s 3/8
th
rule (7M)
b)Evaluate y (0.1) using Taylor?s for
2 2
, (0) 1
dy
x y y
dx
= – =
(7M)
SET – 4
R16
1 of 2

Code No: R161202

5.

a)Find the Fourier series for
, 0( ) , 0
, 0
2
x
f x x x
x
p p
p
p
?
?
– – ?
= ?
?

? =
?

Hence deduce that

+

+

+…=

(7M)
b) Find the Half range cosine series of f(x) = e
x
in [ 0,1]
(7M)
6.
a)Using Fourier integral, Show that
2
1
sin 0 sin
s
in
1
0
0
2
x
xd
x
if
if
x p p p?
? ?
?
p
?
8
?
=
? ?

?
>
?
(7M)
b)Find the Fourier cosine transform of x
n-1
(7M)
7.
a)Solve 2
u u
u
x t
? ?
= +
? ?
, where
3( , 0) 6
x
u x e

= by the method of separation of
variables.
(7M)
b) A bar of 50cm long with insulated sides kept at 0
0
C and that the other end is kept
at 100
0
C until steady state conditions prevail. The two ends are suddenly
insulated so that the temperature is zero at each end thereafter. Find the
temperature distribution. (7M)

2 of 2
SET – 4
R16

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